Quiz 1 Student Handout Quiz 1: Geometry Foundations
Student Copy
Goals 1–3: Notation, Perimeter & Area with Equations
Student Name
Date
Period
Formula Reference Bank
Line Notation
Line: \(\overleftrightarrow{AB}\) • Ray: \(\overrightarrow{AB}\)
Segment Notation
Segment: \(\overline{AB}\)
Perimeter (P)
Rect: \(P = 2l + 2w\)
Area (A)
Rect: \(A = l \cdot w\) • Tri: \(A = \frac{1}{2}bh\)
Section 1: Multiple Choice (15 Questions • 1 Point Each)
Which of the following best describes a line segment?
A It extends forever in both directions.
B It has one endpoint and extends forever.
C It has two endpoints.
D It is a location with no size.
Which symbol correctly names the figure below? The figure starts at point J, passes through point K, and continues forever in one direction.
J K
A \(\overline{JK}\)
B \(\overrightarrow{JK}\)
C \(\overleftrightarrow{JK}\)
D \(\overrightarrow{KJ}\)
Which symbol correctly names the figure below?
R S
A \(\overline{RS}\)
B \(\overrightarrow{RS}\)
C \(\overleftrightarrow{RS}\)
D \(\overline{SR}\)
Geometry Quarter 1 Assessment Suite Page 1 of 5
Quiz 1 • Multiple Choice Continued
Which geometric figure extends forever in exactly one direction?
A Ray
B Line
C Line segment
D Point
The rectangle below has a length of 12 inches and a width of \((x + 3)\) inches. The perimeter of the rectangle is 40 inches. What is the value of \(x\)?
12 in \((x + 3)\) in
A 3
B 5
C 8
D 10
The sides of the triangle below measure \(x\), \((x + 4)\), and \((2x - 1)\). The perimeter of the triangle is 35 units. What is the value of \(x\)?
\(x\) \(x + 4\) \(2x - 1\)
A 7
B 9
C 8
D 15
A square park has a perimeter of 64 feet. What is the length of one side of the park?
A 8 feet
B 16 feet
C 32 feet
D 256 feet
Geometry Quarter 1 Assessment Suite Page 2 of 5
Quiz 1 • Multiple Choice Continued
The rectangle below has a length of \((x + 2)\) cm and a width of 6 cm. The area of the rectangle is 54 \(\text{cm}^2\). What is the value of \(x\)?
\((x + 2)\) cm 6 cm Area = 54 \(\text{cm}^2\)
A 6
B 8
C 9
D 7
The triangle below has a base of 10 meters and an area of 45 \(\text{m}^2\). What is the height, \(h\), of the triangle?
h 10 m Area = 45 \(\text{m}^2\)
A 4.5 m
B 9 m
C 18 m
D 35 m
The parallelogram below has a base of 8 inches and a height of \(x\) inches. The area of the parallelogram is 56 \(\text{in}^2\). What is the value of \(x\)?
x 8 in Area = 56 \(\text{in}^2\)
A 7
B 8
C 48
D 64
Geometry Quarter 1 Assessment Suite Page 3 of 5
Quiz 1 • Multiple Choice Continued
Which notation represents a geometric line that passes through points A and B?
A \(\overline{AB}\)
B \(\overrightarrow{AB}\)
C \(\overleftrightarrow{AB}\)
D \(AB\)
A rectangle has a length of 15 cm and a width of \((x + 2)\) cm. The perimeter of the rectangle is 46 cm. What is the value of \(x\)?
A 6
B 8
C 5
D 10
A triangle has side lengths of \(2x\), \((x + 3)\), and \((x + 5)\) inches. The perimeter is 24 inches. Find the value of \(x\).
A 4
B 6
C 5
D 3
The area of a rectangular garden is 60 square feet. The width of the garden is 5 feet, and the length is \((x + 5)\) feet. What is the value of \(x\)?
A 7
B 12
C 8
D 5
A triangle has a base of 12 cm and an area of 48 \(\text{cm}^2\). What is its height, \(h\)?
A 8 cm
B 4 cm
C 6 cm
D 12 cm
Geometry Quarter 1 Assessment Suite Page 4 of 5
Section 2: Open-Ended Responses (2 Questions • 5 Points Each)
Jerome is building a rectangular garden. The length of the garden is \((x + 4)\) feet and the width is 6 feet. The perimeter of the garden is 44 feet.
\((x + 4)\) ft 6 ft Perimeter = 44 ft
a) Write an equation for the perimeter and solve for \(x\). (2 pts)
b) Find the area of the garden in square feet. (1 pt)
c) Fencing costs $3 per foot. How much will it cost to fence the garden? (2 pts)
A rectangular playground has a length of \((x + 5)\) meters and a width of 8 meters. The perimeter of the playground is 46 meters.
\((x + 5)\) m 8 m Perimeter = 46 m
a) Write an equation for the perimeter and solve for \(x\). (2 pts)
b) Find the area of the playground in square meters. (1 pt)
c) New safety sod costs $4 per square meter. How much will it cost to cover the playground? (2 pts)
Geometry Quarter 1 Assessment Suite Page 5 of 5
Quiz 1 Teacher Key Quiz 1 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Geometry Quiz 1 (Goals 1-3) Key & Alignment Guide
Total Points
25 Points
Section 1 (MC)
15 Pts (1 pt each)
Section 2 (OE)
10 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 1 Define, classify, and name lines, segments, and rays using proper notation 1, 2, 3, 4, 11 — 5 2 Solve perimeter problems using linear equations 5, 6, 7, 12, 13 16a, 16c, 17a 10 3 Solve area problems using linear equations 8, 9, 10, 14, 15 16b, 17b, 17c 10
Section 1: Multiple Choice Answers
Q1. C Goal 1
Q2. B Goal 1
Q3. C Goal 1
Q4. A Goal 1
Q5. B Goal 2
Q6. C Goal 2
Q7. B Goal 2
Q8. D Goal 3
Q9. B Goal 3
Q10. A Goal 3
Q11. C Goal 1
Q12. A Goal 2
Q13. A Goal 2
Q14. A Goal 3
Q15. A Goal 3
Geometry Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 1 of 2
Section 2: Worked Solutions and Scoring
Question 16 — Goals 2 & 3 — Jerome's Garden (5 pts total) Scoring Key
a) Equation & solve \(x\). (2 pts)
\(2(x + 4) + 2(6) = 44\)
b) Area of garden. (1 pt)
Length = \(x + 4\)
c) Fencing cost. (2 pts)
Cost = Perimeter \(\times\) $3
[1 pt setup, 1 pt answer]
Question 17 — Goals 2 & 3 — Playground (5 pts total) Scoring Key
a) Equation & solve \(x\). (2 pts)
\(2(x + 5) + 2(8) = 46\)
b) Area of playground. (1 pt)
Length = \(x + 5\)
c) Sodding cost. (2 pts)
Cost = Area \(\times\) $4
[1 pt setup, 1 pt answer]
Geometry Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 2 of 2
Quiz 2 Student Handout Quiz 2: Segment & Angle Foundations
Student Copy
Goals 5–8: Segment Addition, Midpoints & Angle Notation
Student Name
Date
Period
Formula Reference Bank
Segment Addition Postulate
If B is between A and C:
Midpoint Formula
On coordinate plane:
Angle Vertex Rule
Vertex letter must be in middle:
Section 1: Multiple Choice (15 Questions • 1 Point Each)
In the figure below, point B is between points A and C. If \(AB = 14\) and \(BC = 9\), what is the length of \(AC\)?
A B C 14 9
A 5
B 14
C 23
D 126
In the figure below, \(AB = 2x\), \(BC = x + 6\), and \(AC = 30\). What is the length of segment \(AB\)?
A B C 2x x + 6 AC = 30
A 16
B 8
C 14
D 24
In the figure below, \(GK = 40\), \(GH = 12\), and \(HJ = 10\). What is the length of segment \(JK\)?
G H J K 12 10 ? GK = 40
A 22
B 18
C 62
D 10
Geometry Quarter 1 Assessment Suite Page 1 of 5
Quiz 2 • Multiple Choice Continued
In the figure below, point B is between A and C. If \(AB = x + 5\), \(BC = 2x\), and \(AC = 26\), what is the length of \(BC\)?
A B C x + 5 2x AC = 26
A 7
B 12
C 14
D 21
Point M is the midpoint of segment AB. If \(AM = 13\), what is the length of segment \(AB\)?
A M B 13
A 13
B 6.5
C 52
D 26
Point M is the midpoint of segment PQ. If \(PM = 3x + 2\) and \(MQ = 5x - 8\), what is the value of \(x\)?
P M Q 3x + 2 5x - 8
A 5
B 3
C 17
D 34
In the figure below, line CD bisects segment EF at point M. Which statement must be true?
E F M D C
A \(\overline{CM} \cong \overline{MD}\)
B \(\overline{EM} \cong \overline{MF}\)
C \(\overline{EF} \cong \overline{CD}\)
D \(\overline{EM} \cong \overline{EF}\)
Geometry Quarter 1 Assessment Suite Page 2 of 5
Quiz 2 • Multiple Choice Continued
Point N is the midpoint of segment GH. If \(GN = 2x\) and \(NH = x + 9\), what is the length of segment \(GH\)?
