TSIA2 Math Diagnostic Assessment TSIA2 Math Diagnostic Practice Exam
Mathematics Diagnostic Assessment
Texas Success Initiative Assessment 2.0 • 10 Targeted Benchmark Items
Test Booklet
Form A-10
Standard Calculator Allowed
Student Name:
Date:
Instructor / Section:
TSIA2 Mathematics Reference Formulas For scratch work, use available margins.
Area of Triangle \(A = \frac{1}{2}bh\)
Pythagorean Thm \(a^2 + b^2 = c^2\)
Complement Prob \(P(\text{not } E) = 1 - P(E)\)
Quadratic Form \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Domain 1: Quantitative Reasoning (Items 1–3)
Direct Proportions, Percentages, and Applied Problem Solving
1 TSIA2 Skill: Direct Proportions & Unit Rates
1 Point
A commercial manufacturing machine stamps 360 precision metal brackets in 15 minutes while operating at a constant rate. At this same rate, how many metal brackets will the machine stamp in 50 minutes?
A 720 brackets
B 900 brackets
C 1,200 brackets
D 1,800 brackets
2 TSIA2 Skill: Percent Applications & Financial Math
1 Point
A solar panel distributor purchases an electrical inverter at a wholesale price of \(\$480\). The distributor marks up the wholesale price by \(35\%\). During a promotional seasonal sale, the distributor then offers a \(20\%\) discount off the marked-up retail price. What is the final promotional sale price of the inverter?
A $408.00
B $518.40
C $552.00
D $648.00
3 TSIA2 Skill: Applied Problem Solving & Rates
1 Point
A commuter drives 120 miles outbound from Austin to Houston at an average speed of 60 miles per hour. Due to road construction on the return trip along the identical 120-mile route, the commuter travels at an average speed of 40 miles per hour. What is the commuter’s average speed, in miles per hour, for the entire 240-mile round trip?
A 48 mph
B 50 mph
C 52 mph
D 54 mph
TSIA2 Mathematics Diagnostic Form A-10 Page 1 of 4 • Continue to Domain 2 Quantitative Reasoning: Items 1–3
TSIA2 Mathematics Diagnostic
Domain 2: Algebraic Reasoning & Functions (Items 4–7)
Target Time: ~15 minutes
Focus areas: Solving for \(x\) in multi-step equations, multiplying binomials, factoring trinomials (\(a=1\)), and solving radical equations equal to a constant.
4 TSIA2 Skill: Solving for x (Linear Equations)
1 Point
What real value of \(x\) satisfies the multi-step linear equation: \(5(2x - 3) - 3(x + 4) = 4(x + 2) + 7\)
A \(x = 6\)
B \(x = 11\)
C \(x = 14\)
D \(x = 18\)
5 TSIA2 Skill: Multiplying Binomials
1 Point
Which of the following polynomials is equivalent to the expanded product of the two binomials: \((3x - 4)(2x + 5)\)
A \(6x^2 - 20\)
B \(6x^2 - 7x - 20\)
C \(6x^2 + 23x - 20\)
D \(6x^2 + 7x - 20\)
6 TSIA2 Skill: Factoring Trinomials (\(a=1\))
1 Point
Which of the following expressions is a factor of the quadratic trinomial: \(x^2 + 5x - 24\)
A \(x + 3\)
B \(x - 3\)
C \(x - 8\)
D \(x + 12\)
7 TSIA2 Skill: Solving Radical Equations
1 Point
What is the real solution to the radical equation: \(\sqrt{3x + 4} - 2 = 3\)
A \(x = 1\)
B \(x = 4\)
C \(x = 7\)
D \(x = 9\)
TSIA2 Mathematics Diagnostic Form A-10 Page 2 of 4 • Continue to Domain 3 Algebra & Functions: Items 4–7
TSIA2 Mathematics Diagnostic
Domain 3: Geometry & Statistics (Items 8–10)
Target Time: ~10 minutes
Focus areas: Geometric modeling & composite figures, basic & complementary probability, and data analysis with conditional probability.
