YOUR HiSET STUDY COMPANION

Full-Length HiSET Math Practice Test-Answers and Explanations

TL;DR: Going for the HiSET? Try this full-length HiSET Math practice test as a real rehearsal. It mirrors the actual exam: 50 questions in 90 minutes, with the on-screen TI-30XS calculator on the computer version. Time yourself end to end and check your…

HiSET MATH ANSWERS EXPLAINED — original handwritten comic illustration.

TL;DR: Going for the HiSET? Try this full-length HiSET Math practice test as a real rehearsal. It mirrors the actual exam: 50 questions in 90 minutes, with the on-screen TI-30XS calculator on the computer version. Time yourself end to end and check your answers against the full explanations afterward. You’ll learn the pacing as much as the content, and weak topics will surface in time to fix.

Key takeaways:

HiSET Math has 50 questions and a 90-minute time limit.
On computer-based HiSET, an on-screen TI-30XS calculator is provided.
Paper testers must bring an approved calculator.
Scoring is 1-20 per subtest; you typically need 8 to pass math.
Topics: numbers/operations, algebra, geometry, data analysis.

1- Choice D is correct
Use the order of operations (PEMDAS). Do division and multiplication first: $48 \div 6 = 8$ and $5 \times 3 = 15$.
Then add and subtract from left to right: $8 + 15 – 7 = 16$

2- Choice C is correct
The fraction eaten is $\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{5}{8}$.
Subtract from a whole: $1-\frac{5}{8}=\frac{3}{8}$

3- Choice D is correct
The tip is $15\%$ of $40$: $0.15 \times 40 = 6$.
Total paid $= 40 + 6 = 46$ dollars.

4- Choice C is correct
Set up the proportion $\frac{flour}{sugar}=\frac{2}{3}=\frac{x}{12}$.
Cross multiply: $3x = 24$, so $x = 8$ cups of flour.

5- Choice C is correct
Add $7$ to both sides of $4x-7=21$: $4x=28$.
Divide both sides by $4$: $x=7$

6- Choice D is correct
Area of a rectangle $=$ length $\times$ width.
$15 \times 8 = 120$ ft$^2$

7- Choice C is correct
$average =\frac{sum \space of \space terms}{number \space of \space terms}$
Sum $= 78+85+92+88+67 = 410$. Average $= \frac{410}{5}=82$

8- Choice D is correct
Distance $=$ speed $\times$ time. $2$ hours $30$ minutes $= 2.5$ hours.
$60 \times 2.5 = 150$ miles.

9- Choice A is correct
The ratio of boys to girls is $3:4$, so boys make up $\frac{3}{3+4}=\frac{3}{7}$ of the students.
Number of boys $= \frac{3}{7} \times 350 = 150$

10- Choice D is correct
$\frac{2}{3}$ of $15$ is $\frac{2}{3} \times 15 = 10$. Let $x$ be the unknown number: $\frac{4}{5}x=10$.
Multiply both sides by $\frac{5}{4}$: $x = 10 \times \frac{5}{4}=12.5$

11- Choice E is correct
Distribute: $3(x-1)-15=2(x+4) \Rightarrow 3x-3-15=2x+8$.
Simplify: $3x-18=2x+8$. Subtract $2x$ and add $18$ to both sides: $x=26$

12- Choice C is correct
Translate: $0.50A = 0.25B$. Divide both sides by $0.25$: $2A=B$.
So $B$ is $200\%$ of $A$.

13- Choice B is correct
Use FOIL: $(3x+4y)(2x-5y)=6x^2-15xy+8xy-20y^2$.
Combine like terms: $6x^2-7xy-20y^2$

14- Choice D is correct
Distribute $-3x$ to each term inside the parentheses: $-3x(2y-5)=-6xy+15x$.
Rewrite: $15x-6xy$

15- Choice B is correct
Plug $a=5$ and $b=2$ into the expression: $x=2ab-2b^3=2(5)(2)-2(2)^3$.
$x = 20-2(8) = 20-16 = 4$

16- Choice C is correct
Let the original price be $x$. A $24\%$ decrease means the new price is $76\%$ of $x$: $0.76x=285$.
Divide both sides by $0.76$: $x = \frac{285}{0.76}=375$

17- Choice B is correct
The two parallel sides are $12$ and $18$, and the two legs together are $15$, giving perimeter $12+18+15=45$. The height is $9$.
Area of a trapezoid $=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+18)(9)=\frac{1}{2}(30)(9)=135$ cm$^2$

18- Choice C is correct
After a $25\%$ decrease the price is $0.75D$. After a $15\%$ increase the new price is $0.75D \times 1.15$.
$0.75 \times 1.15 = 0.8625$, so the final price is $0.8625D$.

