GED Math

GED Math Practice Test: 12 Questions Solved Step by Step

Twelve original GED math questions solved step by step, including fill-in-the-blank items, plus what the formula sheet leaves out.

Professor Chacha October 9, 2026 10 min read 13 views

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The GED Mathematical Reasoning test is the math part of the GED. Here is what you are walking into:

Length: 46 questions in 115 minutes.
Two parts: the first few questions must be done without a calculator; after that, an on-screen TI-30XS MultiView calculator is available on most questions. If you test at a center, you may bring your own TI-30XS.
Content: about 45% quantitative problem solving (numbers, percents, measurement, data) and about 55% algebraic problem solving.
Question types: multiple choice, plus drag-and-drop, hot spot, and fill-in-the-blank, where you type the answer yourself.
Formula sheet: provided on paper at the test center and on screen during the test.
Passing score: 145 on a 100 to 200 scale.

Below are 12 original practice questions in the same mix, including three fill-in-the-blank questions, each solved step by step with the trap that costs the most points.

What the formula sheet gives you, and what it doesn't

The official Mathematics Formula Sheet takes a lot of memorizing off your plate. It does not cover everything, though, and the gaps are where many points are lost.

On the formula sheet	Not on the formula sheet
Area and perimeter of squares, rectangles, triangles, parallelograms, trapezoids, and circles	Percents and percent change
Surface area and volume of prisms, cylinders, pyramids, cones, and spheres	Rules for exponents and negative numbers
Mean and median	Probability
Slope, slope-intercept form, point-slope form	Unit conversions, like feet to yards
Quadratic formula and Pythagorean theorem	Fraction operations and order of operations
Simple interest, distance, and total cost	How to set up an equation from a word problem

Spend your study time on the right-hand column. The practice questions below lean on it on purpose. For a worked example of every formula in the left-hand column, see our guide to the GED math formula sheet.

Part 1: no calculator

These questions check number sense. You should be able to do them on scratch paper in under a minute each.

1.No calculator. A $\tfrac{3}{4}$-pound bag of trail mix is split into $\tfrac{1}{8}$-pound portions. How many portions does the bag make?

A6
B$\tfrac{3}{32}$
C$\tfrac{1}{6}$
D8

Show solution

"How many portions" is a division: the total divided by the size of one portion. Dividing by a fraction means multiplying by its reciprocal.

\[\tfrac{3}{4} \div \tfrac{1}{8} = \tfrac{3}{4} \times \tfrac{8}{1} = \tfrac{24}{4} = 6\]

Common trap: Multiplying the fractions instead of dividing, which gives $\tfrac{3}{32}$ of a pound. An answer smaller than one portion can't be the number of portions.

Answer: A (6)

2.No calculator. What is the value of $(-3)^2 - 2^3$?

A$-17$
B1
C17
D$-1$

Show solution

Work out each power first. The parentheses mean the whole $-3$ is squared.

\[\begin{gathered}(-3)^2 = 9 \\ 2^3 = 8 \\ 9 - 8 = 1\end{gathered}\]

Common trap: Treating $(-3)^2$ as $-3^2 = -9$, which leads to $-17$. With parentheses, the negative sign is squared too.

Answer: B (1)

Part 2: quantitative problem solving

From here on, the calculator is available. The questions are about money, measurement, and data from everyday life. Questions 3 and 6 are fill-in-the-blank: there are no choices, so work out the number and check it. Percents are the biggest gap on the formula sheet, so our lesson on percent word problems is a good place to start.

3.A warehouse worker earns $15.50 per hour and gets a 6% raise. What is the new hourly wage, in dollars?

Your answer: ________

Show solution

A 6% raise means the new wage is 106% of the old one.

\[15.50 \times 1.06 = 16.43\]

On the GED you would type 16.43 into the answer box.

Common trap: Typing only the raise, $0.93, instead of the new wage. Reread the question: it asks for the wage after the raise.

Answer: $16.43

4.A 12-ounce box of cereal costs $3.48. An 18-ounce box costs $4.86. Which box is the better buy, and by how much per ounce?

AThe 12-ounce box, by $0.02
BThe 18-ounce box, by $0.02
CThe 18-ounce box, by $1.38
DThey cost the same per ounce

Show solution

Find the price per ounce of each box.

\[\begin{gathered}3.48 \div 12 = 0.29 \\ 4.86 \div 18 = 0.27\end{gathered}\]

The 18-ounce box costs $0.27 per ounce, $0.02 less than the 12-ounce box.

Common trap: Comparing the total prices: $4.86 minus $3.48 is $1.38, but the boxes are different sizes. Unit price (price per ounce) is the only fair comparison.

Answer: B (The 18-ounce box, by $0.02)

5.A cylindrical water tank has a radius of 3 feet and a height of 5 feet. Using $\pi \approx 3.14$, what is its volume?

A47.1 cubic feet
B94.2 cubic feet
C141.3 cubic feet
D565.2 cubic feet

Show solution

The formula sheet gives the volume of a cylinder: $V = \pi r^2 h$.

\[\begin{gathered}V = 3.14 \times 3^2 \times 5 \\ = 3.14 \times 45 \\ = 141.3\end{gathered}\]

Common trap: Using the diameter (6 feet) instead of the radius, which gives 565.2. Another slip is forgetting to square the radius, which gives 47.1.

Answer: C (141.3 cubic feet)

6.Jordan scored 82, 90, and 76 on three practice tests. What score does Jordan need on the fourth test for a mean of exactly 85?

Your answer: ________

Show solution

A mean of 85 over four tests means the four scores must add up to $4 \times 85 = 340$.

\[\begin{gathered}340 - (82 + 90 + 76) \\ = 340 - 248 = 92\end{gathered}\]

Common trap: Answering 85, as if the next score only had to match the target mean. The earlier scores average less than 85, so the last one has to make up the difference.