G N H 2x x + 9
A 9
B 18
C 36
D 45
What is the midpoint of the segment with endpoints A(2, 4) and B(8, 10)?
A (10, 14)
B (5, 7)
C (3, 3)
D (6, 7)
What is the midpoint of the segment with endpoints C(−6, 3) and D(4, 7)?
A (−1, 5)
B (−5, 2)
C (−1, 2)
D (5, −1)
Segment GH is graphed below with endpoints G(2, 5) and H(−4, −1). What is the midpoint of segment GH?
G(2,5) H(-4,-1)
A (−2, 4)
B (3, 2)
C (−1, 3)
D (−1, 2)
Geometry Quarter 1 Assessment Suite Page 3 of 5
Quiz 2 • Multiple Choice Continued
Which of the following correctly names the angle below?
B A C
A \(\angle BAC\)
B \(\angle ABC\)
C \(\angle ACB\)
D \(\angle CAB\)
In angle \(\angle XYZ\), which point is the vertex of the angle?
A Point X
B Point Z
C Point Y
D No vertex
In the figure below, three rays share vertex Q. Which name clearly identifies the marked angle (the angle between ray QP and ray QS)?
Q P S R ?
A \(\angle PQS\)
B \(\angle Q\)
C \(\angle S\)
D \(\angle PSQ\)
An angle is formed by ray BA and ray BC. What is another name for this angle?
A \(\angle ABC\)
B \(\angle ACB\)
C \(\angle BAC\)
D \(\angle CAB\)
Geometry Quarter 1 Assessment Suite Page 4 of 5
Section 2: Open-Ended Responses (2 Questions • 5 Points Each)
In the figure below, points G, H, J, and K are on the same line. If \(GH = x + 4\), \(HJ = 2x\), \(JK = x + 9\), and \(GK = 45\):
G H J K x + 4 2x x + 9 GK = 45
a) Write an equation for segment addition and solve for \(x\). (3 pts)
b) Find the length of segment \(HJ\). (2 pts)
Segment AB has endpoints A(−2, 6) and B(4, −2). Point M is the midpoint of segment AB.
A(-2,6) B(4,-2)
a) Use the midpoint formula to find the coordinates of point M. Show your work. (3 pts)
b) In one sentence, explain what it means for M to be the midpoint of segment AB. (2 pts)
Geometry Quarter 1 Assessment Suite Page 5 of 5
Quiz 2 Teacher Key Quiz 2 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Geometry Quiz 2 (Goals 5-8) Key & Alignment Guide
Total Points
25 Points
Section 1 (MC)
15 Pts (1 pt each)
Section 2 (OE)
10 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 5 Determine segment lengths using segment addition postulate 1, 2, 3, 4 16a, 16b 9 6 Determine segment lengths using midpoints and segment bisectors 5, 6, 7, 8 — 4 7 Determine midpoints on the coordinate plane using the midpoint formula 9, 10, 11 17a, 17b 8 8 Define and name angles using proper notation 12, 13, 14, 15 — 4
Section 1: Multiple Choice Answers
Q1. C Goal 5
Q2. A Goal 5
Q3. B Goal 5
Q4. C Goal 5
Q5. D Goal 6
Q6. A Goal 6
Q7. B Goal 6
Q8. C Goal 6
Q9. B Goal 7
Q10. A Goal 7
Q11. D Goal 7
Q12. B Goal 8
Q13. C Goal 8
Q14. A Goal 8
Q15. A Goal 8
Geometry Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 1 of 2
Section 2: Worked Solutions and Scoring Guide
Question 16 — Goal 5 — Segment Addition Postulate (5 pts total) Scoring Key
a) Write an equation and solve for \(x\). (3 pts)
By segment addition: \(GH + HJ + JK = GK\)
b) Find the length of segment \(HJ\). (2 pts)
Segment expression: \(HJ = 2x\)
Check other pieces: \(GH = 8+4=12\), \(JK = 8+9=17\). \(12 + 16 + 17 = 45\) ✓
Question 17 — Goal 7 — Midpoint Formula (5 pts total) Scoring Key
a) Use midpoint formula to findcoordinates of point M. (3 pts)
Endpoints: \(A(-2, 6)\) and \(B(4, -2)\)
b) Explain what it means for M to be the midpoint of segment AB. (2 pts)
Accept any reasonable conceptual statement, such as:
[2 pts clear explanation of equal parts or halfway property, 1 pt if partially explained]
Geometry Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 2 of 2
Test 1 Student Handout Test 1: Geometry Foundations
Student Copy
Goals 1–4: Notation, Perimeter, Area & Segment Distance
Student Name
Date
Period
Formula Reference Sheet
Notation
Line: \(\overleftrightarrow{AB}\) • Segment: \(\overline{AB}\) • Ray: \(\overrightarrow{AB}\)
Perimeter
Rect: \(P = 2l + 2w\) • Square: \(P = 4s\)
Area
Rect: \(A = lw\) • Tri: \(A = \frac{1}{2}bh\) • Para: \(A = bh\)
Distance Formula
\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Section 1: Multiple Choice (30 Questions • 1 Point Each)
Which of the following best describes a line segment?
A It extends forever in both directions.
B It has one endpoint and extends forever.
C It has two endpoints.
D It is a location with no size.
Which symbol correctly names the figure below? The figure starts at point J, passes through point K, and continues forever in one direction.
J K
A \(\overline{JK}\)
B \(\overrightarrow{JK}\)
C \(\overleftrightarrow{JK}\)
D \(\overrightarrow{KJ}\)
Which symbol correctly names the figure below?
R S
A \(\overline{RS}\)
B \(\overrightarrow{RS}\)
C \(\overleftrightarrow{RS}\)
D \(\overline{SR}\)
Which geometric figure extends forever in exactly one direction?
A Ray
B Line
C Segment
D Point
Geometry Quarter 1 Assessment Suite • Test 1 Page 1 of 7
Test 1 • Multiple Choice Continued
Which notation represents a geometric line segment that ends at points A and B?
A \(\overline{AB}\)
B \(\overrightarrow{AB}\)
C \(\overleftrightarrow{AB}\)
D \(AB\)
A basic geometric term that represents a position in space, has no size, and is denoted by a dot is called:
A Segment
B Ray
C Point
D Line
Points that lie on the same straight line are called:
A Coplanar
B Collinear
C Congruent
D Bisectors
Which of the following pairs are opposite rays if point X is between points Y and Z?
A \(\overrightarrow{XY}\) and \(\overrightarrow{XZ}\)
B \(\overrightarrow{YX}\) and \(\overrightarrow{ZX}\)
C \(\overline{XY}\) and \(\overline{XZ}\)
D \(\overleftrightarrow{YX}\) and \(\overleftrightarrow{XZ}\)
The rectangle below has a length of 12 inches and a width of \((x + 3)\) inches. The perimeter is 40 inches. What is the value of \(x\)?
12 in \((x + 3)\) in
A 3
B 5
C 8
D 10
The sides of the triangle below measure \(x\), \((x + 4)\), and \((2x - 1)\). The perimeter of the triangle is 35 units. What is the value of \(x\)?
\(x\) \(x + 4\) \(2x - 1\)
A 7
B 9
C 8
D 15
Geometry Quarter 1 Assessment Suite • Test 1 Page 2 of 7
Test 1 • Multiple Choice Continued
A square park has a perimeter of 64 feet. What is the length of one side of the park?
A 8 feet
B 16 feet
C 32 feet
D 256 feet
A rectangle has a perimeter of 48 cm. Its length is \(2x\) cm and its width is 8 cm. What is the value of \(x\)?
A 4
B 8
C 12
D 16
The perimeter of an equilateral triangle is 27 cm. If one side measures \((2x - 3)\) cm, what is the value of \(x\)?
A 3
B 6
C 5
D 9
A rectangular frame has length \((2x + 5)\) cm and width \((x + 2)\) cm. If its perimeter is 44 cm, find \(x\).
A 5
B 4
C 6
D 12
A square courtyard has side lengths of \((3x - 2)\) meters. If the perimeter is 40 meters, find the value of \(x\).
A 4
B 10
C 3
D 2
A regular pentagon has five equal sides, each measuring \((x + 2)\) cm. If the perimeter of the pentagon is 35 cm, what is the value of \(x\)?
A 7
B 5
C 6
D 9
The rectangle below has a length of \((x + 2)\) cm and a width of 6 cm. The area is 54 \(\text{cm}^2\). What is the value of \(x\)?
A 6
B 8
C 9
D 7
Geometry Quarter 1 Assessment Suite • Test 1 Page 3 of 7
Test 1 • Multiple Choice Continued
The triangle below has a base of 10 meters and an area of 45 \(\text{m}^2\). What is the height, \(h\), of the triangle?
A 4.5 m
B 9 m
C 18 m
D 35 m
The parallelogram below has a base of 8 inches and a height of \(x\) inches. The area is 56 \(\text{in}^2\). What is the value of \(x\)?
A 7
B 8
C 48
D 64
A rectangle has an area of 120 square meters. Its length is 15 meters and its width is \((2x - 4)\) meters. What is the value of \(x\)?