19- Choice C is correct
Surface area of a cylinder $=2\pi r^2+2\pi r h$.
$=2\pi(5)^2+2\pi(5)(11)=50\pi+110\pi=160\pi$ in$^2$

20- Choice B is correct
$average =\frac{sum \space of \space terms}{number \space of \space terms}$
$\frac{11+16+21+x}{4}=15 \Rightarrow 48+x=60 \Rightarrow x=12$

21- Choice D is correct
For five consecutive numbers, the average equals the middle number, so the third number is $72$.
The five numbers are $70, 71, 72, 73, 74$, and the smallest is $70$.

22- Choice D is correct
Let the original price be $x$. A $20\%$ decrease means $80\%$ of $x$ equals $240$: $0.80x=240$.
$x = \frac{240}{0.80}=300$ dollars.

23- Choice C is correct
Factor out the common $x$: $f(x)=x(x^2+9x+20)=x(x+4)(x+5)$.
Set each factor equal to zero: $x=0$, $x=-4$, $x=-5$

24- Choice C is correct
Area of a circle $=\pi r^2=36\pi$, so $r^2=36$ and $r=6$.
Circumference $=2\pi r=2\pi(6)=12\pi$

25- Choice B is correct
Arrange the numbers in order: $3, 4, 6, 8, 11, 13, 17$.
With $7$ values the median is the middle ($4$Th) value: $8$.

26- Choice C is correct
Starting salary is $\$17{,}000$ and it grows by $\$1{,}500$ per year, so average income after $x$ years is $1500x+17000$.
Income greater than average means $I > 1500x+17000$, which matches choice C.

27- Choice B is correct
Volume of a pyramid $=\frac{1}{3} \times \text{base area} \times \text{height}$.
Base area $= 4 \times 4 = 16$ cm$^2$. Volume $= \frac{1}{3} \times 16 \times 15 = 80$ cm$^3$

28- Choice D is correct
The new price as a percent of the original is $\frac{1.8}{1.2} \times 100\%$.
$\frac{1.8}{1.2}=1.5 = 150\%$

29- Choice D is correct
List products of consecutive primes: $2 \times 3 = 6$, $3 \times 5 = 15$, $5 \times 7 = 35$, $7 \times 11 = 77$.
Among the choices, only $35$ matches.

30- Choice C is correct
Use the percent-of-change formula: $\frac{400-360}{400} \times 100\%$.
$=\frac{40}{400} \times 100\%=10\%$

31- Choice C is correct
From $\$34{,}000$ to $\$25{,}500$: $\frac{25500}{34000}=0.75$, a $25\%$ decrease.
From $\$25{,}500$ to $\$19{,}125$: $\frac{19125}{25500}=0.75$, again a $25\%$ decrease per year.

32- Choice D is correct
The south and east legs form a right angle, so use the Pythagorean theorem: $c^2=50^2+120^2$.
$c^2=2500+14400=16900 \Rightarrow c=\sqrt{16900}=130$ miles.

33- Choice C is correct
Width $=\frac{1}{4}$ of $24=6$ cm. Height $=\frac{1}{3}$ of $6=2$ cm.
Volume $=$ length $\times$ width $\times$ height $=24 \times 6 \times 2=288$ cm$^3$

34- Choice B is correct
Use the formula for Percent of Change: $\frac{New \space Value-Old \space Value}{Old \space Value} × 100\%$
$\frac{60-80}{80}×100\% = -25\%$ (negative sign here means that the new price is less than old price).

35- Choice D is correct
To find the number of possible outfit combinations, multiply the number of options for each factor: $5 × 2 × 7 = 70$

36- Choice D is correct
Let $x$ be the number. Write the equation and solve for $x$: $(18 – x) \div x = 2$
Multiply both sides by: $(18 – x) = 2x$, then add x both sides: $18 = 3x$, now divide both sides by 3. $x= 6$

37- Choice C is correct
The sum of supplement angles is $180$. Let $x$ be that angle. Therefore, $x + 4x = 180$.
$5x = 180$, divide both sides by $5$: $x = 36$

38- Choice D is correct
The average speed of john is: $180 ÷ 3 = 60$, The average speed of Alice is: $350 ÷ 7 = 50$, Write the ratio and simplify. $60: 50 ⇒ 6: 5$

39- Choice B is correct
The percent of girls playing tennis is: $65\% × 20\% = 0.65 × 0.20 = 0.13 = 13 \%$

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40- Choice B is correct
Solving Systems of Equations by Elimination
$\begin{cases}-2x+5y= 9 \\ x-2y=-6 \end{cases}$
Add second equation to the first equation.
$\begin{cases}-x+3y= 3 \\ x-2y=-6 \end{cases}$ ⇒$\begin{cases}x=3y -3 \\ (3y-3)-2y=-6 \end{cases}$ ⇒ $y=-3$, then $x = 3y – 3 = 3(-3) – 3 = -12$. The solution is $(x, y) = (-12, -3)$.

