# FREE HiSET Math Practice Test

Welcome to our FREE HiSET Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the HiSET Math test. Not only does the test closely match what you will see on the real HiSET, but it also comes with detailed answer explanations.

For this practice test, we’ve selected 20 real questions from past exams for your HiSET Practice test. You will have the chance to try out the most common HiSET Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free HiSET Math practice tests and study resources (updated for 2021) to ace the HiSET Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

## The Absolute Best Book** to Ace the HiSET** **Math** Test

## 10 Sample **HiSET** Math Practice Questions

1- Solve for \(x\):

\(4(x + 1) = 6(x − 4) + 20\)

A. 12

B. 8

C. 6.2

D. 5.5

E. 4

2- What is \(2.5\%\) of 1,200?

A. 900

B. 600

C. 300

D. 60

E. 30

3- \((2x + 2y)(5x + 2y) = ?\)

A. \(2x^2+ 14xy + 2y^2\)

B. \(2x^2+ 4xy + 2y^2\)

C. \(7x^2+ 14xy + y^2\)

D. \(10x^2+ 14xy + 2y\)

E. \(10x^2 + 14xy + 4y^2\)

4- Which of the following expressions is equivalent to

\(2x (4 + 2y)\)?

A. \(6xy + 8x\)

B. \(8xy + 8x\)

C. \(xy + 8\)

D. \(2xy + 8x\)

E. \(4xy + 8x\)

5- If \(y = 4ab + 3b³\), what is\( y\) when \(a = 2\) and \(b = 3\)?

A. 24

B. 31

C. 36

D. 51

E. 105

6- 11 yards 6 feet and 4 inches equals to how many inches?

A. 388

B. 468

C. 472

D. 476

E. 486

7- 5 less than twice a positive integer is 83. What is the integer?

A. 39

B. 41

C. 42

D. 44

E. 50

8- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) – 200 (0.30)\)

C. \((200) (0.15) – (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

E. \((200) (0.85) (0.85) – (200) (0.15)\)

9- Which of the following points lies on the line \(2x + 4y = 10\)

A. \((2, 1)\)

B. \((–1, 3)\)

C. \((–2, 2)\)

D. \((2, 2)\)

E. \((2, 8)\)

10- \(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 =\) ?

A. 120

B. 88

C. \(-45\)

D. \(-40\)

E. \(-30\)

11- The price of a car was $20,000 in 2014, $16,000 in 2015 and $12,800 in 2016. What is the rate of depreciation of the price of car per year?

A. \(15 \%\)

B. \(20 \%\)

C. \(25 \%\)

D. \(30 \%\)

E. \(30 \%\)

12- The width of a box is one third of its length. The height of the box is one third of its width. If the length of the box is 27 cm, what is the volume of the box?

A. \(81 cm^3\)

B. \(162 cm^3\)

C. \(243 cm^3\)

D. \(729 cm^3\)

E. \(1880 cm^3\)

13- If \(60 \%\) of A is \(20 \%\) of B, then B is what percent of A?

A. \(3 \%\)

B. \(30 \%\)

C. \(200 \%\)

D. \(300 \%\)

E. \(900 \%\)

14- How many possible outfit combinations come from six shirts, three slacks, and five ties?

A. 11

B. 14

C. 15

D. 30

E. 90

15- A ladder leans against a wall forming a 60\(^\circ\)angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?

A. 30 feet

B. 40 feet

C. 50 feet

D. 60 feet

E. 120 feet

16- If \(f(x)= 2x^3+5x^2+2x\) and\( g(x) = -2\), what is the value of \(f(g(x))\)?

A. 36

B. 32

C. 24

D. 4

E. 0

17- The diagonal of a rectangle is 10 inches long and the height of the rectangle is 8 inches. What is the perimeter of the rectangle?

A. 10 inches

B. 12 inches

C. 16 inches

D. 18 inches

E. 28 inches

18- The perimeter of the trapezoid below is 36 cm. What is its area?

A. \(48 cm^2\)

B. \(70 cm^2\)

C. \(140 cm^2\)

D. \(576 cm^2\)

E. \(986 cm^2\)

19- A card is drawn at random from a standard 52–card deck, what is the probability that the card is of Hearts? (The deck includes 13 of each suit clubs, diamonds, hearts, and spades)

A. \(\frac{1}{3}\)

B. \(\frac{1}{4}\)

C. \(\frac{1}{6}\)

D. \(\frac{1}{52}\)

E. \(\frac{1}{104}\)

20- Which of the following shows the numbers in descending order?