8 TSIA2 Skill: Pythagorean Theorem & Composite Figure Area
1 Point
A park pavilion is constructed in the shape of a composite figure consisting of a rectangle and an adjoining right triangle. The rectangle has a length of 20 feet and a width of 12 feet. The adjoining right triangle shares the 12-foot side as one of its perpendicular legs and has a hypotenuse measuring 13 feet. What is the total area of the pavilion composite figure, in square feet?
A 270 sq ft
B 288 sq ft
C 300 sq ft
D 318 sq ft
9 TSIA2 Skill: Complementary Probability & Sample Spaces
1 Point
A bag contains 6 red marbles, 10 blue marbles, 5 green marbles, and 9 yellow marbles. If one marble is randomly selected from the bag, what is the probability that the marble selected is NOT red?
A \(\frac{1}{5}\)
B \(\frac{4}{5}\)
C \(\frac{1}{4}\)
D \(\frac{2}{3}\)
10 TSIA2 Skill: Data Analysis & Conditional Probability
1 Point
A college academic center tracked 120 students enrolled in introductory statistics. The two-way frequency table below classifies the students by study group participation and course completion outcome:
Group Category
Passed Course
Did Not Pass
Total
Participated in Study Group
68
12
80
Did Not Participate
22
18
40
Total
90
30
120
If one student is selected at random from the 120 students, given that the student participated in a study group, what is the probability that the student passed the course?
A \(\frac{17}{30}\)
B \(\frac{34}{45}\)
C \(\frac{17}{20}\)
D \(\frac{2}{3}\)
Diagnostic Items Complete: Turn to Page 4 to score your exam and determine your review priority plan.
Raw Score: ___ / 10
TSIA2 Mathematics Diagnostic Form A-10 Page 3 of 4 • Scoring Guide Next Geometry & Statistics: Items 8–10
Evaluation Guide Diagnostic Scoring & Remediation
TSIA2 Diagnostic Scoring Guide & Review Priorities
Readiness Benchmark TSIA2 CRC Target: 950+
Quantitative Reasoning Items 1–3
Score: ___ / 3 Goal: 3/3
Algebra & Functions Items 4–7
Score: ___ / 4 Goal: ≥ 3/4
Geometry & Statistics Items 8–10
Score: ___ / 3 Goal: ≥ 2/3
Item Diagnostic Key & Sub-Skill Alignment
Compare your choices against the verified solution key below
#
Key
TSIA2 Skill Strand
Target Concept Tested
Common Diagnostic Error to Remedy
1
C
Direct Proportions
Setting up proportion \(\frac{360}{15} = \frac{x}{50} \Rightarrow x = 1,200\) (rate: 24/min)
Inverting proportion terms or multiplying time by total units incorrectly
2
B
Percent Applications
Successive percent change (\(480 \times 1.35 \times 0.80\))
Subtracting percents directly (\(35\% - 20\% = 15\%\))
3
A
Applied Travel Rates
Harmonic round-trip average: \(\frac{240\text{ mi}}{5\text{ hrs}} = 48\)
Taking simple arithmetic average of speeds (\(\frac{60+40}{2}=50\))
4
C
Solving for x
Distributing & linear isolation (\(7x - 27 = 4x + 15 \Rightarrow x=14\))
Sign error when distributing negative coefficient \(-3(x + 4)\)
5
D
Multiplying Binomials
FOIL expansion: \((3x-4)(2x+5) = 6x^2 + 7x - 20\)
Omitting inner/outer middle terms or sign errors on \((-4)(5)\)
6
B
Factoring (\(a=1\))
Factor \(x^2+5x-24 = (x+8)(x-3)\); select factor \((x-3)\)
Selecting sign-inverted distractor \(x + 3\) or \(x - 8\) instead of valid factor
7
C
Radical Equations
Isolate & square: \(\sqrt{3x+4}=5 \Rightarrow 3x+4=25 \Rightarrow x=7\)
Squaring without isolating radical first or arithmetic slip subtracting constant
8
A
Composite Figure Area
Missing leg \(a=\sqrt{13^2-12^2}=5\); Area \(= (20 \times 12) + \frac{1}{2}(5 \times 12) = 270\)
Omitting \(\frac{1}{2}\) on triangle (\(300\)) or multiplying leg by hypotenuse (\(318\))
9
B
Complementary Probability
Total = \(30\); \(P(\text{not red}) = \frac{10+5+9}{30} = \frac{24}{30} = \frac{4}{5}\)
Finding \(P(\text{red}) = \frac{1}{5}\) instead of complement or computing odds ratio (\(\frac{6}{24}\))
10
C
Conditional Probability
Restricted condition row total: \(P = \frac{68}{80} = \frac{17}{20}\)
Using entire grand total (\(120\)) or column total (\(90\)) as denominator
Targeted Review Priorities by Domain
If You Missed Items 1, 2, or 3
Prioritize direct proportional models and multi-step financial arithmetic.
