TSIA2 Practice Test Document TSIA2 Math
Comprehensive Practice Assessment
Student Identity
Name: ________________________
Date: _________
Test Instructions
This assessment covers all four core domains. For each question, choose the best answer choice and show your work in the provided workspace.
Calculator Permitted for all items
Part 1: Quantitative Reasoning
1
A construction crew can pave 2.5 miles of road in 8 hours. At this rate, how many miles can they pave in a 40-hour work week?
A 10 miles
B 12.5 miles
C 15.5 miles
D 20 miles
Show your work here
TSIA2 Practice • Page 2
2
If a store marks up the wholesale price of a jacket by 45%, and the retail price is $87.00, what was the approximate wholesale price?
A $39.15
B $47.85
C $60.00
D $126.15
Show your work here
Part 2: Algebraic Reasoning
3
Solve for \( x \): \( 3(2x - 4) + 5 = 4x - 1 \)
A \( x = 3 \)
B \( x = 4 \)
C \( x = 6 \)
D \( x = -3 \)
Show your work here
TSIA2 Practice • Page 3
4
Equivalent expression for: \( (2x^2 - 3x + 4) - (x^2 + 5x - 2) \)?
A \( x^2 + 2x + 2 \)
B \( x^2 - 8x + 6 \)
C \( 3x^2 + 2x + 6 \)
D \( x^2 - 8x + 2 \)
Show your work here
5
Solutions for: \( x^2 - 5x - 6 = 0 \)?
A \( x = -1, x = 6 \)
B \( x = 1, x = -6 \)
C \( x = 2, x = 3 \)
D \( x = -2, x = -3 \)
Show your work here
TSIA2 Practice • Page 4
6
Solve the system of equations:
\( 2x + 3y = 12 \)
A \((2, 1)\)
B \((3, 2)\)
C \((4, 3)\)
D \((0, 4)\)
Show your work here
Part 3: Geometric & Statistical
7
A garden's length is 3ft longer than twice its width. If perimeter is 66ft, width?
A 10 feet
B 12 feet
C 23 feet
D 30 feet
Show your work here
TSIA2 Practice • Page 5
8
Area of circle with diameter 12 inches? (Use \( \pi \approx 3.14 \))
A 37.68 sq in
B 113.04 sq in
C 452.16 sq in
D 18.84 sq in
Show your work here
9
Bag with 4 red, 6 blue, 10 green. Selected at random, probability NOT red?
A 1/5
B 1/4
C 3/4
D 4/5
Show your work here
TSIA2 Practice • Page 6
10
Heights: 62, 65, 70, 72, 72. What is the mean height?
A 68.2 inches
B 70 inches
C 71 inches
D 72 inches
Show your work here
STOP
Do not turn the page until you have finished all questions.
Step-by-Step Solutions
Detailed Answer Guide
1. Answer B (12.5)
Rate = \( 2.5 \text{ miles} / 8 \text{ hours} \). In 40 hours: \( (2.5 / 8) \times 40 \). 40 divided by 8 is 5. So, \( 2.5 \times 5 = 12.5 \).
2. Answer C ($60.00)
Let \( W \) be wholesale. \( W + 0.45W = 87 \Rightarrow 1.45W = 87 \). \( 87 \div 1.45 = 60 \).
3. Answer A (x = 3)
\( 3(2x-4)+5 = 4x-1 \Rightarrow 6x-12+5 = 4x-1 \Rightarrow 6x-7 = 4x-1 \Rightarrow 2x = 6 \Rightarrow x=3 \).
4. Answer B (x² - 8x + 6)
\( 2x^2 - 3x + 4 - x^2 - 5x + 2 \). Combine \( 2x^2 - x^2 = x^2 \); \( -3x - 5x = -8x \); \( 4 + 2 = 6 \).
5. Answer A (-1, 6)
Factor \( x^2 - 5x - 6 \): \( (x-6)(x+1) = 0 \). Setting factors to zero gives \( x = 6 \) and \( x = -1 \).
6. Answer B (3, 2)
From \( x-y=1 \), \( x=y+1 \). Substitute: \( 2(y+1)+3y = 12 \Rightarrow 5y+2=12 \Rightarrow 5y=10 \Rightarrow y=2 \). Then \( x=2+1=3 \).
7. Answer A (10 feet)
\( P = 2(L+W) \). \( L = 2w+3 \). \( 66 = 2(2w+3 + w) = 2(3w+3) = 6w+6 \). \( 6w = 60 \Rightarrow w=10 \).
8. Answer B (113.04)
Radius \( r = 12/2 = 6 \). Area \( A = \pi r^2 = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \).
9. Answer D (4/5)
Total = \( 4+6+10 = 20 \). Not Red = \( 6+10=16 \). Probability = \( 16/20 \). Simplified = \( 4/5 \).
10. Answer A (68.2)
Sum = \( 62+65+70+72+72 = 341 \). Mean = \( 341 \div 5 = 68.2 \).