A 6
B 8
C 12
D 10
The area of a triangle is 24 square inches. If the height is 6 inches, what is the length of its base?
A 8 inches
B 4 inches
C 12 inches
D 16 inches
A parallelogram has a base of \(2x\) cm and a height of 5 cm. If its area is 80 \(\text{cm}^2\box\), what is the value of \(x\)?
A 8
B 16
C 4
D 10
A rectangular rug has a width of 4 feet and a length of \((x + 3)\) feet. If its area is 32 square feet, what is the value of \(x\)?
A 5
B 8
C 4
D 12
What is the distance between point A(1, 2) and point B(4, 6)?
A 25
B 7
C 5
D \(\sqrt{5}\)
Geometry Quarter 1 Assessment Suite • Test 1 Page 4 of 7
Test 1 • Multiple Choice Continued
What is the length of the segment with endpoints C(−3, 2) and D(3, −6)?
A 10
B 100
C 14
D 2
What is the distance between point G(2, 5) and point H(2, −3)?
A 2
B 4
C 6
D 8
Segment JK has endpoints J(1, 1) and K(7, 9). The segment is cut into two equal pieces. What is the length of one of the pieces?
A 10
B 5
C 20
D 2.5
What is the length of the segment with endpoints X(−1, 3) and Y(5, 3)?
A 6
B 5
C 4
D 8
What is the distance between the origin (0,0) and the point Q(6, 8)?
A 14
B 10
C 48
D \(\sqrt{14}\)
What is the length of the segment with endpoints S(2, −2) and T(6, 1)?
A 25
B 5
C 7
D \(\sqrt{7}\)
Geometry Quarter 1 Assessment Suite • Test 1 Page 5 of 7
Section 2: Open-Ended Responses (4 Questions • 5 Points Each)
Jerome is building a rectangular garden. The length of the garden is \((x + 4)\) feet and the width is 6 feet. The perimeter of the garden is 44 feet.
\((x + 4)\) ft 6 ft Perimeter = 44 ft
a) Write an equation for the perimeter and solve for \(x\). (2 pts)
b) Find the area of the garden in square feet. (1 pt)
c) Fencing costs $3 per foot. How much will it cost to fence the garden? (2 pts)
A park is located at the point (2, 1) on a coordinate map. Jordan’s house is located at (8, 9). Alex’s house is located at (−1, 5). Who lives closer to the park — Jordan or Alex?
Use the distance formula and show your work for BOTH distances to justify your answer. (5 pts total)
Jordan's House to Park distance work: (2 pts)
Alex's House to Park distance work: (2 pts)
Final statement of comparison: (1 pt)
Geometry Quarter 1 Assessment Suite • Test 1 Page 6 of 7
Test 1 • Open-Ended Continued
A rectangular dog park has a length of \((x + 6)\) meters and a width of 8 meters. The perimeter of the dog park is 52 meters.
\((x + 6)\) m 8 m Perimeter = 52 m
a) Write an equation for the perimeter and solve for \(x\). (2 pts)
b) Find the area of the dog park in square meters. (1 pt)
c) Landscaping turf costs $5 per square meter. How much will it cost to turf the park? (2 pts)
Two delivery trucks start at the central warehouse located at W(1, 2) on a coordinate grid. Truck A delivers to Customer A located at A(4, 10). Truck B delivers to Customer B located at B(9, −4). Which customer is located further from the warehouse?
Use the distance formula and show your work for BOTH distances to justify your answer. (5 pts total)
Warehouse W to Customer A distance work: (2 pts)
Warehouse W to Customer B distance work: (2 pts)
Final statement of comparison: (1 pt)
Geometry Quarter 1 Assessment Suite • Test 1 Page 7 of 7
Test 1 Teacher Key Test 1 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Geometry Test 1 (Goals 1-4) Key & Alignment Guide
Total Points
50 Points
Section 1 (MC)
30 Pts (1 pt each)
Section 2 (OE)
20 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 1 Define, classify, and name lines, segments, and rays using proper notation 1, 2, 3, 4, 5, 6, 7, 8 — 8 2 Solve perimeter problems using linear equations 9, 10, 11, 12, 13, 14, 15, 16 31a, 31c, 33a 14 3 Solve area problems using linear equations 17, 18, 19, 20, 21, 22, 23 31b, 33b, 33c 13 4 Determine segment length using the distance formula 24, 25, 26, 27, 28, 29, 30 32, 34 15
Section 1: Multiple Choice Answers (Questions 1-15)
Q1. C Goal 1
Q2. B Goal 1
Q3. C Goal 1
Q4. A Goal 1
Q5. A Goal 1
Q6. C Goal 1
Q7. B Goal 1
Q8. A Goal 1
Q9. B Goal 2
Q10. C Goal 2
Q11. B Goal 2
Q12. B Goal 2
Q13. B Goal 2
Q14. A Goal 2
Q15. A Goal 2
Geometry Quarter 1 Assessment Suite • Test 1 Key Page 1 of 3
Test 1 Key Continued
Multiple Choice (Questions 16-30)
Q16. B Goal 2
Q17. D Goal 3
Q18. B Goal 3
Q19. A Goal 3
Q20. A Goal 3
Q21. A Goal 3
Q22. A Goal 3
Q23. A Goal 3
Q24. C Goal 4
Q25. A Goal 4
Q26. D Goal 4
Q27. B Goal 4
Q28. A Goal 4
Q29. B Goal 4
Q30. B Goal 4
Q31 — Jerome's Garden Key Goals 2, 3
a) Equation & Solve for \(x\): (2 pts)
\(2(x+4) + 2(6) = 44\)
b) Find Area: (1 pt)
Length = \(x + 4 = 12 + 4 = 16\) ft
c) Fencing Cost: (2 pts)
Cost = \(44 \text{ ft} \times \$3/\text{ft} = \$132\)
Q32 — Distance Formula: Park to Houses Key (5 pts total) Goal 4
Jordan's House to Park: (2 pts)
\(J(8, 9)\) to \(P(2, 1)\)
Alex's House to Park: (2 pts)
\(A(-1, 5)\) to \(P(2, 1)\)
Final Comparison Statement: (1 pt)
Alex lives closer (distance of 5 < 10 for Jordan). Stated clearly with mathematical work.
Geometry Quarter 1 Assessment Suite • Test 1 Key Page 2 of 3
Test 1 Key Continued
Question 33 — Goals 2 & 3 — Dog Park Key (5 pts total) Scoring Key
a) Equation & solve \(x\). (2 pts)
\(2(x + 6) + 2(8) = 52\)
b) Find Area of Dog Park. (1 pt)
Length = \(x + 6\)
c) Find Landscaping Cost. (2 pts)
Cost = Area \(\times\) $5
[1 pt setup, 1 pt answer]
Question 34 — Goal 4 — Delivery Trucks Distance Key (5 pts total) Scoring Key
Warehouse W to Customer A: (2 pts)
\(W(1, 2)\) to \(A(4, 10)\)
Warehouse W to Customer B: (2 pts)
\(W(1, 2)\) to \(B(9, -4)\)
Final Comparison Statement: (1 pt)
Customer B is located further from the warehouse (distance of 10 > 8.54 for Customer A). Stated clearly with appropriate comparisons.
Geometry Quarter 1 Assessment Suite • Test 1 Key Page 3 of 3
Test 2 Student Handout Test 2: Segments & Angles
Student Copy
Goals 5–11: Segment Addition, Midpoints, Notation, Classification & Angle Measures
Student Name
Date
Period
Formula Reference Sheet
Segment Addition
If B is between A and C:
Midpoint Formula
\(M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\)
Angle Addition
If S is inside \(\angle PQR\):
Angle Bisector
If BD bisects \(\angle ABC\):
Section 1: Multiple Choice (30 Questions • 1 Point Each)
In the figure below, point B is between points A and C. If \(AB = 14\) and \(BC = 9\), what is the length of \(AC\)?
A 5
B 14
C 23
D 126
In the figure below, \(AB = 2x\), \(BC = x + 6\), and \(AC = 30\). What is the length of segment \(AB\)?
A 16
B 8
C 14
D 24
In the figure below, \(GK = 40\), \(GH = 12\), and \(HJ = 10\). What is the length of segment \(JK\)?
A 22
B 18
C 62
D 10
In the figure below, point B is between A and C. If \(AB = x + 5\), \(BC = 2x\), and \(AC = 26\), what is the length of segment \(BC\)?
A 7
B 12
C 14
D 21
Geometry Quarter 1 Assessment Suite • Test 2 Page 1 of 7
Test 2 • Multiple Choice Continued
Point P is between points O and Q. If \(OP = 3x\), \(PQ = 15\), and \(OQ = 45\), what is the value of \(x\)?
A 10
B 15
C 30
D 5
Point M is the midpoint of segment AB. If \(AM = 13\), what is the length of segment \(AB\)?
A 13
B 6.5
C 52
D 26
Point M is the midpoint of segment PQ. If \(PM = 3x + 2\) and \(MQ = 5x - 8\), what is the value of \(x\)?
A 5
B 3
C 17
D 34
Line CD bisects segment EF at point M. Which of the following statements must be true?