Set up direct proportions: \(\frac{a}{b} = \frac{c}{d}\).
Master percent factors: \(P \times (1 \pm r)\).
Use \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) for travel rates.
If You Missed Items 4, 5, 6, or 7
Prioritize algebraic operations , binomial products, and radical isolation.
Expand & isolate \(x\) across parentheses.
Drill FOIL expansion on binomials.
Factor trinomials \(x^2+bx+c\) & isolate radicals before squaring.
If You Missed Items 8, 9, or 10
Prioritize composite figures , complementary probability, and two-way tables.
Use \(a^2 + b^2 = c^2\) for composite shape dimensions.
Apply complement rule: \(P(\text{not } A) = 1 - P(A)\).
Identify given condition in 2-way tables.
Action Plan: If overall score is ≤ 7/10, review flagged target concepts above before sitting for the TSIA2 College Placement Exam.
Target CRC: 950+
TSIA2 Mathematics Diagnostic Form A-10 Page 4 of 4 • Diagnostic Scoring Guide Complete Texas Success Initiative Assessment 2.0
TSIA2 Diagnostic Answer Key Guide Teacher & Student Guide TSIA2 Mathematics
Diagnostic Answer Key & Solutions Guide
Full Worked Solutions • Distractor Misconceptions • Instructional Remediation
Form A-10 Key
Verified Solutions
10 Diagnostic Items
Quick Master Key Matrix Score benchmark: 7/10 for near-readiness, 9/10 for college placement
Q1C
Q2B
Q3A
Q4C
Q5D
Q6B
Q7C
Q8A
Q9B
Q10C
Domain 1: Quantitative Reasoning Solutions (Items 1–3)
1 Direct Proportions & Unit Rates Correct Answer: C (1,200 brackets)
360 in 15 min → ? in 50 min
Step-by-Step Solution: Set up a direct proportion of brackets stamped to elapsed time: \(\frac{360\text{ brackets}}{15\text{ minutes}} = \frac{x\text{ brackets}}{50\text{ minutes}}\). First find the constant unit rate: \(\frac{360}{15} = 24\text{ brackets per minute}\). Multiply by the target duration: \(x = 24 \times 50 = 1,200\text{ brackets}\). Alternatively, cross-multiply: \(15x = 360 \times 50 = 18,000 \Rightarrow x = 1,200\).
Distractor Analysis: A (720): Calculated \(360 \times 2\) or evaluated for 30 minutes instead of 50. B (900): Arithmetic scaling error. D (1,800): Multiplied 360 by 5 without dividing by 15.
2 Percent Applications & Financial Math Correct Answer: B ($518.40)
$480 markup 35% & discount 20%
Step-by-Step Solution: Successive percent changes apply sequentially, not additively. 1) Compute marked-up price: \(\text{Retail} = \$480 \times (1 + 0.35) = 480 \times 1.35 = \$648.00\). 2) Apply promotional 20% discount to retail: \(\text{Sale Price} = \$648.00 \times (1 - 0.20) = 648 \times 0.80 = \$518.40\).
