| x (items) |
|---|
| y (cost $) |
|---|
| 3 | 12.00 |
| 20.00 | |
| 8 | |
| 10 |
Convert the following fractions to decimals. Identify if they are terminating (T) or repeating (R).
\( \frac{3}{8} \)
Dec: _____ T/R: _____
\( \frac{2}{3} \)
Dec: _____ T/R: _____
\( \frac{4}{25} \)
Dec: _____ T/R: _____
Solving Unit Rate & Percentage Problems
Packet 01
When a problem gives you a complex fraction rate, follow these steps:
STEP 1
Write the relationship as a complex fraction: \( \frac{\text{unit } A}{\text{unit } B} \)
STEP 2
Divide the numerator by the denominator (KFC: Keep Change Flip).
STEP 3
Simplify and add your unit label (e.g., miles per hour).
A snail travels \( \frac{1}{8} \) of a mile in \( \frac{1}{4} \) of an hour. At this rate, how far can the snail travel in 1 hour?
"To find distance per 1 hour, I need to divide total distance by total time."
Workspace
\( \frac{ \frac{1}{8} }{ \frac{1}{4} } = \frac{1}{8} \times \frac{4}{1} = \frac{4}{8} \)
Self-Check Questions:
A recipe calls for \( \frac{3}{4} \) cup of sugar for every \( 1 \frac{1}{2} \) batches of cookies. How much sugar is needed for exactly 1 batch?
Show your work below
Answer:
cups
SESSION 1: MULTIPLE CHOICE
Page 1 of 4
1
A store sells 5 pounds of apples for $7.25. Which equation can be used to determine the cost, \(c\), in dollars, for any number of pounds of apples, \(p\)?
A \( c = 1.45p \)
B \( c = 7.25p \)
C \( p = 1.45c \)
D \( p = 7.25c \)
2
The table below shows a proportional relationship between \(x\) and \(y\).
| \(x\) | \(y\) |
|---|---|
| 4 | 6 |
| 10 | 15 |
| 12 | 18 |
What is the constant of proportionality for this relationship?
A 0.67
B 1.5
C 2.0
D 4.0
3
A technician earns $140 for every 4 hours worked. If the technician works 35 hours in a week, how much money will the technician earn?
A $350
B $490
C $1,225
D $1,400
GO ON
NY STATE TEST PREP
Page 2 of 4
4
Which number represents the absolute value of \( -8.2 \)?
A -8.2
B -8
C 8
D 8.2
5
What is the value of the expression \( -12.5 + (-4.2) - (-6.1) \)?
A -22.8
B -10.6
C -1.2
D 10.6
6
Which expression is equivalent to \( 4(x - 3) + 2x \)?
A \( 6x - 3 \)
B \( 6x - 12 \)
C \( 4x - 12 \)
D \( 6x + 12 \)
7
A cell phone company charges a monthly fee of $25 plus $0.10 for every minute of international calling. Which inequality can be used to find the maximum number of minutes, \(m\), a customer can use if they want their bill to be no more than $40?
A \( 25 + 0.10m \geq 40 \)
B \( 25 + 0.10m \leq 40 \)
C \( 0.10 + 25m \leq 40 \)
D \( 25m + 0.10m \leq 40 \)
GO ON
GRADE 7 MATHEMATICS
Page 3 of 4
8
A student incorrectly simplified the expression below:
\( -5(x - 2) \)
The student's answer was \( -5x - 10 \). Which statement best describes the error the student made?
A The student did not multiply -5 by -2 correctly.
B The student should have added -5 and -2 first.
C The student only multiplied -5 by the variable \(x\).
D The student multiplied incorrectly and got -10 instead of 10.
9
A scale drawing of a rectangular park has a length of 5 inches and a width of 3 inches. If the scale of the drawing is 1 inch = 20 feet, what is the actual perimeter, in feet, of the park?
A 160 feet
B 320 feet
C 15 feet
D 300 feet
10
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If one marble is selected at random, what is the probability that it will be a blue marble?