A \(CM \cong MD\)
B \(EM \cong MF\)
C \(EF \cong CD\)
D \(EM \cong EF\)
Point N is the midpoint of segment GH. If \(GN = 2x\) and \(NH = x + 9\), what is the length of segment \(GH\)?
A 9
B 18
C 36
D 45
What is the midpoint of the segment with endpoints A(2, 4) and B(8, 10)?
A (10, 14)
B (5, 7)
C (3, 3)
D (6, 7)
Geometry Quarter 1 Assessment Suite • Test 2 Page 2 of 7
Test 2 • Multiple Choice Continued
What is the midpoint of the segment with endpoints C(−6, 3) and D(4, 7)?
A (−1, 5)
B (−5, 2)
C (−1, 2)
D (5, −1)
Segment GH is graphed below with endpoints G(2, 5) and H(−4, −1). What is the midpoint of segment GH?
A (−2, 4)
B (3, 2)
C (−1, 3)
D (−1, 2)
What is the midpoint of a segment with endpoints P(0, 0) and Q(8, 12)?
A (8, 12)
B (2, 3)
C (4, 6)
D (4, 8)
Which of the following correctly names the angle formed by vertex B and sides BA and BC?
A \(\angle BAC\)
B \(\angle ABC\)
C \(\angle ACB\)
D \(\angle CAB\)
In the angle \(\angle XYZ\), which point represents the vertex?
A Point X
B Point Z
C Point Y
D No vertex
In a diagram, three rays share vertex Q. Which name clearly identifies the marked angle between ray QP and ray QS?
A \(\angle PQS\)
B \(\angle Q\)
C \(\angle S\)
D \(\angle PSQ\)
If three rays share a vertex, what is the vertex of angle \(\angle MNO\)?
A Point M
B Point N
C Point O
D No vertex
Geometry Quarter 1 Assessment Suite • Test 2 Page 3 of 7
Test 2 • Multiple Choice Continued
Classify the angle shown below:
A Right
B Obtuse
C Straight
D Acute
An angle measures 121°. Classify the angle.
A Acute
B Right
C Obtuse
D Straight
Which angle measure represents a right angle?
A 45°
B 90°
C 120°
D 180°
An angle measures 89°. Classify this angle.
A Acute
B Right
C Obtuse
D Straight
Ray QS is inside \(\angle PQR\). If \(m\angle PQS = 32^\circ\) and \(m\angle SQR = 41^\circ\), what is \(m\angle PQR\)?
A 9°
B 41°
C 73°
D 90°
In a diagram, \(m\angle ABD = 110^\circ\) and \(m\angle ABC = 45^\circ\) where ray BC is inside \(\angle ABD\). What is \(m\angle CBD\)?
A 65°
B 45°
C 110°
D 155°
Angle \(\angle JKL\) is a right angle. Ray KM is inside \(\angle JKL\). If \(m\angle JKM = (2x)^\circ\) and \(m\angle MKL = (x + 15)^\circ\), what is \(x\)?
A 15
B 75
C 30
D 25
Geometry Quarter 1 Assessment Suite • Test 2 Page 4 of 7
Test 2 • Multiple Choice Continued
In the figure below, \(m\angle FGH = 124^\circ\), \(m\angle FGJ = (3x + 4)^\circ\), and \(m\angle JGH = (2x)^\circ\) where ray GJ is inside \(\angle FGH\). What is \(m\angle JGH\)?
A 24°
B 48°
C 76°
D 120°
Ray BD is inside right angle \(\angle ABC\). If \(m\angle ABD = (3x)^\circ\) and \(m\angle DBC = (x + 10)^\circ\), what is the value of \(x\)?
A 10
B 15
C 20
D 25
Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = 27^\circ\), what is the measure of the entire angle \(\angle ABC\)?
A 13.5°
B 27°
C 54°
D 108°
Ray QS bisects angle \(\angle PQR\). If \(m\angle PQS = (4x)^\circ\) and \(m\angle SQR = (2x + 22)^\circ\), what is the value of \(x\)?
A 11
B 22
C 44
D 88
Ray KM bisects angle \(\angle JKL\). If the entire angle \(m\angle JKL = 76^\circ\), what is \(m\angle MKL\)?
A 19°
B 76°
C 152°
D 38°
Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = (4x - 2)^\circ\) and \(m\angle DBC = (2x + 10)^\circ\), find \(x\).
A 4
B 6
C 8
D 12
Geometry Quarter 1 Assessment Suite • Test 2 Page 5 of 7
Section 2: Open-Ended Responses (4 Questions • 5 Points Each)
Points G, H, J, and K are collinear on the same line segment. If \(GH = x + 4\), \(HJ = 2x\), \(JK = x + 9\), and the entire segment \(GK = 45\):
G H J K x + 4 2x x + 9 GK = 45
a) Write an equation for segment addition and solve for \(x\). (3 pts)
b) Find the length of segment \(HJ\). (2 pts)
Ray QS is inside angle \(\angle PQR\). If \(m\angle PQR = 98^\circ\), \(m\angle PQS = (3x + 5)^\circ\), and \(m\angle SQR = (2x + 3)^\circ\):
Q P S R 98° 3x + 5 2x + 3
a) Write an equation using the Angle Addition Postulate and solve for \(x\). (3 pts)
b) Find both angle measures: \(m\angle PQS\) and \(m\angle SQR\). (2 pts)
Geometry Quarter 1 Assessment Suite • Test 2 Page 6 of 7
Test 2 • Open-Ended Continued
Ray BD bisects angle \(\angle ABC\). If \(m\angle ABD = (5x - 6)^\circ\) and \(m\angle DBC = (3x + 12)^\circ\):
B A D C 5x − 6 3x + 12
a) Write an equation and solve for \(x\). (3 pts)
b) Find the measure of the entire angle, \(m\angle ABC\). (2 pts)
Segment AB has endpoints A(−4, 8) and B(2, −2). Point M is the midpoint of segment AB.
A(-4,8) B(2,-2)
a) Use the midpoint formula to find the coordinates of point M. Show your work. (3 pts)
b) In one sentence, explain what it means for M to be the midpoint of segment AB. (2 pts)
Geometry Quarter 1 Assessment Suite • Test 2 Page 7 of 7
Test 2 Teacher Key Test 2 ANSWER KEY • Teacher Copy
Teacher Answer Key
Segments & Angles Test 2 (Goals 5-11) Key & Alignment Guide
Total Points
50 Points
Section 1 (MC)
30 Pts (1 pt each)
Section 2 (OE)
20 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 5 Determine segment lengths using segment addition postulate 1, 2, 3, 4, 5 31a, 31b 10 6 Determine segment lengths using midpoints and segment bisectors 6, 7, 8, 9 34b 6 7 Determine midpoints on coordinate plane with midpoint formula 10, 11, 12, 13 34a 7 8 Define and name angles using proper notation 14, 15, 16, 17 — 4 9 Measure and classify angles as acute, right, or obtuse 18, 19, 20, 21 — 4 10 Solve for missing angle measures using angle addition postulate 22, 23, 24, 25, 26 32a, 32b 10 11 Solve for missing angle measures using angle bisectors 27, 28, 29, 30 33a, 33b 9
Section 1: Multiple Choice Answers (Questions 1-15)
Q1. C Goal 5
Q2. A Goal 5
Q3. B Goal 5
Q4. C Goal 5
Q5. A Goal 5
Q6. D Goal 6
Q7. A Goal 6
Q8. B Goal 6
Q9. C Goal 6
Q10. B Goal 7
Q11. A Goal 7
Q12. D Goal 7
Q13. C Goal 7
Q14. B Goal 8
Q15. C Goal 8
Geometry Quarter 1 Assessment Suite • Test 2 Key Page 1 of 3
Test 2 Key Continued
Multiple Choice (Questions 16-30)
Q16. A Goal 8
Q17. B Goal 8
Q18. D Goal 9
Q19. C Goal 9
Q20. B Goal 9
Q21. A Goal 9
Q22. C Goal 10
Q23. A Goal 10
Q24. D Goal 10
Q25. B Goal 10
Q26. C Goal 10
Q27. C Goal 11
Q28. A Goal 11
Q29. D Goal 11
Q30. B Goal 11
Q31 — Segment Addition Key Goal 5
a) Write equation and solve for \(x\): (3 pts)
\(GH + HJ + JK = GK\)
b) Find HJ length: (2 pts)
\(HJ = 2x = 2(8) = 16\)
Q32 — Angle Addition Postulate Key (5 pts total) Goal 10
a) Write equation and solve: (3 pts)
\(m\angle PQS + m\angle SQR = m\angle PQR\)
b) Find both angle measures: (2 pts)
\(m\angle PQS = 3(18) + 5 = 59^\circ\)
Geometry Quarter 1 Assessment Suite • Test 2 Key Page 2 of 3
Test 2 Key Continued
Question 33 — Goal 11 — Angle Bisector Key (5 pts total) Scoring Key
a) Write an equation and solve for \(x\). (3 pts)
Since BD bisects \(\angle ABC\):
b) Find measure of entire \(\angle ABC\). (2 pts)
Each half angle:
Question 34 — Goals 6 & 7 — Midpoint Coordinate Key (5 pts total) Scoring Key
a) Find midpoint coordinate: (3 pts)
Endpoints: \(A(-4, 8)\) and \(B(2, -2)\)
b) Midpoint explanation sentence: (2 pts)
Accept any reasonable conceptual statement, such as:
[2 pts clear conceptual sentence, 1 pt if partially complete]
Geometry Quarter 1 Assessment Suite • Test 2 Key Page 3 of 3
Statistics Quiz 1 Student Handout Quiz 1: Statistics Foundations
Student Copy
Goals 1–3: Data Displays, Shapes of Distributions & Summary Statistics
Student Name
Date
Period
Formula Reference Bank
Median
Middle number when values are in order.
