TSIA2 Math Practice Test
TSIA2 Math Practice
Diagnostic Assessment • Version B
Name:
Date:
Instructions
Solve each problem and select the best answer from the choices provided. Show your work in the space provided. This practice test contains 20 questions covering Quantitative Reasoning, Algebraic Reasoning, Geometry, and Statistics.
1
A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker uses 10.5 cups of flour, how many cups of sugar are needed?
A) 6.5 cups
B) 7.0 cups
C) 7.5 cups
D) 8.0 cups
2
The price of a laptop was originally $850. During a clearance sale, the price was reduced by 20%. Two weeks later, the sale price was reduced by an additional 10%. What is the final price of the laptop?
A) $595
B) $612
C) $637
D) $680
3
A car travels 330 miles on 15 gallons of gas. At this same rate, how many gallons of gas are needed to travel 550 miles?
A) 20 gallons
B) 22 gallons
C) 25 gallons
D) 30 gallons
4
A piece of lumber is \(12 \frac{1}{2}\) feet long. If a carpenter cuts off pieces that are \(1 \frac{3}{4}\) feet long, how many full pieces can be cut?
A) 6
B) 7
C) 8
D) 9
5
A printer can print 45 pages in 3 minutes. At this same rate, how many seconds will it take to print 12 pages?
A) 36 seconds
B) 48 seconds
C) 54 seconds
D) 72 seconds
6
What is the distance between \(-8.5\) and \(4.2\) on a number line?
A) 4.3
B) 12.3
C) 12.7
D) 13.1
7
Solve for \(x\): \(4(2x - 3) = 2(x + 9)\)
A) \(x = 3\)
B) \(x = 4\)
C) \(x = 5\)
D) \(x = 6\)
8
What is the value of \(y\) in the solution to the system of equations?
\(3x + 2y = 16\)
\(x - y = 2\)
A) \(y = 2\)
B) \(y = 4\)
C) \(y = -2\)
D) \(y = 0\)
9
Which inequality represents all possible values of \(x\) for \(5 - 2x \geq 13\)?
A) \(x \geq -4\)
B) \(x \leq -4\)
C) \(x \geq 4\)
D) \(x \leq 4\)
10
Which of the following expressions is equivalent to \((3x^2y^4)^2(2xy^2)\)?
A) \(6x^5y^{10}\)
B) \(12x^5y^{10}\)
C) \(18x^5y^{10}\)
D) \(18x^4y^8\)
11
If \(f(x) = -x^2 + 4x - 7\), what is the value of \(f(-2)\)?
A) -19
B) -11
C) -3
D) 5
12
Simplify the expression: \(\frac{x^2 - 16}{x^2 + 8x + 16}\)
A) \(\frac{x-4}{x+4}\)
B) \(\frac{x+4}{x-4}\)
C) \(x-4\)
D) \(1\)
13
Solve for \(k\): \(\sqrt{3k + 1} - 4 = 1\)
A) \(k = 5\)
B) \(k = 8\)
C) \(k = 10\)
D) \(k = 24\)
14
A 13-foot ladder is leaning against a vertical wall. If the base of the ladder is 5 feet from the wall, how high up the wall does the ladder reach?
A) 8 feet
B) 10 feet
C) 12 feet
D) 15 feet
15
What is the area of a circle with a diameter of 10 centimeters? (Use \(\pi \approx 3.14\))
A) \(31.4 \text{ cm}^2\)
B) \(62.8 \text{ cm}^2\)
C) \(78.5 \text{ cm}^2\)
D) \(314 \text{ cm}^2\)
16
A rectangular prism has a length of 6 inches, a width of 4 inches, and a height of 10 inches. What is its volume?
A) \(240 \text{ in}^3\)
B) \(120 \text{ in}^3\)
C) \(100 \text{ in}^3\)
D) \(48 \text{ in}^3\)
17
A set of numbers consists of {12, 15, 15, 18, 20, 22, 31}. What is the median of this set?
A) 15
B) 18
C) 19
D) 20
18
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue?
A) \(3/10\)
B) \(1/2\)
C) \(7/10\)
D) \(4/5\)
19
A class of 20 students took a math quiz. The mean score for the first 15 students was 80, and the mean score for the remaining 5 students was 92. What was the mean score for the entire class?
A) 82
B) 83
C) 85
D) 86
20
A fair coin is flipped twice. What is the probability of getting "Heads" on the first flip and "Tails" on the second flip?
A) \(1/4\)
B) \(1/2\)
C) \(3/4\)
D) \(1\)
Quant
1 - 6
Algebra
7 - 13
Geometry
14 - 16
Stats
17 - 20
TSIA2 Math Answer Key
Answer Key
TSIA2 Math Practice • Version B (Updated)
Teacher Resource
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Detailed Solutions
1. (B) 7.0 Set up a proportion: \(\frac{3}{2} = \frac{10.5}{x}\). \(3x = 21 \rightarrow x = 7\).
2. (B) $612 \(850 \times 0.80 = 680\). Then \(680 \times 0.90 = 612\).
3. (C) 25 gal \(\frac{330}{15} = 22\) miles per gallon. \(\frac{550}{22} = 25\).
4. (B) 7 \(\frac{25/2}{7/4} = \frac{25}{2} \times \frac{4}{7} = \frac{50}{7} \approx 7.14\). Full pieces = 7.
5. (B) 48 sec Rate is 15 pages/min. 12 pages takes \(12/15 = 0.8\) mins. \(0.8 \times 60 = 48\).
6. (C) 12.7 \(|4.2 - (-8.5)| = |4.2 + 8.5| = 12.7\).
7. (C) \(x = 5\) \(8x - 12 = 2x + 18 \rightarrow 6x = 30 \rightarrow x = 5\).
8. (A) \(y = 2\) Substitute \(x = y + 2\): \(3(y+2) + 2y = 16 \rightarrow 5y + 6 = 16 \rightarrow 5y = 10 \rightarrow y = 2\).
9. (B) \(x \leq -4\) \(-2x \geq 8 \rightarrow x \leq -4\).
10. (C) \(18x^5y^{10}\) \((3x^2y^4)^2(2xy^2) = (9x^4y^8)(2xy^2) = 18x^5y^{10}\).
11. (A) -19 \(-(-2)^2 + 4(-2) - 7 = -4 - 8 - 7 = -19\).
12. (A) \(\frac{x-4}{x+4}\) \(\frac{(x-4)(x+4)}{(x+4)(x+4)} = \frac{x-4}{x+4}\).
13. (B) \(k = 8\) \(\sqrt{3k+1} = 5 \rightarrow 3k+1 = 25 \rightarrow 3k = 24 \rightarrow k = 8\).
14. (C) 12 ft \(5^2 + h^2 = 13^2 \rightarrow 25 + h^2 = 169 \rightarrow h = 12\).
15. (C) 78.5 \(r = 5\). \(A = \pi(5)^2 = 25 \times 3.14 = 78.5\).
16. (A) 240 \(V = 6 \times 4 \times 10 = 240\).
17. (B) 18 {12, 15, 15, **18**, 20, 22, 31}.
18. (C) 7/10 Total = 10. Blue = 3. Not blue = 7. \(7/10\).
19. (B) 83 Sum for 15: \(15 \times 80 = 1200\). Sum for 5: \(5 \times 92 = 460\). Total: \(1660 / 20 = 83\).
20. (A) 1/4 \(1/2 \times 1/2 = 1/4\).
Diagnostic Score Interpretation