Distractor Analysis: C ($552.00): Classic error of subtracting percentages directly (\(35\% - 20\% = 15\%\) net increase, so \(480 \times 1.15 = 552\)). D ($648.00): Omitted promotional discount step. A ($408.00): Applied discount before markup or inverted base.
3 Applied Travel Rates & Round-Trip Averages Correct Answer: A (48 mph)
120 mi @ 60 mph & 120 mi @ 40 mph
Step-by-Step Solution: Average speed requires \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\). 1) Outbound time: \(\frac{120\text{ mi}}{60\text{ mph}} = 2\text{ hours}\). 2) Return trip time: \(\frac{120\text{ mi}}{40\text{ mph}} = 3\text{ hours}\). 3) Total distance = \(120 + 120 = 240\text{ miles}\); Total time = \(2 + 3 = 5\text{ hours}\). 4) \(\text{Average Speed} = \frac{240\text{ mi}}{5\text{ hours}} = 48\text{ mph}\).
Distractor Analysis: B (50 mph): Fatal average trap: taking the simple arithmetic mean of the two speeds (\(\frac{60 + 40}{2} = 50\)). Because more time is spent at 40 mph (3 hrs) than at 60 mph (2 hrs), the true average must weight toward 40 mph.
TSIA2 Diagnostic Answer Key Guide • Form A-10 Page 1 of 3 • Domain 2 Solutions Next Quantitative Reasoning: Items 1–3
TSIA2 Mathematics Diagnostic Solutions
Domain 2: Algebraic Reasoning & Functions Solutions (Items 4–7)
Items 4–7 Worked Steps
4 Solving for x in Multi-Step Equations Correct Answer: C (\(x = 14\))
5(2x-3) - 3(x+4) = 4(x+2) + 7
Step-by-Step Solution: 1) Distribute parentheses on both sides: \(10x - 15 - 3x - 12 = 4x + 8 + 7\). 2) Combine like terms on both sides: \(7x - 27 = 4x + 15\). 3) Subtract \(4x\) from both sides: \(3x - 27 = 15\). 4) Add 27 to both sides: \(3x = 42 \Rightarrow x = 14\).
Distractor Analysis: A (\(x=6\)): Sign error distributing \(-3(x+4)\) as \(-3x + 12\), giving \(7x - 3 = 4x + 15 \Rightarrow 3x = 18 \Rightarrow x=6\). B (\(x=11\)): Inversion adding 27 to right side. D (\(x=18\)): Dropped \(-15\) constant.
5 Multiplying Binomials (Polynomial Expansion) Correct Answer: D (\(6x^2 + 7x - 20\))
\((3x - 4)(2x + 5)\)
Step-by-Step Solution: Apply the FOIL (First, Outer, Inner, Last) method: 1) First: \((3x)(2x) = 6x^2\). 2) Outer: \((3x)(5) = 15x\). 3) Inner: \((-4)(2x) = -8x\). 4) Last: \((-4)(5) = -20\). Combine like middle terms: \(15x - 8x = +7x\). Result: \(6x^2 + 7x - 20\).
Distractor Analysis: A (\(6x^2 - 20\)): Completely omitted outer and inner middle products. B (\(6x^2 - 7x - 20\)): Incorrect sign subtraction (\(8 - 15 = -7\)). C (\(6x^2 + 23x - 20\)): Added coefficients without accounting for negative sign (\(15 + 8 = 23\)).
6 Factoring Trinomials with \(a = 1\) (Finding a Factor) Correct Answer: B (\(x - 3\))
Factor \(x^2 + 5x - 24\)
Step-by-Step Solution: For quadratic trinomial \(x^2 + bx + c = x^2 + 5x - 24\) where \(a = 1\): 1) Identify two integers whose product is \(c = -24\) and whose sum is \(b = +5\). 2) Test integer pairs: \((+8)(-3) = -24\) and \(+8 + (-3) = +5\). 3) Express as the product of two linear binomials: \((x + 8)(x - 3)\). The two linear factors are \((x + 8)\) and \((x - 3)\). Among the answer options, \((x - 3)\) is the correct factor.
