# Full-Length TSI Math Practice Test-Answers and Explanations

Did you take the TSI Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## TSI Mathematical Reasoning Practice Test Answers and Explanations

1- **Choice D is correct**

If \(1.05 < x ≤ 3.04\), then \(x\) cannot be equal to 3.40. Because: \(3.04<3.40\)

2- **Choice B is correct**

\(a=8⇒\) area of triangle is \(=\frac{1}{2} (8×8)=\frac{64}{2}=32\) cm

3- **Choice C is correct**

\(66^\circ + 42^\circ = 108^\circ\)

\(180^\circ – 108^\circ = 72^\circ\)

The value of the third angle is \(72^\circ\).

4-** Choice B is correct**

Simplify:

\(10 – \frac{2}{3} x ≥ 12 ⇒ – \frac{2}{3} x ≥ 2 ⇒ – x ≥ 3 ⇒ x ≤ – 3\)

5- **Choice A is correct**

Factor each trinomial \(x^2 – 2x – 8\) and \(x^2 – 6x + 8\)

\(x^2 – 2x – 8 ⇒ (x – 4)(x + 2) \)

\(x^2 – 6x + 8 ⇒ (x – 2)(x – 4) \)

\((x – 4)\) is a factor of both trinomial.

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6- **Choice B is correct**

\(\frac{1+b}{6b^2}=\frac{1}{b^2} ⇒(b≠0) b^2+b^3=6b^2⇒b^3-5b^2=0⇒b^2 (b-5)=0⇒b-5=0⇒b=5\)

7- **Choice D is correct**

Use FOIL (First, Out, In, Last)

\((x + 7) (x + 5) = x^2 + 5x + 7x + 35 = x^2 + 12x + 35\)

8- **Choice A is correct**

\(\frac{54}{6}=\frac{27}{3}=9, \frac{48}{6}=\frac{24}{3}=8, \frac{36}{6}=\frac{18}{3}=6, \frac{59}{6}=\frac{59}{6} \)

59 is prime number

The answer is 54.

9- **Choice B is correct**

\(x^2 – 64 = 0 ⇒ x^2 = 64 ⇒ x = 8\)

10- **Choice C is correct**

If \(a = 8\) then \(b = \frac{8^2}{4} + 4 ⇒ b = \frac{64}{4} + 4 ⇒b = 16 + 4 = 20\)

11- **Choice D is correct**

tan \((– π/6) = – \frac{\sqrt{3}}{3}\)

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12- **Choice A is correct**

\(\frac{\sqrt{32a^5 b^3 }}{\sqrt{2ab^2}}= \frac{4a^2 b\sqrt{2ab}}{b\sqrt{2a}} = 4a^2\sqrt{b}\)

13- **Choice D is correct**

\(E = 4 + A\)

\(A = S – 3\)

14- **Choice C is correct**

\(\begin{cases}5x + y = 9\\10x-7y= -18\end{cases} ⇒\) Multiplication \((–2)\) in first equation \(⇒ \begin{cases}-10x- 2y = -18\\10x-7y= -18\end{cases}\) Add two equations together \(⇒ –9y = –36 ⇒ y = 4\) then: \(x = 1\)

15- **Choice B is correct**

\((x – h)^2 + (y – k)^2 = r^2\) ⇒ center: (h,k) and radius: r

\((x – 3)^2 + (y + 6)^2 = 12\) ⇒ center: \((3,-6)\) and radius: \(2\sqrt{3}\)

16- **Choice D is correct**

c\((3)=(3)^2+10(3)+30=9+30+30=69 \)

\(4×3=12⇒12-69=-57⇒57,000\) loss

17- **Choice B is correct**

sinB\(=\frac{the length of the side that is opposite that angle}{the length of the longest side of the triangle}=\frac{4}{5}\)

18- **Choice C is correct**

\(-7y=-6x-12⇒y=\frac{-6}{-7} x-\frac{12}{-7}⇒y=\frac{6}{7} x+\frac{12}{7}\)

19- **Choice D is correct**

\((g – f)(x) = g(x) – f(x) = (– x^2 – 1 – 2x) – (5 + x) – x^2 – 1 – 2x – 5 – x = – x^2 – 3x – 6\)

20- **Choice B is correct**

\(\frac{|3+x|}{7}≤5⇒|3+x|≤35⇒-35≤3+x≤35⇒-35-3≤x≤35-3⇒-38≤x≤32\)

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