Mode & Range
Mode: Most common value.
Mean
\(\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}\)
Section 1: Multiple Choice (15 Questions • 1 Point Each)
Questions 1–2 refer to the stemplot below, which shows the ages of 10 people at a family reunion.
1 | 2 4 7
2 | 0 3 3 5 8
3 | 1 6
Key: 1 | 2 means 12 years old
How many data values (people) are represented in the stemplot?
A 3
B 8
C 10
D 13
What is the smallest value (youngest age) in the data set?
A 1
B 10
C 12
D 17
Based on the frequency table below, how many students scored in the 80s (80–89)?
Score Range Frequency 60–69 2 70–79 6 80–89 9 90–99 3
A 6
B 9
C 3
D 20
Statistics Quarter 1 Assessment Suite • Quiz 1 Page 1 of 5
Quiz 1 • Multiple Choice Continued
How many students took the test in total according to the frequency table on Page 1?
A 18
B 20
C 22
D 9
According to the reunion stemplot on Page 1, what is the age of the oldest person represented?
A 31 years
B 36 years
C 3 years
D 16 years
A dataset has a long tail extending to the left, while most of the values are clustered on the right side. What is the shape of this distribution?
A Skewed right
B Skewed left
C Symmetric
D Uniform
In a dot plot, most values cluster between 20 and 30, but there is a single data value at 65 that is far from the rest. What term describes the value of 65?
20 30 50 65
A Cluster
B Gap
C Outlier
D Mode
A distribution has two separate “humps” (peaks) when graphed. What term describes this feature?
A Bimodal
B Skewed
C Uniform
D Symmetric
Statistics Quarter 1 Assessment Suite • Quiz 1 Page 2 of 5
Quiz 1 • Multiple Choice Continued
A dataset is shaped like a bell where the left side and right side are mirror images. What shape is this?
A Skewed left
B Skewed right
C Symmetric
D Bimodal
A gap in a dot plot refers to:
A A cluster of many data points.
B An area with no data points between values.
C The highest data point in the display.
D The average height of all columns.
Questions 11–13 refer to the following sorted data set:
4, 7, 7, 9, 12, 15, 20
Find the median of the data set.
A 7
B 9
C 12
D 10.75
Find the mode of the data set.
A 4
B 7
C 9
D No mode
Statistics Quarter 1 Assessment Suite • Quiz 1 Page 3 of 5
Quiz 1 • Multiple Choice Continued
Find the range of the data set: 4, 7, 7, 9, 12, 15, 20.
A 7
B 9
C 16
D 20
Find the range of the following data set: 10, 15, 20, 25, 30.
A 10
B 15
C 20
D 30
Find the median of the following sorted data set: 5, 8, 12, 15.
A 8
B 10
C 12
D 15
Statistics Quarter 1 Assessment Suite • Quiz 1 Page 4 of 5
Section 2: Open-Ended Responses (2 Questions • 5 Points Each)
The data set below shows the number of books read by 9 students over the summer.
12, 15, 18, 18, 21, 24, 27, 30, 33
a) Find the median and the mode of the data set. (2 pts)
b) Find the range of the data set. (1 pt)
c) Calculate the mean (average) of the data set. Show your work. (2 pts)
A small group of 7 families recorded the number of hours they spent reading together in a month:
10, 14, 14, 16, 20, 22, 28
a) Find the median and the mode of the reading hours. (2 pts)
b) Find the range of the reading hours. (1 pt)
c) Calculate the mean (average) of the reading hours. Show your work. (2 pts)
Statistics Quarter 1 Assessment Suite • Quiz 1 Page 5 of 5
Statistics Quiz 1 Teacher Key Statistics Quiz 1 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Statistics Quiz 1 (Goals 1-3) Key & Alignment Guide
Total Points
25 Points
Section 1 (MC)
15 Pts (1 pt each)
Section 2 (OE)
10 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 1 Represent quantitative data using a stemplot or histogram 1, 2, 3, 4, 5 — 5 2 Identify the shape of a distribution and unusual features (outliers, gaps, clusters, peaks) 6, 7, 8, 9, 10 — 5 3 Determine the median, mode, and range of a data set 11, 12, 13, 14, 15 16, 17 15
Section 1: Multiple Choice Answers
Q1. C Goal 1
Q2. C Goal 1
Q3. B Goal 1
Q4. B Goal 1
Q5. B Goal 1
Q6. B Goal 2
Q7. C Goal 2
Q8. A Goal 2
Q9. C Goal 2
Q10. B Goal 2
Q11. B Goal 3
Q12. B Goal 3
Q13. C Goal 3
Q14. C Goal 3
Q15. B Goal 3
Statistics Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 1 of 2
Section 2: Worked Solutions and Scoring
Question 16 — Goal 3 — Books Read over Summer (5 pts total) Scoring Key
a) Find the median and the mode of the data set. (2 pts)
Sorted data: 12, 15, 18, 18, 21, 24, 27, 30, 33
b) Find the range of the data set. (1 pt)
Range = Max − Min = 33 − 12 = 21
c) Calculate the mean (average) of the data set. (2 pts)
Sum = 12 + 15 + 18 + 18 + 21 + 24 + 27 + 30 + 33 = 198
Question 17 — Goal 3 — Reading Hours Family Group (5 pts total) Scoring Key
a) Find the median and the mode of the reading hours. (2 pts)
Sorted data: 10, 14, 14, 16, 20, 22, 28
b) Find the range of the reading hours. (1 pt)
Range = Max − Min = 28 − 10 = 18
c) Calculate the mean (average) of the reading hours. (2 pts)
Sum = 10 + 14 + 14 + 16 + 20 + 22 + 28 = 124
Statistics Quarter 1 Assessment Suite • Quiz 1 Answer Key Page 2 of 2
Statistics Quiz 2 Student Handout Quiz 2: Spread, Outliers & Boxplots
Student Copy
Goals 5–8: Boxplots, Outliers, Standard Deviation & Skewness
Student Name
Date
Period
Formula Reference Bank
Interquartile Range (IQR)
\(IQR = Q_3 - Q_1\)
Lower & Upper Fences
Lower: \(Q_1 - 1.5(IQR)\)
Outliers Definition
Any value lower than the Lower Fence or higher than the Upper Fence.
Section 1: Multiple Choice (15 Questions • 1 Point Each)
Questions 1–4 refer to the boxplot below, which represents the data set: 3, 4, 4, 5, 6, 7, 8, 9, 25.
3 4 6 8.5 9 25
What is the median of the data set represented in the boxplot above?
A 4
B 6
C 8.5
D 25
What is the interquartile range (IQR) of the data set? (Given \(Q_1 = 4\) and \(Q_3 = 8.5\))
A 4
B 4.5
C 5
D 21
Based on the boxplot, how would you best describe the shape of the distribution?
A Skewed left
B Skewed right
C Symmetric
D Uniform
Statistics Quarter 1 Assessment Suite • Quiz 2 Page 1 of 5
Quiz 2 • Multiple Choice Continued
Identify \(Q_1\) and \(Q_3\) of the data set shown in the boxplot on Page 1.
A \(Q_1 = 4\) and \(Q_3 = 8.5\)
B \(Q_1 = 3\) and \(Q_3 = 25\)
C \(Q_1 = 6\) and \(Q_3 = 9\)
D \(Q_1 = 4\) and \(Q_3 = 6\)
Using the \(1.5 \times IQR\) outlier rule and an IQR of 4.5, what is the upper fence for outliers? (Given \(Q_3 = 8.5\))
A 12.75
B 13.75
C 15.25
D 17.5
Using the \(1.5 \times IQR\) rule, what is the lower fence for outliers of the data set? (Given \(Q_1 = 4\) and \(IQR = 4.5\))
A −2.75
B 0
C 1.25
D 2.75
Which value in the data set (3, 4, 4, 5, 6, 7, 8, 9, 25) is confirmed as an outlier using the fences?
A 3
B 9
C 25
D No outliers
Statistics Quarter 1 Assessment Suite • Quiz 2 Page 2 of 5
Quiz 2 • Multiple Choice Continued
If the outlier value 25 were removed from the data set, what would happen to the range?
A Increase
B Decrease
C Stay same
D Cannot tell
Which data set would have the LARGER standard deviation?
A Set A
B Set B
C They are equal
D Cannot tell
A data set has a mean of 50 and a standard deviation of 5. Which value is more unusual (further away from the mean)?
A 40
B 58
C Equally unusual
D Cannot tell
What does a standard deviation of 0 tell you about a data set?
A All the data values are identical.
B The data is perfectly symmetric.
C The data has absolutely no outliers.
D The mean is equal to 0.