Distractor Analysis: A (\(x + 3\)): Inverted the negative factor sign. C (\(x - 8\)): Inverted the positive factor sign. D (\(x + 12\)): Selected incorrect factor pair of 24 (\(12 \times 2\)).
7 Solving Radical Equations Equal to a Constant Correct Answer: C (\(x = 7\))
\(\sqrt{3x + 4} - 2 = 3\)
Step-by-Step Solution: 1) Isolate the radical term by adding 2 to both sides: \(\sqrt{3x + 4} = 3 + 2 = 5\). 2) Square both sides to eliminate the radical: \((\sqrt{3x + 4})^2 = 5^2 \Rightarrow 3x + 4 = 25\). 3) Subtract 4 from both sides: \(3x = 21\). 4) Divide by 3: \(x = \frac{21}{3} = 7\). Check solution: \(\sqrt{3(7) + 4} - 2 = \sqrt{21 + 4} - 2 = \sqrt{25} - 2 = 5 - 2 = 3\). Verified!
Distractor Analysis: A (\(x=1\)): Subtracted 2 instead of adding, solving \(\sqrt{3x+4}=1 \Rightarrow 3x= -3\). B (\(x=4\)): Squared before isolating radical (\(3x + 4 - 4 = 9 \Rightarrow 3x = 9\)). D (\(x=9\)): Arithmetic slip dividing by coefficient.
TSIA2 Diagnostic Answer Key Guide • Form A-10 Page 2 of 3 • Domain 3 Solutions Next Algebra & Functions: Items 4–7
TSIA2 Mathematics Diagnostic Solutions
Domain 3: Geometry & Statistics Solutions (Items 8–10)
Items 8–10 Worked Steps
8 Pythagorean Theorem & Composite Figure Area Correct Answer: A (270 sq ft)
Rectangle \(20 \times 12\) + Triangle leg 12, hyp 13
Step-by-Step Solution: 1) Area of rectangle: \(\text{Area}_{\text{rect}} = \text{length} \times \text{width} = 20 \times 12 = 240\text{ sq ft}\). 2) Find missing leg of right triangle via Pythagorean theorem: \(a^2 + 12^2 = 13^2 \Rightarrow a^2 + 144 = 169 \Rightarrow a^2 = 25 \Rightarrow a = 5\text{ ft}\). 3) Area of attached triangle: \(\text{Area}_{\text{tri}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 12 = 30\text{ sq ft}\). 4) Total composite area: \(240 + 30 = 270\text{ sq ft}\).
Distractor Analysis: C (300): Forgot \(\frac{1}{2}\) factor on triangle (\(240 + 60 = 300\)). D (318): Multiplied leg by hypotenuse (\(240 + \frac{1}{2}(12)(13) = 240 + 78 = 318\)). B (288): Arithmetic computation slip.
9 Complementary Probability & Sample Spaces Correct Answer: B (\(\frac{4}{5}\))
6 Red, 10 Blue, 5 Green, 9 Yellow
Step-by-Step Solution: 1) Find total sample space: \(\text{Total marbles} = 6 + 10 + 5 + 9 = 30\). 2) Count favorable outcomes (marbles that are NOT red): \(10\text{ (blue)} + 5\text{ (green)} + 9\text{ (yellow)} = 24\) (or \(30 - 6 = 24\)). 3) Calculate probability: \(P(\text{not red}) = \frac{24}{30}\). Reduce fraction by dividing numerator and denominator by 6: \(\frac{24 \div 6}{30 \div 6} = \frac{4}{5}\). Alternatively, use complement rule: \(P(\text{not red}) = 1 - P(\text{red}) = 1 - \frac{6}{30} = 1 - \frac{1}{5} = \frac{4}{5}\).
Distractor Analysis: A (\(\frac{1}{5}\)): Calculated probability of selecting red (\(\frac{6}{30}\)) rather than NOT red. C (\(\frac{1}{4}\)): Computed odds ratio of red to non-red (\(\frac{6}{24}\)). D (\(\frac{2}{3}\)): Miscounted non-red total as 20.
