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**

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