Answer: 92

Part 2: algebraic problem solving

More than half of the test is algebra: writing and solving equations and inequalities, slope, quadratics, and functions. For a refresher, see how to find slope and systems of equations word problems.

7.A taxi charges $3.50 to start the ride plus $2.25 per mile. How much does an 8-mile ride cost?

A$18.00
B$46.00
C$31.25
D$21.50

Show solution

The fixed charge is paid once; only the per-mile charge is multiplied by the miles.

\[\begin{gathered}3.50 + 2.25 \times 8 \\ = 3.50 + 18.00 \\ = 21.50\end{gathered}\]

Common trap: Adding $3.50 and $2.25 first and then multiplying by 8, which gives $46.00. The order of operations (and common sense) says the starting fee is charged once.

Answer: D ($21.50)

8.Solve for $x$: $\tfrac{x}{4} + 3 = 11$

Show solution

Undo the operations in reverse order: subtract 3, then multiply by 4.

\[\begin{gathered}\tfrac{x}{4} = 8 \\ \Rightarrow\; x = 32\end{gathered}\]

Check: $\tfrac{32}{4} + 3 = 11$.

Common trap: Stopping at 8, or dividing by 4 instead of multiplying and getting 2. The $x$ is divided by 4, so multiply to undo it.

Answer: B (32)

9.What is the slope of the line that passes through $(1, 7)$ and $(5, -1)$?

A2
B$-\tfrac{1}{2}$
C$-2$
D$\tfrac{3}{2}$

Show solution

Use the slope formula from the formula sheet, $m = \tfrac{y_2 - y_1}{x_2 - x_1}$, keeping the same order on top and bottom.

\[m = \tfrac{-1 - 7}{5 - 1} = \tfrac{-8}{4} = -2\]

Common trap: Mixing the order, for example $\tfrac{-1 - 7}{1 - 5}$, which gives 2. A line that goes down from left to right, like this one, must have a negative slope.

Answer: C ($-2$)

10.A phone plan costs $40 per month plus $0.10 for each text message. Sam wants the bill to be no more than $55. What is the greatest number of texts Sam can send?

Your answer: ________

Show solution

Write an inequality and solve it.

\[\begin{gathered}40 + 0.10t \le 55 \\ \Rightarrow\; 0.10t \le 15 \\ \Rightarrow\; t \le 150\end{gathered}\]

Common trap: Dividing $55 by $0.10 and answering 550. The $40 monthly charge comes out of the $55 before any texts are paid for.

Answer: 150

11.Solve: $2x^2 + 3x - 5 = 0$

A$x = -1$ or $x = \tfrac{5}{2}$
B$x = 1$ or $x = -5$
C$x = 5$ or $x = -1$
D$x = 1$ or $x = -\tfrac{5}{2}$

Show solution

Use the quadratic formula from the formula sheet with $a = 2$, $b = 3$, $c = -5$.

\[\begin{gathered}x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-5)}}{2(2)} \\ = \frac{-3 \pm \sqrt{49}}{4} = \frac{-3 \pm 7}{4}\end{gathered}\]\[\begin{gathered}x = \tfrac{4}{4} = 1 \\ x = \tfrac{-10}{4} = -\tfrac{5}{2}\end{gathered}\]

Common trap: Starting with $+3$ instead of $-b = -3$, which flips both signs and gives $-1$ and $\tfrac{5}{2}$. Write $-b$ out before you substitute.

Answer: D ($x = 1$ or $x = -\tfrac{5}{2}$)

12.If $f(x) = 3x - 4$, for what value of $x$ is $f(x) = 11$?

A5
B29
C$\tfrac{7}{3}$
D15

Show solution

Set the function equal to 11 and solve for $x$.

\[\begin{gathered}3x - 4 = 11 \\ \Rightarrow\; 3x = 15 \\ \Rightarrow\; x = 5\end{gathered}\]

Common trap: Plugging 11 in for $x$ and getting $f(11) = 29$. The question gives the output and asks for the input.

Answer: A (5)

Teacher's note: Students often trust the formula sheet so much that they stop thinking about units. Before you plug numbers into a formula, say out loud what each letter stands for and what unit it is in. Question 5 is a good example: the formula is right there, but the diameter is waiting for anyone who rushes.

What your GED math score means

Score	What it means
Below 145	Not passing yet. You can retake the math test without retaking the other subjects.
145 to 164	Passing. Counts toward your high school equivalency credential.
165 to 174	GED College Ready. You may qualify to skip placement testing or remedial math at your college.
175 to 200	GED College Ready + Credit. You may qualify for college credit, if the college accepts it.

A 165 matters even if you are only aiming to pass. Some colleges accept it in place of a placement test, and in Texas a 165 on Mathematical Reasoning exempts you from the TSI math test. Check with the college you plan to attend.

Getting the most out of the calculator

Practice on the same model. If you can, borrow or buy a TI-30XS MultiView and use it for all your practice, so the on-screen version feels familiar on test day.
Learn three things on it: entering fractions, entering exponents, and switching an answer between fraction and decimal form.
Don't use it for everything. Estimate first. If the calculator says a cylinder holds 565 cubic feet and your estimate says about 140, one of you made a mistake, and it is usually the typing.

For official practice, the GED Testing Service offers a free Math Study Guide and the GED Ready practice test on GED.com. GED Ready predicts whether you are likely to pass, which is worth knowing before you pay for the real test.

Tags: Algebra Formula sheet GED Percents Practice test

$Professor Chacha$

Professor Chacha Math teacher and educational psychologist

Math teacher and educational psychologist with more than 20 years of classroom experience. He writes every practice question on this site from scratch and solves it step by step, the way he explains it to his own students.

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