10 Two-Way Frequency Tables & Conditional Probability Correct Answer: C (\(\frac{17}{20}\))
P(Passed | Study Group)
Step-by-Step Solution: The condition "given that the student participated in a study group" restricts the denominator exclusively to the "Participated in Study Group" row total. 1) Restricted subpopulation (Study Group row total): \(68 + 12 = 80\). 2) Favorable outcome within restricted group (Passed course and in study group): \(68\). 3) Conditional probability: \(P(\text{Passed} \mid \text{Study Group}) = \frac{68}{80}\). Divide numerator and denominator by 4: \(\frac{68 \div 4}{80 \div 4} = \frac{17}{20}\) (or 0.85).
Distractor Analysis: A (\(\frac{17}{30}\)): Used entire sample size of 120 as denominator (\(\frac{68}{120}\)), which is joint probability \(P(\text{Passed and Group})\). B (\(\frac{34}{45}\)): Inverted condition using "Passed Course" column total of 90 (\(\frac{68}{90}\)). D (\(\frac{2}{3}\)): Marginal probability of study group (\(\frac{80}{120}\)).
TSIA2 Readiness Scoring Matrix & Instructional Intervention Plan CRC Benchmark Threshold: 950+
9–10 Correct (90–100%) College Ready Classification
Demonstrates strong quantitative fluency across all strands. Eligible for credit-bearing college algebra without corequisite support.
7–8 Correct (70–80%) Near-Readiness (Diagnostic Level 5–6)
Solid foundational knowledge. Target specific missed sub-skills (e.g. radical isolation or travel averages) for rapid remediation before exam.
0–6 Correct (≤ 60%) Intensive Intervention Required
Core weaknesses in algebraic manipulation or quantitative reasoning. Recommend targeted corequisite support and structured practice sets.
TSIA2 Diagnostic Answer Key Guide • Form A-10 Page 3 of 3 • Diagnostic Guide Complete Texas Success Initiative Assessment 2.0
TSIA2 Practice Form B Assessment TSIA2 Math Diagnostic Practice Exam
Mathematics Diagnostic Assessment
Texas Success Initiative Assessment 2.0 • Form B Parallel Benchmark
Test Booklet
Form B-10
Standard Calculator Allowed
Student Name:
Date:
Instructor / Section:
TSIA2 Mathematics Reference Formulas For scratch work, use available margins.
Area of Triangle \(A = \frac{1}{2}bh\)
Pythagorean Thm \(a^2 + b^2 = c^2\)
Complement Prob \(P(\text{not } E) = 1 - P(E)\)
Quadratic Form \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Domain 1: Quantitative Reasoning (Items 1–3)
Direct Proportions, Percentages, and Applied Problem Solving
1 TSIA2 Skill: Direct Proportions & Unit Rates
1 Point
An automated beverage packaging line seals 450 glass bottles in 18 minutes while operating at a constant rate. At this same rate, how many glass bottles will the line seal in 40 minutes?
A 850 bottles
B 900 bottles
C 1,000 bottles
D 1,250 bottles
2 TSIA2 Skill: Percent Applications & Financial Math
1 Point
A commercial supplier purchases a professional restaurant blender at a wholesale cost of \(\$350\). The supplier marks up the wholesale cost by \(40\%\). During a restaurant association convention, the supplier then discounts the marked-up price by \(15\%\). What is the final promotional convention price of the blender?
A $322.00
B $416.50
C $437.50
D $490.00
3 TSIA2 Skill: Applied Problem Solving & Rates
1 Point
A field technician drives 90 miles outbound from Dallas to Waco at an average speed of 45 miles per hour. Returning along the identical 90-mile route during evening traffic, the technician travels at an average speed of 30 miles per hour. What is the technician’s average speed, in miles per hour, for the entire 180-mile round trip?