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41- Choice D is correct
The area of the floor is: $180 cm × 240 cm = 43200 $ cm$^2$
The number is tiles needed $= 43200 ÷ 60 = 720$

42- Choice B is correct
The weight of 15.8 meters of this rope is: 15.8 × 700 g = 11060 g
1 kg = 1000 g, therefore, 11060 g ÷ 1000 = 11.06 kg

43- Choice D is correct
$16\%$ of the volume of the solution is alcohol. Let $x$ be the volume of the solution.
Then: $16\%$ of $x = 60$ ml ⇒ $0.16 x= 60 ⇒x = 60 ÷ 0.16 = 375$

44- Choice A is correct
$average =\frac{sum \space of \space terms}{number \space of \space terms}$
The sum of the weight of all girls is: $38 × 50 = 1900$ kg
The sum of the weight of all boys is: $22 × 68 = 1496$ kg
The sum of the weight of all students is: $1900 + 1496 = 3396$ kg
$average =\frac{3396}{60} = 56.6$

45- Choice D is correct
Use simple interest formula: $I=prt$ (I = interest, p = principal, r = rate, t = time)
$I=(17,000)(0.036)(5)=3,060$

46- Choice C is correct
The relationship among all sides of a 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 ladder is the hypotenuse. Therefore, the ladder is 24 ft.

47- Choice C is correct
$(4.7 \times 10^8) \times (3.4 \times 10^{-4}) = (4.7 \times 3.4) \times (10^8 \times 10^{-4}) = 15.98 \times 10^{8+(-4)} = 15.98 \times 10^{4}$

48- Choice A is correct
Since the triangle ABC is reflected over the $y$-axis, then all values of $y$’s of the points don’t change and the sign of all $x$’s change. (remember: when a point is reflected over the $y$-axis, the value of $y$ does not change and the sign of $x$ flips; when a point is reflected over the $x$-axis, the value of $x$ does not change and the sign of $y$ flips). Therefore: $(−1,4)$ changes to (1, 4), (5, 1) changes to $(-5, 1), (1, -6)$ changes to $(−1, -6)$.

49- Choice C is correct
Use Pythagorean theorem: $a^2 + b^2 = c^2, 6^2 + 8^2 = x^2$, $36 + 64 = x^2$
$100 = x^2$, so $x = 10$

50- Choice C is correct
If 13 balls are removed from the bag at random, there will be one ball in the bag. The probability of choosing a red ball is 1 out of 14. Therefore, the probability of not choosing a red ball is 13 out of 14 and the probability of having not a red ball after removing 13 balls is the same.

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If you want a workbook to study before tackling this practice test, the HiSET Math for Beginners (resource currently unavailable) walks through every topic with worked examples. For complete prep with multiple full practice tests, see the HiSET Math Test Prep Bundle.

Frequently Asked Questions

Is a HiSET a GED?

No. The HiSET and the GED are two different high school equivalency exams made by different organizations, but both can lead to a state-issued high school equivalency credential. Which one you can take depends on your state, since some states offer only the GED, some only the HiSET, and some both. Check your state’s adult education office before you register.

What is the difference between the GED and HiSET?

The GED has four subject tests and is mostly computer-based, while the HiSET has five subtests (reading, writing, math, science and social studies) and is offered on computer and, in many places, on paper. On HiSET math you get 50 multiple-choice questions in 90 minutes, and you need at least 8 out of 20 on each subtest plus a total of 45 to pass.

Is the HiSET easier than the GED?

Neither is clearly easier; they cover similar high school skills. Many test takers like that HiSET math is all multiple choice and gives a bit more time per question, while others prefer the GED’s format. The better choice is the one your state offers that fits how you test. Either way, solid skills like solving 4x − 7 = 21 (x = 7) are what count.

How long does it take to complete the HiSET?

All five HiSET subtests together add up to roughly seven hours of testing, and most people split them across several days, since you can take each subtest separately. The math subtest alone is 90 minutes for 50 questions, which works out to under two minutes per question. Study time is separate and depends on how rusty your skills are.

Is there a HiSET full-length practice test?

Yes. This full-length HiSET math practice test has 50 questions with answers and step-by-step explanations, matching the real test length. Set a 90-minute timer, then check each answer. For example, the average of 78, 85, 92, 88 and 67 is 410 ÷ 5 = 82. The official HiSET site also offers free practice tests you can use alongside it.

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