A \( \frac{1}{2} \)
B \( \frac{1}{5} \)
C \( \frac{3}{10} \)
D \( \frac{5}{10} \)
GO ON
SESSION 2: CONSTRUCTED RESPONSE
Page 4 of 4
11
This question is worth 1 point.
The graph below represents a proportional relationship. What is the constant of proportionality (\( \frac{y}{x} \)) for the graph?
Graph: Line passing through (0,0) and (2, 5)
Answer:
12
This question is worth 1 point.
What is the value of the expression \( -\frac{3}{4} \div 0.25 \)?
Answer:
13
This question is worth 1 point.
Simplify the expression \( 0.5(8x - 12) + 4 \).
Answer:
14
This question is worth 2 points.
A store owner buys shirts for $15 each and sells them at a 60% markup. Later, a customer uses a coupon for 15% off the selling price. What is the final price of the shirt?
Show your work.
Final Price: $
15
This question is worth 3 points.
A local library has a goal to collect 500 books for a fundraiser. On Monday, they collected 20% of their goal. On Tuesday, they collected 45 more books. On Wednesday, they collected \( \frac{1}{4} \) of the remaining goal amount.
How many books were collected on Wednesday? How many more books do they still need to reach their total goal of 500?
Show your work.
Books collected on Wednesday:
Books still needed:
STOP
"A car travels \( 10 \frac{1}{2} \) miles in \( \frac{1}{4} \) hour. What is its speed?"
1
Write as fraction:
\( \frac{10.5 \text{ mi}}{0.25 \text{ hr}} \)
2
Divide (KFC Method):
\( \frac{21}{2} \div \frac{1}{4} = \frac{21}{2} \times \frac{4}{1} \)
Self-Check Checklist:
"A recipe requires \( \frac{2}{3} \) cup of milk for every \( \frac{1}{3} \) stick of butter. How much milk is needed for 1 full stick?"
Final Answer:
Session 1: Multiple Choice
Page 5
1
A store sells 4.5 pounds of bananas for $2.70. What is the unit price, in dollars, per pound of bananas?
A 0.60
B 1.67
C 2.70
D 12.15
2
The table shows a proportional relationship between \(x\) and \(y\). Which equation represents this relationship?
A \( y = 2x + 1 \)
B \( y = x^2 \)
C \( y = \frac{1}{2}x \)
D \( y = 5 \)
3
A customer leaves an 18% tip on a restaurant bill of $42.50. What is the total amount, including tip, the customer pays?
A $7.65
B $34.85
C $50.15
D $60.50
GO ON
Empire Blitz: Packet 01
Page 6
4
Which expression is equivalent to \( -3(x - 5) \)?
A \( -3x - 15 \)
B \( -3x + 15 \)
C \( 3x - 15 \)
D \( -3x + 5 \)
5
A temperature decreased by 12 degrees each hour for 3 hours. Which expression represents the total change in temperature?
A \( 3 \times (-12) \)
B \( 3 + (-12) \)
C \( -12 \div 3 \)
D \( 12 \times 3 \)
6
What is the distance between \( -4 \) and \( 5 \) on a number line?
A 1
B 9
C -9
D -1
GO ON
Empire Blitz: Packet 01
Page 7
7
Which number line shows the solution to \( 2x - 4 < 2 \)?
0 1 3 5 7
A Open circle at 3, shading left
B Closed circle at 3, shading left
C Open circle at 1, shading left
D Open circle at 3, shading right
8
A scale drawing has a scale of 1 inch = 12 feet. If a room is 2.5 inches long on the drawing, how long is the actual room?
A 4.8 feet
B 14.5 feet
C 30 feet
D 36 feet
GO ON
Session 1 Finale & Session 2
Page 8
9
Which represents a random sample of a school's population?
A Surveying math teachers.
B Surveying every 10th student.
C Surveying basketball players.
D Surveying cafeteria staff.
10
Probability of rolling a number greater than 4 on a standard die?
A 1/6
B 1/3
C 1/2
D 2/3
11
Value of \( -\frac{1}{2} + 0.75 \)?