A 36 mph
B 37.5 mph
C 38.5 mph
D 40 mph
TSIA2 Mathematics Diagnostic Form B-10 Page 1 of 4 • Continue to Domain 2 Quantitative Reasoning: Items 1–3
TSIA2 Mathematics Diagnostic
Domain 2: Algebraic Reasoning & Functions (Items 4–7)
Target Time: ~15 minutes
Focus areas: Solving for \(x\) in multi-step equations, multiplying binomials, factoring trinomials (\(a=1\)), and solving radical equations equal to a constant.
4 TSIA2 Skill: Solving for x (Linear Equations)
1 Point
What real value of \(x\) satisfies the multi-step linear equation: \(4(3x - 2) - 2(x + 5) = 3(2x + 1) + 11\)
A \(x = 3\)
B \(x = 6\)
C \(x = 8\)
D \(x = 12\)
5 TSIA2 Skill: Multiplying Binomials
1 Point
Which of the following polynomials is equivalent to the expanded product of the two binomials: \((4x - 3)(3x + 2)\)
A \(12x^2 - 6\)
B \(12x^2 + x - 6\)
C \(12x^2 - 17x - 6\)
D \(12x^2 - x - 6\)
6 TSIA2 Skill: Factoring Trinomials (\(a=1\))
1 Point
Which of the following expressions is a factor of the quadratic trinomial: \(x^2 + 2x - 35\)
A \(x + 5\)
B \(x - 5\)
C \(x - 7\)
D \(x + 10\)
7 TSIA2 Skill: Solving Radical Equations
1 Point
What is the real solution to the radical equation: \(\sqrt{2x + 5} - 1 = 4\)
A \(x = 2\)
B \(x = 6\)
C \(x = 10\)
D \(x = 15\)
TSIA2 Mathematics Diagnostic Form B-10 Page 2 of 4 • Continue to Domain 3 Algebra & Functions: Items 4–7
TSIA2 Mathematics Diagnostic
Domain 3: Geometry & Statistics (Items 8–10)
Target Time: ~10 minutes
Focus areas: Geometric modeling & composite figures, basic & complementary probability, and data analysis with conditional probability.
8 TSIA2 Skill: Pythagorean Theorem & Composite Figure Area
1 Point
An outdoor recreation patio is constructed in the shape of a composite figure consisting of a rectangle and an adjoining right triangle. The rectangle has a length of 18 feet and a width of 8 feet. The adjoining right triangle shares the 8-foot side as one of its perpendicular legs and has a hypotenuse measuring 10 feet. What is the total area of the patio composite figure, in square feet?
A 168 sq ft
B 176 sq ft
C 184 sq ft
D 192 sq ft
9 TSIA2 Skill: Complementary Probability & Sample Spaces
1 Point
A container holds 8 red tokens, 12 blue tokens, 7 green tokens, and 13 yellow tokens. If one token is randomly selected from the container, what is the probability that the token selected is NOT red?
A \(\frac{1}{5}\)
B \(\frac{4}{5}\)
C \(\frac{1}{4}\)
D \(\frac{3}{4}\)
10 TSIA2 Skill: Data Analysis & Conditional Probability
1 Point
An engineering department tracked 150 students enrolled in introductory calculus. The two-way frequency table below classifies the students by tutoring attendance and midterm exam outcome:
Tutoring Category
Passed Exam
Did Not Pass
Total
Attended Tutoring
72
18
90
Did Not Attend
28
32
60
Total
100
50
150
If one student is selected at random from the 150 students, given that the student attended tutoring, what is the probability that the student passed the exam?
A \(\frac{12}{25}\)
B \(\frac{18}{25}\)
C \(\frac{4}{5}\)
D \(\frac{3}{5}\)
Form B Diagnostic Complete: Turn to Page 4 to evaluate performance and compare readiness metrics with Form A.