Generally, standard deviation is a direct mathematical measure of:
A Center
B Spread/variation
C Shape
D Sample size
Statistics Quarter 1 Assessment Suite • Quiz 2 Page 3 of 5
Quiz 2 • Multiple Choice Continued
In a right-skewed (positively skewed) distribution, which measure of center is typically LARGER?
A Mean
B Median
C Mode
D They are equal
A data set has a mean of 45 and a median of 60. What does this suggest about the shape of the distribution?
A Skewed right
B Skewed left
C Symmetric
D Uniform
Why is the median often preferred over the mean when a data set contains major outliers?
A The median is always larger than the mean.
B The mean is much more difficult to calculate.
C The median is resistant (not affected heavily) by outliers.
D The median uses every single value in the calculations.
Statistics Quarter 1 Assessment Suite • Quiz 2 Page 4 of 5
Section 2: Open-Ended Responses (2 Questions • 5 Points Each)
Construct a boxplot representing the books read over the summer. The five-number summary is:
a) Construct a correct boxplot on the number line below: (2 pts)
0 6 12 18 24 30 36
b) Clearly label where the median line is inside your boxplot. (1 pt)
c) Calculate the Interquartile Range (IQR) for this data set. (2 pts)
The data set below shows the ages (in years) of 8 dogs at an animal shelter:
5, 8, 9, 10, 11, 12, 14, 34
a) Find the values of \(Q_1\) and \(Q_3\). (1 pt)
b) Calculate the IQR and find the Upper Fence value (\(Q_3 + 1.5 \times IQR\)). (2 pts)
c) Is the dog age of 34 an outlier? Explain your reasoning using the upper fence. (2 pts)
Statistics Quarter 1 Assessment Suite • Quiz 2 Page 5 of 5
Statistics Quiz 2 Teacher Key Statistics Quiz 2 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Statistics Quiz 2 (Goals 5-8) Key & Alignment Guide
Total Points
25 Points
Section 1 (MC)
15 Pts (1 pt each)
Section 2 (OE)
10 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 5 Represent quantitative data using a boxplot 1, 2, 3, 4 16a, 16b, 16c 9 6 Identify outliers using the 1.5 × IQR rule 5, 6, 7, 8 17a, 17b, 17c 9 7 Define and interpret standard deviation 9, 10, 11, 12 — 4 8 Explain how outliers and skewness affect center and spread 13, 14, 15 — 3
Section 1: Multiple Choice Answers
Q1. B Goal 5
Q2. B Goal 5
Q3. B Goal 5
Q4. A Goal 5
Q5. D Goal 6
Q6. A Goal 6
Q7. C Goal 6
Q8. B Goal 6
Q9. B Goal 7
Q10. A Goal 7
Q11. A Goal 7
Q12. B Goal 7
Q13. A Goal 8
Q14. B Goal 8
Q15. C Goal 8
Statistics Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 1 of 2
Section 2: Worked Solutions and Scoring
Question 16 — Goal 5 — Boxplot Construction (5 pts total) Scoring Key
a) Construct a correct boxplot on the number line. (2 pts)
The student boxplot must have:
b) Clearly label the median line inside your boxplot. (1 pt)
• A vertical line must be drawn inside the box at the value of \(21\) and labeled as “Median” or “M”. [1 pt]
c) Calculate the Interquartile Range (IQR). (2 pts)
IQR = \(Q_3 - Q_1 = 28.5 - 16.5 = 12\)
Question 17 — Goal 6 — Outliers with 1.5 × IQR Rule (5 pts total) Scoring Key
a) Find the values of \(Q_1\) and \(Q_3\). (1 pt)
Lower half: 5, 8, 9, 10 → \(Q_1 = (8 + 9) / 2 = 8.5\)
b) Calculate the IQR and the Upper Fence. (2 pts)
\(IQR = Q_3 - Q_1 = 13 - 8.5 = 4.5\)
c) Is 34 an outlier? Explain using the upper fence. (2 pts)
Yes, 34 is an outlier.
Statistics Quarter 1 Assessment Suite • Quiz 2 Answer Key Page 2 of 2
Statistics Test 1 Student Handout Test 1: Statistics Foundations
Student Copy
Goals 1–4: Data Displays, Shapes, Centers & Five-Number Summaries
Student Name
Date
Period
Formula Reference Sheet
Centers
Median: Middle number in ordered list.
Five-Number Summary
Min • \(Q_1\) (25th %) • Median • \(Q_3\) (75th %) • Max
Range • IQR
Range = Max − Min
Section 1: Multiple Choice (30 Questions • 1 Point Each)
Questions 1–2 refer to the stemplot below, which shows the ages of 10 people at a family reunion.
1 | 2 4 7
2 | 0 3 3 5 8
3 | 1 6
Key: 1 | 2 means 12 years old
How many data values (people) are represented in the stemplot?
A 3
B 8
C 10
D 13
What is the smallest value (youngest age) in the data set?
A 1
B 10
C 12
D 17
Based on the frequency table below, how many students scored in the 80s (80–89)?
Score Range Frequency 60–69 2 70–79 6 80–89 9 90–99 3
A 6
B 9
C 3
D 20
Statistics Quarter 1 Assessment Suite • Test 1 Page 1 of 7
Test 1 • Multiple Choice Continued
How many students took the test in total according to the frequency table on Page 1?
A 18
B 20
C 22
D 9
According to the reunion stemplot on Page 1, what is the age of the oldest person represented?
A 31 years
B 36 years
C 3 years
D 16 years
According to the score frequency table on Page 1, how many total students scored below 80?
A 2
B 6
C 8
D 9
How many students scored in the 90s (90–99) according to the frequency table on Page 1?
A 3
B 6
C 9
D 20
On a standard frequency histogram, the height of each vertical bar represents:
A The raw data value itself.
B The range of the values.
C The frequency (count) of values in that interval.
D The mean of the entire data set.
A dataset has a long tail extending to the left, while most of the values are clustered on the right side. What is the shape of this distribution?
A Skewed right
B Skewed left
C Symmetric
D Uniform
In a dot plot, most values cluster between 20 and 30, but there is a single data value at 65 that is far from the rest. What term describes the value of 65?
A Cluster
B Gap
C Outlier
D Mode
Geometry Quarter 1 Assessment Suite • Test 1 Page 2 of 7
Test 1 • Multiple Choice Continued
A distribution has two separate “humps” (peaks) when graphed. What term describes this feature?
A Bimodal
B Skewed
C Uniform
D Symmetric
A dataset is shaped like a bell where the left side and right side are mirror images. What shape is this?
A Skewed left
B Skewed right
C Symmetric
D Bimodal
A dot plot has many points from 10 to 15, then no points between 15 and 35, then a point at 35. The space between 15 and 35 is called:
A Outlier
B Gap
C Peak
D Cluster
A distribution has a long tail extending to the right. What is its shape?
A Skewed right
B Skewed left
C Symmetric
D Uniform
In a uniform distribution, the heights of all the bars on a histogram are:
A Heavily pulled to the left.
B Heavily pulled to the right.
C Approximately equal across all values.
D Showing two distinct and equal peaks.
Questions 16–18 refer to the following sorted data set:
4, 7, 7, 9, 12, 15, 20
Find the median of the data set.
A 7
B 9
C 12
D 10.75
Geometry Quarter 1 Assessment Suite • Test 1 Page 3 of 7
Test 1 • Multiple Choice Continued
Find the mode of the data set: 4, 7, 7, 9, 12, 15, 20.
A 4
B 7
C 9
D No mode
Find the range of the data set: 4, 7, 7, 9, 12, 15, 20.
A 7
B 9
C 16
D 20
Find the range of the following data set: 10, 15, 20, 25, 30.
A 10
B 15
C 20
D 30
Find the median of the following sorted data set: 5, 8, 12, 15.
A 8
B 10
C 12
D 15
Find the mode of the following data set: 2, 3, 3, 4, 5.
A 2
B 3
C 4
D 5
Which equation correctly calculates the range of a numeric dataset?
A \(\text{Range} = \text{Median} - \text{Mean}\)
B \(\text{Range} = \text{Maximum} - \text{Minimum}\)
C \(\text{Range} = Q_3 - Q_1\)
D \(\text{Range} = \frac{\text{Sum of values}}{\text{Total count}}\)
Questions 23–27 refer to the following sorted data set of 9 test scores:
2, 5, 6, 9, 12, 15, 18, 20, 23
What is the minimum value of this data set?
A 2
B 5.5
C 12
D 23
Geometry Quarter 1 Assessment Suite • Test 1 Page 4 of 7
Test 1 • Multiple Choice Continued
What is \(Q_1\) (the first quartile) of this data set?
A 5
B 5.5
C 6
D 9
What is \(Q_3\) (the third quartile) of this data set?
A 18
B 19
C 20
D 23
What is the maximum value of this data set?
A 12
B 18
C 20
D 23
What is the median value of this data set?
A 12
B 9
C 15
D 6
The five-number summary contains all of the following statistics EXCEPT:
A Mean
B Median
C Q1
D Minimum
For the sorted data set: 3, 5, 8, 10, 12, what is the value of \(Q_1\)?
