Full-Length HiSET Math Practice Test-Answers and Explanations

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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Frequently Asked Questions

How many questions are on the HiSET math test?

50 multiple-choice questions on the math subtest. The questions are split roughly: 19% numbers and operations, 28% algebra, 18% geometry, and 35% data analysis, probability, and statistics. Time limit is 90 minutes.

Is a calculator allowed on the HiSET math?

Yes. On the computer-based HiSET, an on-screen TI-30XS scientific calculator is available throughout the math subtest. On paper-based HiSET, you bring your own approved calculator (a TI-30XS or any non-graphing scientific calculator on the approved list).

Is there a formula sheet on the HiSET?

Yes. The HiSET provides a formula reference page on every administration of the math subtest. It covers area, perimeter, volume, the Pythagorean theorem, simple interest, slope, and the distance formula. Quadratic formula and trig identities are NOT on the sheet.

What score do I need to pass the HiSET math?

You need 8 out of 20 on the math subtest, plus a total of 45 across all five subtests, with no subtest below 8. The essay must also score at least 2 out of 6. Some states require a higher minimum — check your state.

How long is the HiSET math section?

90 minutes for 50 questions, so about 1 minute 48 seconds per question. Most testers finish with a few minutes to spare if they don’t dwell. The on-screen calculator can chew up time if you’re unfamiliar with it — practice with a TI-30XS before test day.

Is the HiSET easier than the GED?

The HiSET and GED test similar content, but the HiSET gives you a formula sheet and a longer time-per-question. Many adult learners find the HiSET more forgiving for that reason. GED Math is shorter (115 min, 46 questions) but denser per question.

Can I retake just the HiSET math subtest?

Yes. The HiSET lets you retake individual subtests. Most states allow up to 3 attempts per subject per year. Your passing scores on other subtests carry over, so you don’t have to retake the whole battery if you only fall short on math.

What’s on the HiSET math test?

Five content areas: numbers and operations (19%), algebra/measurement/geometry (47% combined), and data analysis, probability, and statistics (35%). Specific skills: fractions, decimals, percent, ratios, linear equations, polynomials, geometric properties, measurement, mean/median/mode, and reading charts.

Is the HiSET computer-based or paper-based?

Both. The HiSET is offered on computer at PSI test centers and on paper at many adult learning centers. Content and scoring are identical. Computer-based is faster (results in 3 business days vs 10 for paper) and includes the on-screen calculator.

How long should I study for the HiSET math test?

Most adult learners need 6 to 12 weeks of consistent study at 30-60 minutes a day to go from rusty to ready. If you’ve recently studied for the GED or similar test, 3-4 weeks of targeted review may be enough. Start with a full-length practice test as your diagnostic.

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