Raw Score: ___ / 10
TSIA2 Mathematics Diagnostic Form B-10 Page 3 of 4 • Scoring Guide Next Geometry & Statistics: Items 8–10
Evaluation Guide Form B Diagnostic Scoring & Remediation
TSIA2 Form B Scoring Guide & Review Priorities
Readiness Benchmark TSIA2 CRC Target: 950+
Quantitative Reasoning Items 1–3
Score: ___ / 3 Goal: 3/3
Algebra & Functions Items 4–7
Score: ___ / 4 Goal: ≥ 3/4
Geometry & Statistics Items 8–10
Score: ___ / 3 Goal: ≥ 2/3
Form B Item Diagnostic Key & Sub-Skill Alignment
Compare your choices against the verified solution key below
#
Key
TSIA2 Skill Strand
Target Concept Tested
Common Diagnostic Error to Remedy
1
C
Direct Proportions
\(\frac{450}{18} = 25\text{/min} \Rightarrow 25 \times 40 = 1,000\) bottles
Inverted proportion or arithmetic rate division slip
2
B
Percent Applications
Successive multipliers: \(350 \times 1.40 \times 0.85 = \$416.50\)
Subtracting percentages (\(40\% - 15\% = 25\%\)) to get \(\$437.50\)
3
A
Applied Travel Rates
Total distance / total time: \(\frac{180\text{ mi}}{2 + 3\text{ hrs}} = 36\text{ mph}\)
Taking simple arithmetic average of speeds (\(\frac{45+30}{2} = 37.5\))
4
C
Solving for x
Expand & combine: \(10x - 18 = 6x + 14 \Rightarrow 4x = 32 \Rightarrow x = 8\)
Sign error when distributing \(-2(x+5)\) as \(-2x + 10\)
5
D
Multiplying Binomials
FOIL: \((4x-3)(3x+2) = 12x^2 + 8x - 9x - 6 = 12x^2 - x - 6\)
Omitting inner/outer terms or sign subtraction mistake
6
B
Factoring (\(a=1\))
Factor \(x^2+2x-35 = (x+7)(x-5)\); select factor \((x-5)\)
Selecting inverted constant \(x + 5\) or \(x - 7\) instead of valid factor
7
C
Radical Equations
Isolate & square: \(\sqrt{2x+5}=5 \Rightarrow 2x+5=25 \Rightarrow x=10\)
Squaring before isolating radical or arithmetic slip dividing by 2
8
A
Composite Figure Area
Leg \(b=\sqrt{10^2-8^2}=6\); Area \(= (18 \times 8) + \frac{1}{2}(6 \times 8) = 168\)
Omitting \(\frac{1}{2}\) on triangle (\(192\)) or multiplying leg by hypotenuse
9
B
Complementary Probability
Total = \(40\); \(P(\text{not red}) = \frac{12+7+13}{40} = \frac{32}{40} = \frac{4}{5}\)
Finding \(P(\text{red}) = \frac{1}{5}\) instead of complement or computing odds ratio
10
C
Conditional Probability
Restricted condition row total: \(P = \frac{72}{90} = \frac{4}{5}\)
Using total 150 as denominator (\(\frac{12}{25}\)) or column total (\(\frac{18}{25}\))
Targeted Review Priorities by Domain
If You Missed Items 1, 2, or 3
Prioritize direct proportional models and multi-step financial arithmetic.
Set up direct proportions: \(\frac{a}{b} = \frac{c}{d}\).
Master percent factors: \(P \times (1 \pm r)\).
Use \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) for travel rates.
If You Missed Items 4, 5, 6, or 7
Prioritize algebraic operations , binomial products, and radical isolation.
Expand & isolate \(x\) across parentheses.
Drill FOIL expansion on binomials.
Factor trinomials \(x^2+bx+c\) & isolate radicals before squaring.
If You Missed Items 8, 9, or 10
Prioritize composite figures , complementary probability, and two-way tables.
Use \(a^2 + b^2 = c^2\) for composite shape dimensions.
Apply complement rule: \(P(\text{not } A) = 1 - P(A)\).
Identify given condition in 2-way tables.
Growth Tracking: Compare your Form B raw score against Form A to measure readiness gains before testing.
Target CRC: 950+
TSIA2 Mathematics Diagnostic Form B-10 Page 4 of 4 • Diagnostic Scoring Guide Complete Texas Success Initiative Assessment 2.0