TSIA2 Solutions Teacher Guide Master Solutions
Detailed Step-by-Step Explanations
TSIA2 Reference
1
Answer: B (12.5 miles)
Calculation Logic:
1. Find the rate in miles per hour: \( 2.5 \text{ miles} \div 8 \text{ hours} = 0.3125 \text{ mph} \).
2. Apply the rate to the target time: \( 0.3125 \text{ mph} \times 40 \text{ hours} \).
3. Alternative proportion method: \( \frac{2.5}{8} = \frac{x}{40} \Rightarrow 8x = 100 \).
Result: \( x = 12.5 \text{ miles} \)
2
Answer: C ($60.00)
Calculation Logic:
1. The retail price is the wholesale price plus 45% of wholesale.
2. Equation: \( W + 0.45W = \$87.00 \) or \( 1.45W = 87 \).
3. Solve for W: \( W = 87 \div 1.45 \).
Result: \( W = \$60.00 \)
3
Answer: A (x = 3)
Algebraic Process:
1. Distribute: \( 6x - 12 + 5 = 4x - 1 \).
2. Simplify: \( 6x - 7 = 4x - 1 \).
3. Move \( 4x \) left and \( -7 \) right: \( 2x = 6 \).
Result: \( x = 3 \)
Solutions Reference • Continued
4
Answer: B (x² - 8x + 6)
Algebraic Process:
1. Rewrite without parentheses, distributing the negative: \( 2x^2 - 3x + 4 - x^2 - 5x + 2 \).
2. Combine \( x^2 \) terms: \( 2x^2 - x^2 = x^2 \).
3. Combine \( x \) terms: \( -3x - 5x = -8x \).
4. Combine constants: \( 4 + 2 = 6 \).
Result: \( x^2 - 8x + 6 \)
5
Answer: A (x = -1, x = 6)
Factoring Process:
1. Find numbers that multiply to \( -6 \) and add to \( -5 \): \( -6 \text{ and } 1 \).
2. Form factors: \( (x - 6)(x + 1) = 0 \).
3. Set each factor to zero: \( x - 6 = 0 \) or \( x + 1 = 0 \).
Result: \( x = 6, x = -1 \)
6
Answer: B (3, 2)
System of Equations:
1. Use substitution from \( x - y = 1 \): \( x = y + 1 \).
2. Substitute into \( 2x + 3y = 12 \): \( 2(y + 1) + 3y = 12 \Rightarrow 5y + 2 = 12 \).
3. Solve for y: \( 5y = 10 \Rightarrow y = 2 \).
4. Solve for x: \( x = 2 + 1 = 3 \).
Result: \((3, 2)\)
Solutions Reference • Final Page
7
Answer: A (10 feet)
Geometric Logic:
1. Define variables: Width = \( w \), Length = \( 2w + 3 \).
2. Perimeter: \( 2(L + W) = 66 \Rightarrow 2(2w + 3 + w) = 66 \).
TSIA2 Mastery Presentation Slides College Readiness
TSIA2 MATH
Mastering the Core Domains for Success
Quantitative
Algebraic
Geometric
Test Specs
Placement Goal
Determines if you are ready for credit-bearing college math.
Untimed Format
Accuracy over speed. Take all the time you need.
Target Scores
Ready Score 950+
Diagnostic Level 1 - 6
Content Scope
The four pillars of the assessment.
Quantitative
Fractions, Decimals, Percents, Ratios, and Proportions.
Algebraic
Linear Equations, Systems, Quadratics, and Factoring.
Geometric
Area, Volume, Pythagorean Theorem, Coordinate Plane.
Statistical
Probability, Mean, Median, Mode, Data Interpretation.
Back-Solving Method
Don't guess—test! If an equation looks difficult, plug in the answer choices starting with B or C.
?
Example: Solve 2x + 5 = 11
Test (3): 2(3) + 5 = 11. It works!
Accuracy First
Common Pitfalls
Diameter Trap
Does the question give Diameter but the formula needs Radius? Remember to divide by 2 first!
Markup Formula
A 45% markup is 1.45 times the Original price. Equation: 1.45 * Original = Retail.
Sign Flipping
When subtracting expressions, flip EVERY sign inside the parenthesis. -(x - 5) becomes -x + 5.
Solutions Guide
Let's walk through the 10 Mastery Questions from your Practice Test document.
Self-Correction Phase
Part 1: Quantitative
Question 1
Paving 2.5 miles in 8 hours. Miles in 40 hours?
• Rate = 2.5 ÷ 8 = 0.3125 mph
• Calculation: 0.3125 * 40 = 12.5
Correct: B (12.5 miles)
Question 2
45% Markup. Retail = $87. Wholesale?
• Wholesale + 45% = 1.45 * Wholesale
• 1.45 * W = 87 → W = 87 / 1.45
Correct: C ($60.00)
Part 2: Algebraic
Question 3
Solve: 3(2x - 4) + 5 = 4x - 1
• 6x - 12 + 5 = 4x - 1
• 6x - 7 = 4x - 1 → 2x = 6
Correct: A (x = 3)
Question 4
Simplify: (2x² - 3x + 4) - (x² + 5x - 2)