A 3
B 4
C 5
D 8
For the same sorted data set: 3, 5, 8, 10, 12, what is the value of \(Q_3\)?
A 8
B 10
C 11
D 12
Geometry Quarter 1 Assessment Suite • Test 1 Page 5 of 7
Section 2: Open-Ended Responses (4 Questions • 5 Points Each)
The data set below shows the number of books read by 9 students over the summer.
12, 15, 18, 18, 21, 24, 27, 30, 33
a) Find the median and the mode of the data set. (2 pts)
b) Find the range of the data set. (1 pt)
c) Determine \(Q_1\) and \(Q_3\) of the data set. (2 pts)
The data set below shows the exam preparation hours of 9 high school students:
5, 8, 10, 10, 12, 14, 16, 18, 22
a) Find the median and the mode of the preparation hours. (2 pts)
b) Find the range of the preparation hours. (1 pt)
c) Find the \(Q_1\) and \(Q_3\) quartile values. (2 pts)
Geometry Quarter 1 Assessment Suite • Test 1 Page 6 of 7
Test 1 • Open-Ended Continued
The mathematics test scores of 10 students are recorded below:
62, 65, 71, 74, 78, 80, 83, 83, 85, 92
a) Construct a stemplot to represent these test scores. Include a clear key! (3 pts)
b) Find the range of the scores. (1 pt)
c) Identify the mode of the scores. (1 pt)
Two basketball players scored the following points in their last 5 games:
Player A: 10, 12, 15, 18, 20 • Player B: 5, 15, 15, 15, 25
a) Calculate the Mean score for both: (2 pts)
b) State the Median score for both: (1 pt)
c) Which player is more consistent? Explain using the range. (2 pts)
Geometry Quarter 1 Assessment Suite • Test 1 Page 7 of 7
Statistics Test 1 Teacher Key Statistics Test 1 ANSWER KEY • Teacher Copy
Teacher Answer Key
Foundations of Statistics Test 1 (Goals 1-4) Key & Alignment Guide
Total Points
50 Points
Section 1 (MC)
30 Pts (1 pt each)
Section 2 (OE)
20 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 1 Represent quantitative data using a stemplot or histogram 1, 2, 3, 4, 5, 6, 7, 8 33a 11 2 Identify shape and features of a distribution (outliers, gaps, clusters, peaks) 9, 10, 11, 12, 13, 14, 15 — 7 3 Determine the median, mode, and range of a data set 16, 17, 18, 19, 20, 21, 22 31a, 31b, 32a, 32b, 33b, 33c, 34a, 34b, 34c 21 4 Identify the five-number summary of a data set 23, 24, 25, 26, 27, 28, 29, 30 31c, 32c 11
Section 1: Multiple Choice Answers (Questions 1-15)
Q1. C Goal 1
Q2. C Goal 1
Q3. B Goal 1
Q4. B Goal 1
Q5. B Goal 1
Q6. C Goal 1
Q7. A Goal 1
Q8. C Goal 1
Q9. B Goal 2
Q10. C Goal 2
Q11. A Goal 2
Q12. C Goal 2
Q13. B Goal 2
Q14. A Goal 2
Q15. C Goal 2
Statistics Quarter 1 Assessment Suite • Test 1 Key Page 1 of 3
Test 1 Key Continued
Multiple Choice (Questions 16-30)
Q16. B Goal 3
Q17. B Goal 3
Q18. C Goal 3
Q19. C Goal 3
Q20. B Goal 3
Q21. B Goal 3
Q22. B Goal 3
Q23. A Goal 4
Q24. B Goal 4
Q25. B Goal 4
Q26. D Goal 4
Q27. A Goal 4
Q28. A Goal 4
Q29. B Goal 4
Q30. C Goal 4
Q31 — Books Read Over Summer Key Goals 3, 4
a) Median & Mode: (2 pts)
Ordered: 12, 15, 18, 18, 21, 24, 27, 30, 33
b) Find Range: (1 pt)
Range = 33 − 12 = 21
c) Find Q1 and Q3: (2 pts)
Lower half: 12, 15, 18, 18 → \(Q_1 = 16.5\)
Q32 — Exam Preparation Hours Key (5 pts total) Goals 3, 4
a) Find the median and the mode: (2 pts)
Ordered: 5, 8, 10, 10, 12, 14, 16, 18, 22
b) Find range: (1 pt)
Range = 22 − 5 = 17
c) Find Q1 and Q3: (2 pts)
Lower half: 5, 8, 10, 10 → \(Q_1 = 9\)
Statistics Quarter 1 Assessment Suite • Test 1 Key Page 2 of 3
Test 1 Key Continued
Question 33 — Goals 1 & 3 — Score Stemplot • Key (5 pts total) Scoring Key
a) Stemplot Construction: (3 pts)
6 | 2 5
b) Find Range: (1 pt)
Range = 92 − 62 = 30
c) Determine Mode: (1 pt)
Mode = 83 (appears twice)
Question 34 — Goals 3 & 4 — Consistency Comparison (5 pts total) Scoring Key
a) Calculate Means: (2 pts)
Player A mean:
b) Find Medians: (1 pt)
Player A median = 15
Both medians are equal.
c) Which player is more consistent? Explain using range: (2 pts)
Player A range: \(20 - 10 = 10\) points. • Player B range: \(25 - 5 = 20\) points.
Statistics Quarter 1 Assessment Suite • Test 1 Key Page 3 of 3
Statistics Test 2 Student Handout Test 2: Statistics Analysis
Student Copy
Goals 5–11: Boxplots, Outliers, Spread, Skewness, z-scores & Relative Performance
Student Name
Date
Period
Formula Reference Sheet
Quartiles & IQR
\(IQR = Q_3 - Q_1\)
Standard Deviation (SD)
SD measures the typical (average) distance of data points from the mean.
z-score formula
\(z = \frac{x - \mu}{\sigma} \rightarrow \frac{\text{Value} - \text{Mean}}{\text{Standard Deviation}}\)
Section 1: Multiple Choice (30 Questions • 1 Point Each)
Questions 1–4 refer to the boxplot below, which represents the data set: 3, 4, 4, 5, 6, 7, 8, 9, 25.
3 4 6 8.5 9 25
What is the median of the data set represented in the boxplot above?
A 4
B 6
C 8.5
D 25
What is the interquartile range (IQR) of the data set represented in the boxplot above? (Given \(Q_1 = 4\), \(Q_3 = 8.5\))
A 4
B 4.5
C 5
D 21
Based on the boxplot, how would you best describe the shape of the distribution?
A Skewed left
B Skewed right
C Symmetric
D Uniform
Identify the values of \(Q_1\) and \(Q_3\) of the data set represented in the boxplot above.
A \(Q_1 = 4\) and \(Q_3 = 8.5\)
B \(Q_1 = 3\) and \(Q_3 = 25\)
C \(Q_1 = 6\) and \(Q_3 = 9\)
D \(Q_1 = 4\) and \(Q_3 = 6\)
Statistics Quarter 1 Assessment Suite • Test 2 Page 1 of 7
Test 2 • Multiple Choice Continued
Using the \(1.5 \times IQR\) outlier rule and an IQR of 4.5, what is the upper fence for outliers? (Given \(Q_3 = 8.5\))
A 12.75
B 13.75
C 15.25
D 17.5
Using the \(1.5 \times IQR\) rule, what is the lower fence for outliers of the data set? (Given \(Q_1 = 4\) and \(IQR = 4.5\))
A −2.75
B 0
C 1.25
D 2.75
Which value in the data set (3, 4, 4, 5, 6, 7, 8, 9, 25) is confirmed as an outlier using the fences?
A 3
B 9
C 25
D No outliers
If the outlier value 25 were removed from the data set, what would happen to the range?
A Increase
B Decrease
C Stay same
D Cannot tell
Which data set would have the LARGER standard deviation?
A Set A
B Set B
C They are equal
D Cannot tell
A data set has a mean of 50 and a standard deviation of 5. Which value is more unusual (further away from the mean)?
A 40
B 58
C Equally unusual
D Cannot tell
Statistics Quarter 1 Assessment Suite • Test 2 Page 2 of 7
Test 2 • Multiple Choice Continued
What does a standard deviation of 0 tell you about a data set?
A All the data values are identical.
B The data is perfectly symmetric.
C The data has absolutely no outliers.
D The mean is equal to 0.
Generally, standard deviation is a direct mathematical measure of:
A Center
B Spread/variation
C Shape
D Sample size
In a right-skewed (positively skewed) distribution, which measure of center is typically LARGER?
A Mean
B Median
C Mode
D They are equal
A data set has a mean of 45 and a median of 60. What does this suggest about the shape of the distribution?
A Skewed right
B Skewed left
C Symmetric
D Uniform
Why is the median often preferred over the mean when a data set contains major outliers?
A The median is always larger than the mean.
B The mean is much more difficult to calculate.
C The median is resistant (not affected heavily) by outliers.
D The median uses every single value in the calculations.
If a very high outlier data score is added to a symmetric dataset, which summary statistic will change the most?
A Median
B Mode
C Mean
D None of these
Statistics Quarter 1 Assessment Suite • Test 2 Page 3 of 7
Test 2 • Multiple Choice Continued
Which of the following is NOT a feature typically used to describe and compare two different distributions?