Answer:
12
Solve for \(x\): \( 5x = 45 \).
Answer:
GO ON
13
Map scale is 1 cm = 50 miles. What distance in cm represents 225 miles?
Answer:
14
2 Points
A store sale is 25% off. A jacket costs $80. After discount, a 7% tax is applied. What is the final price? Show work.
Final Price: $
15
3 Points
A survey showed 12 of 30 prefer digital books. If there are 450 students, how many likely prefer digital books? Explain and show work.
Answer:
STOP
B 2\(m\) + 15
C 17\(m\)
D 30\(m\)
6
What is the value of 0.5(4\(x\) - 10) when \(x\) = 5 ?
A 0
B 5
C 10
D 20
GO ON
Empire Blitz: Packet 02
Page 6
7
Which inequality is shown on the number line?
0 1 2 3 4
A \(x\) < 2
B \(x\) ≤ 2
C \(x\) > 2
D \(x\) ≥ 2
8
What is the product of -4 and (\(x\) - 3) ?
A -4\(x\) - 12
B -4\(x\) + 12
C 4\(x\) - 12
D -4\(x\) - 3
GO ON
Empire Blitz: Packet 02
Page 7
9
Which value makes the inequality -2\(x\) + 5 < 1 true?
A 1
B 2
C 0
D 3
10
Simplify: 0.5\(x\) + 0.5\(x\) - 8
A \(x\) - 8
B 0.5\(x\) - 8
C 1.0 - 8\(x\)
D -7\(x\)
11
Simplify: 4(3\(x\) - 5) + 12
Answer:
12
Solve for \(x\): \(x\)/5 = -4
Answer:
GO ON
13
"Sum of a number, \(n\), and eight, all multiplied by three."
Write as Expression:
14
2 Points
A flat fee of $35 plus $45 per hour for repairs. Total bill was $170. Write an equation to find \(h\), number of hours. Solve the equation. Show work.
Equation:
Final Answer:
15
3 Points
Spend at most $120. Sam buys a $35 headset and wants $15 games. Write an inequality for max games, \(g\). Solve and explain context. Show work.
Max Games:
STOP
Page 5
4
A bag contains 5 red, 3 blue, and 2 yellow marbles. Probability of selecting a marble NOT red?
A 1/2
B 3/10
C 1/5
D 5/10
5
The diameter of a circle is 12 cm. What is its circumference? (Use pi = 3.14)
A 18.84 cm
B 37.68 cm
C 75.36 cm
D 113.04 cm
6
A representative sample of 50 students found 15 play soccer. In a school of 600, how many expect to play soccer?
A 150
B 180
C 200
D 300
GO ON
Empire Blitz: Packet 03
Page 6
7
Which represents a random sample for studying middle school lunch preferences?
A Surveying the first 20 students who enter.
B Surveying all students in the cooking club.
C Assigning numbers and picking 50 at random.
D Surveying students only in the 8th grade.
8
A square pyramid has a base side length of 6 cm. What is the area of its base?
A 12 sq. cm.
B 24 sq. cm.
C 36 sq. cm.
D 60 sq. cm.
9
Spinner has 8 equal sections. 2 are green. If spun 40 times, about how many land on green?
A 5
B 10
C 15
D 20
GO ON
Session 1 Finale & Session 2
Page 7
10
Which value describes a certain event?
A 0.00
B 0.50
C 1.00
D 100
11
Circular table has radius of 2 feet. What is its area? (pi = 3.14)
Answer:
12
Scale: 1 cm = 4 m. How many actual meters is represented by 5.5 cm?
Answer:
GO ON
13
A standard coin is flipped twice. Probability it lands on heads both times?
Answer (Fraction):
14
2 Points
A school survey showed 12 of 30 prefer math. If there are 450 total students, how many would you expect to prefer math? Show your work.
Expected Students:
15
3 Points
Garden is 20 ft by 15 ft. A circular fountain (r=4) is in the middle. The rest is grass. What is the grass area? (Use pi = 3.14). Show your work.
Area (sq. ft.):
STOP
