GED Math
GED Math is a trademark of its owner, which is not affiliated with and does not endorse Test Treasure Publication or TTP Prep.
GED Math is a trademark of its owner, which is not affiliated with and does not endorse Test Treasure Publication or TTP Prep.
10 sample questions for the GED Math, with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.
Sections covered on the exam: Basic Math, Thenumberline, Operations,Powers,Androots, Rationalnumbersandpercents, Ratios,Rates,Andproportions, Geometry, Linesandplanes, Two-Dimensionalshapes, Three-Dimensionalshapes, Triangleclassificationandproperties, Statistics And Probability, Statisticalanalysis, Probabilityandcounting, Algebra, Unitsofmeasurement, Inequalities, Systemsofequations, Polynomialalgebra, Quadratics.
Question 1 · Basic Math
Consider the numbers √49, √20, 0.3̄ (0.333… repeating), irrational numbers in this set and no others?
Answer: D. Option D
The correct answer is D: Option D.
Question 2 · Ratios,Rates,Andproportions
A lemonade recipe mixes 3 cups of concentrate with every 8 cups of water. A caterer needs 55 cups of lemonade in all. How many cups of concentrate should be used?
Answer: A. 15 cups
Each batch of 3 cups concentrate and 8 cups water makes 11 cups, so concentrate is 3/11 of the total: 3/11 × 55 = 15 cups (with 40 cups of water). Using the part-to-part ratio 3/8 × 55 gives 20⅝ cups, and 40 cups is the amount of water.
Question 3 · Statisticalanalysis
Rosa's scores on her first four tests are 78, 85, 72, and 90. What score does she need on the fifth test so that the mean of all five tests is exactly 84?
Answer: C. 95
A mean of 84 on five tests requires a total of 84 × 5 = 420 points. Her current total is 78 + 85 + 72 + 90 = 325, so she needs 420 − 325 = 95. Averaging her current mean (81.25) with the unknown score and setting the result equal to 84 gives 86.75, which ignores that the first four tests carry four times the weight.
Question 4 · Basic Math
Solve for x: 5(x − 3) + 2 = 3(x + 4) − 7
Answer: C. x = 9
Distribute and simplify each side: 5x − 15 + 2 = 3x + 12 − 7, so 5x − 13 = 3x + 5. Subtract 3x and add 13: 2x = 18, so x = 9. Distributing the 5 to x only (5x − 3) leads to x = 3.
Question 5 · Systemsofequations
For what value of k does the system 3x − 4y = 7 and kx + 8y = 5 have no solution?
Answer: D. −6
No solution means parallel lines with different intercepts. Multiplying the first equation by −2 gives −6x + 8y = −14, which matches the y-coefficient of the second equation, so k = −6; since 5 ≠ −14, the lines never meet. Using k = 6 ignores the sign change from multiplying by −2.
Question 6 · Quadratics
The volume of water in a tank, in gallons, t minutes after a drain is opened is modeled by V = 1,200 − 45t. Which statement correctly interprets the model?
Answer: B. Starts at 1,200 gal; loses 45 gal per min
The constant 1,200 is the value of V when t = 0, the starting volume. The coefficient −45 is the slope, so the volume decreases by 45 gallons each minute. The 1,155 gallons is the volume after 1 minute, not at the start.
Question 7 · Rationalnumbersandpercents
A sales representative earns a base salary of $1,850 per month plus a 4.5% commission on her total sales. What amount of sales must she make in a month to earn a total of $3,200?
Answer: D. $30,000
The commission must make up 3,200 − 1,850 = $1,350. Solve 0.045s = 1,350: s = 1,350 ÷ 0.045 = $30,000. Writing 4.5% as 0.45 gives $3,000, and forgetting to subtract the base salary gives 3,200 ÷ 0.045 ≈ $71,111.
Question 8 · Triangleclassificationandproperties
A carpenter checks triangular frames to see which one has a right angle. Which set of side lengths, in inches, forms a right triangle?
Answer: A. 9, 40, 41
By the converse of the Pythagorean theorem, the triangle is right when the squares of the two shorter sides add up to the square of the longest side: 9² + 40² = 81 + 1,600 = 1,681 = 41². For 7, 24, 26: 49 + 576 = 625, which is 25², not 26² = 676. The other sets fail the same way (289 ≠ 256 and 400 ≠ 441).
Question 9 · Unitsofmeasurement
Which expression is equivalent to (2a⁻³b⁰) ÷ a⁻⁵ for all nonzero values of a and b?
Answer: A. 2a²
Any nonzero base to the zero power equals 1, so b⁰ = 1. When dividing powers of a, subtract exponents: −3 − (−5) = 2, giving 2a². Adding the exponents gives 2a⁻⁸, and treating b⁰ as b gives 2a²b.
Question 10 · Systemsofequations
Which ordered pair (x, y) satisfies both y = 2x − 7 and 3x + 2y = 7?
Answer: A. (3, −1)
Substitute y = 2x − 7 into the second equation: 3x + 2(2x − 7) = 7, so 7x − 14 = 7 and x = 3; then y = 2(3) − 7 = −1. The pair (2, −3) satisfies only the first equation, and (1, 2) satisfies only the second.
TTP Prep has 196 GED Math practice questions with explanations, timed and mock-exam modes, 167 flashcards, interactive lessons, a printable cheat sheet and a readiness score. Start free, no card needed.
More free questions: browse every exam.