A Shape
B Center
C Spread
D Total digits
Two classes took the same test. Class 1: median = 78, IQR = 10. Class 2: median = 78, IQR = 25. Which class has more consistent (less variable) scores?
A Class 1
B Class 2
C They are equal
D Cannot tell
Data Set A has a mean of 80 and standard deviation of 4. Data Set B has a mean of 80 and standard deviation of 12. Which statement is true?
A Data Set A has more variability than Data Set B.
B Data Set B has more variability than Data Set A.
C Both data sets have the exact same variability.
D The datasets cannot be compared mathematically.
When comparing two boxplots visually, which measure of center is easiest to compare directly?
A Mean
B Median
C Mode
D SD
A data set has a mean of 70 and a standard deviation of 5. What is the z-score for a value of 80?
A 0.5
B 2
C 10
D 50
A data set has a mean of 100 and a standard deviation of 15. What is the z-score for a value of 85?
A −1
B −15
C 1
D 15
Statistics Quarter 1 Assessment Suite • Test 2 Page 3 of 7
Test 2 • Multiple Choice Continued
A value has a z-score of 1.5 in a distribution with a mean of 60 and standard deviation of 8. What is the actual value?
A 61.5
B 68
C 72
D 90
A value has a z-score of −2 in a distribution with a mean of 50 and standard deviation of 4. What is the actual value?
A 42
B 46
C 48
D 58
A calculated z-score of exactly 0 tells us that the corresponding raw data value is:
A Equal to the median value.
B Exactly equal to the mean value.
C The maximum score in the set.
D A mathematically extreme outlier.
Questions 26–28 refer to the following scenario:
On a mathematics exam, the class mean was 75 with standard deviation 5. On a science exam, the mean was 70 with standard deviation 4. Maria scored 85 on mathematics and 78 on science.
Calculate Maria’s z-score on the mathematics test.
A 1
B 2
C 5
D 10
Statistics Quarter 1 Assessment Suite • Test 2 Page 4 of 7
Test 2 • Multiple Choice Continued
Calculate Maria’s z-score on the science test.
A 1
B 2
C 8
D 78
Based on the z-scores above, on which test did Maria perform relatively better compared to her class peers?
A Mathematics Exam
B Science Exam
C She performed equally well on both.
D Cannot be determined mathematically.
John scored 90 on a test with mean 80 and SD 5. Mike scored 85 on a test with mean 70 and SD 10. Who performed relatively better?
A John (z-score of 2.0 vs 1.5)
B Mike (z-score of 1.5 vs 2.0)
C They performed equally well.
D Cannot tell without more statistics.
A negative z-score mathematically indicates that the corresponding raw score value is:
A Below the mean
B Above the mean
C An outlier
D Equal to mean
Statistics Quarter 1 Assessment Suite • Test 2 Page 5 of 7
Section 2: Open-Ended Responses (4 Questions • 5 Points Each)
Construct a boxplot representing the books read over the summer. The five-number summary is:
a) Construct a correct boxplot on the number line below: (2 pts)
0 6 12 18 24 30 36
b) Clearly label the median line inside your boxplot. (1 pt)
c) Calculate the Interquartile Range (IQR). (2 pts)
The data set below shows the ages (in years) of 8 dogs at an animal shelter:
5, 8, 9, 10, 11, 12, 14, 34
a) Find the values of \(Q_1\) and \(Q_3\). (1 pt)
b) Calculate the IQR and find the Upper Fence value (\(Q_3 + 1.5 \times IQR\)). (2 pts)
c) Is the dog age of 34 an outlier? Explain your reasoning using the upper fence. (2 pts)
Statistics Quarter 1 Assessment Suite • Test 2 Page 6 of 7
Test 2 • Open-Ended Continued
Standard Deviation & Skewness analysis.
a) Two vending machines fill bags of chips. Machine A has a mean weight of 8 oz with standard deviation 0.1 oz. Machine B has a mean weight of 8 oz with standard deviation 0.5 oz. Which machine is more consistent? Explain your reasoning. (2 pts)
b) Explain in one sentence what standard deviation represents or measures in statistics. (1 pt)
c) A set of quiz scores has a mean of 72 and a median of 85. Based on this relationship, is the distribution skewed left, skewed right, or symmetric? Justify. (2 pts)
Jamal's height is 70 inches. Heights of students in his grade have a mean of 66 inches with standard deviation 2.5 inches. Diego's height is 74 inches. Heights of students in his older grade have a mean of 69 inches with standard deviation 3 inches.
Determine who is relatively taller inside their own grades. (5 pts total)
a) Calculate Jamal's z-score: (2 pts)
b) Calculate Diego's z-score: (2 pts)
c) Who is relatively taller? Justify your answer using the z-scores you calculated: (1 pt)
Geometry Quarter 1 Assessment Suite • Test 2 Page 7 of 7
Statistics Test 2 Teacher Key Statistics Test 2 ANSWER KEY • Teacher Copy
Teacher Answer Key
Spread, Skewness & z-scores Test 2 (Goals 5-11) Key & Alignment Guide
Total Points
50 Points
Section 1 (MC)
30 Pts (1 pt each)
Section 2 (OE)
20 Pts (5 pts each)
Goal Alignment Table
Goal # Goal Description MC Questions OE Questions Total Pts 5 Represent quantitative data using a boxplot 1, 2, 3, 4 31a, 31b, 31c 9 6 Identify outliers using the 1.5 × IQR rule 5, 6, 7, 8 32a, 32b, 32c 9 7 Define and interpret standard deviation 9, 10, 11, 12 33a, 33b 7 8 Explain how outliers and skewness affect center and spread 13, 14, 15, 16 33c 7 9 Describe and compare distributions of data 17, 18, 19, 20 — 4 10 Use the z-score formula to find a value relative to the mean 21, 22, 23, 24, 25 34a, 34b 9 11 Use z-scores to compare values from different distributions 26, 27, 28, 29, 30 34c 6
Section 1: Multiple Choice Answers (Questions 1-15)
Q1. B Goal 5
Q2. B Goal 5
Q3. B Goal 5
Q4. A Goal 5
Q5. D Goal 6
Q6. A Goal 6
Q7. C Goal 6
Q8. B Goal 6
Q9. B Goal 7
Q10. A Goal 7
Q11. A Goal 7
Q12. B Goal 7
Q13. A Goal 8
Q14. B Goal 8
Q15. C Goal 8
Statistics Quarter 1 Assessment Suite • Test 2 Key Page 1 of 3
Test 2 Key Continued
Multiple Choice (Questions 16-30)
Q16. C Goal 8
Q17. D Goal 9
Q18. A Goal 9
Q19. B Goal 9
Q20. B Goal 9
Q21. B Goal 10
Q22. A Goal 10
Q23. C Goal 10
Q24. A Goal 10
Q25. B Goal 10
Q26. B Goal 11
Q27. B Goal 11
Q28. C Goal 11
Q29. A Goal 11
Q30. A Goal 11
Q31 — Summer Books Boxplot Key Goal 5
a) Construct Boxplot: (2 pts)
• Box drawn from \(16.5\) (\(Q_1\)) to \(28.5\) (\(Q_3\)). [1 pt]
b) Median Label: (1 pt)
Vertical line labeled inside box at the value of \(21\). [1 pt]
c) Calculate IQR: (2 pts)
\(IQR = Q_3 - Q_1 = 28.5 - 16.5 = 12\)
Q32 — Shelter Dogs Outlier Key (5 pts total) Goal 6
a) Find \(Q_1\) and \(Q_3\): (1 pt)
Lower: 5, 8, 9, 10 → \(Q_1 = (8+9)/2 = 8.5\)
b) Calculate IQR & Fence: (2 pts)
\(IQR = 13 - 8.5 = 4.5\)
c) Outlier decision & why: (2 pts)
Yes, 34 is an outlier. Since \(34 > 19.75\), the score value is outside the fence limits.
Statistics Quarter 1 Assessment Suite • Test 2 Key Page 2 of 3
Test 2 Key Continued
Question 33 — Goals 7 & 8 — SD and Skewness Analysis Key (5 pts total) Scoring Key
a) Which machine is more consistent? Explain: (2 pts)
Machine A is more consistent because it has a smaller standard deviation (0.1 oz vs 0.5 oz for Machine B), which means the bag weights vary much less and are closer to the 8 oz target.
b) What does SD measure? (1 pt)
Accept any statement showing it measures the typical or average distance of values from the mean. [1 pt]
c) Find and justify skewness shape: (2 pts)
Skewed left.
Question 34 — Goals 10 & 11 — Jamal & Diego Z-Score Key (5 pts total) Scoring Key
a) Calculate Jamal's z-score: (2 pts)
\(z_J = \frac{70 - 66}{2.5}\)
b) Calculate Diego's z-score: (2 pts)
\(z_D = \frac{74 - 69}{3}\)
c) Who is relatively taller and why? (1 pt)
Diego is relatively taller because his z-score (1.67) is higher than Jamal's z-score (1.6), indicating Diego is further above his peer group's mean in terms of standard deviations. [1 pt]
Statistics Quarter 1 Assessment Suite • Test 2 Key Page 3 of 3