\(\frac{2}{3}, 0.68 , 67\%,\frac{4}{5} \)

A. \(67\%, 0.68, 2/3 , 4/5\)

B. \(67\%, 0.68, 4/5, 2/3\)

C. \(0.68, 67\%, 2/3 , 4/5\)

D. \(2/3 , 67\%, 0.68, 4/5\)

E. \(2/3 , 67\%, 4/5 , 0.68\)

## Best **HiSET** Math Prep Resource for 2021

## Answers:

1- **E**

Simplify:

\(4(x + 1) = 6(x − 4) + 20\)

\(4x + 4 = 6x − 24 + 20\)

\(4x + 4 = 6x – 4\)

Subtract \(4x\) from both sides:

\(4 = 2x – 4\)

Add 4 to both sides:

\(8 = 2x\)

\(4 = x\)

2- **E**

\(2.5\%\) of \(1,200 = 0.025 × 1200 = 30\)

3-** E**

Use FOIL (First, Out, In, Last)

\((2x + 2y)(5x + 2y) = 10x^2+ 4xy + 10xy + 2y^2 = 10x^2+ 14xy + 4y^2\)

4- **E**

Use distributive property:

\(2x (4 + 2y) = 8x + 4xy = 4xy+ 8x\)

5- **E**

\(y = 4ab + 3b³\)

Plug in the values of a and b in the equation: \(a = 2 \)and \(b = 3\)

\(y = 4 (2) (3) + 3 (3)3 = 24 + 3(27) = 24 + 81 = 105\)

6- **C**

\(11 × 36 + 6 × 12 + 4 = 472\)

7- **D**

Let \(x\) be the integer. Then:

\(2x – 5 = 83\)

Add 5 both sides: \(2x = 88\)

Divide both sides by \(2: x = 44\)

8- **D**

To find the discount, multiply the number by \((100\% – rate of discount)\).

Therefore, for the first discount we get: \((200) (100\% – 15\%) = (200) (0.85) = 170\)

For the next \(15 \%\) discount: \((200) (0.85) (0.85)\)

9- **B**

Plug in each pair of number in the equation:

A. \((2, 1): 2 (2) + 4 (1) = 8\)

B. \((–1, 3): 2 (–1) + 4 (3) = 10\)

C. \((–2, 2): 2 (–2) + 4 (2) = 4\)

D. \((2, 2): 2 (2) + 4 (2) = 12\)

10- **E**

Use PEMDAS (order of operation):

\(5 + 8 × (–2) – [4 + 22 ×5] ÷ 6 = 5 + 8 × (–2) – [4 + 110] ÷ 6 = 5 + 8 × (–2) – [114] ÷ 6 = 5 + (–16) – 19 = 5 + (–16) – 19 = –11 – 19 = –30\)

11- **B**

Use this formula: Percent of Change

\(\frac{New \space Value-Old \space Value}{Old \space Value}× 100 \%\)

\(\frac{16000-20000}{20000}× 100 \% = 20 \%\)

and

\(\frac{12800-16000}{16000}× 100 \% = 20 \%\)

12- **D**

If the length of the box is 27, then the width of the box is one third of it, 9, and the height of the box is 3 (one third of the width). The volume of the box is:

\(V = lwh = (27) (9) (3) = 729\)

13- **D**

Write the equation and solve for B:

\(0.60 A = 0.20 B\), divide both sides by 0.20, then you will have \(0.60/0.20 A = B\), therefore:

\(B = 3\) A, and B is 3 times of A or it’s \(300\%\) of A.

14- **E**

To find the number of possible outfit combinations, multiply number of options for each factor:

\(6 × 3 × 5 = 90\)

15- **D**

The relationship among all sides of special right triangle

30\(^\circ\)-60\(^\circ\)- 90\(^\circ\) is provided in this triangle:

In this triangle, the opposite side of 30\(^\circ\) angle is half of the hypotenuse.

Draw the shape of this question:

The latter is the hypotenuse. Therefore, the latter is 60 ft

16- **E**

\(g(x)=-2, then f(g(x))= f(-2)=2 (-2)^3+5(-2)^2+2(-2)= -16+20-4=0\)

## The Best Quick Study Guide for the **HiSET **Math Test

17- **E**

Let \(x\) be the width of the rectangle. Use Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

\(x^2 + 8^2 = 10^2 ⇒ x^2 + 64 = 100 ⇒ x^2 = 100 – 64 = 36 ⇒ x = 6\)

Perimeter of the rectangle \(= 2 (length + width) = 2 (8 + 6) = 2 (14) = 28\)

18- **B**

The perimeter of the trapezoid is 36.

Therefore, the missing side (height) is \(= 36 – 8 – 12 – 6 = 10\)

Area of a trapezoid: \(A = \frac{1}{2}h (b_{1} + b_{2}) = \frac{1}{2} (10) (6 + 8) = 70\)

19- **B**

The probability of choosing a Hearts is \(13/52 = 1/4\)

20- **D**

Change the numbers to decimal and then compare.

\(\frac{2}{3}= 0.666…\)

0.68

\(67% = 0.67\)

\(\frac{4}{5} = 0.80\)

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### HiSET Math Workbook 2020 – 2021 The Most Comprehensive Review for the Math Section of the HiSET Test

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