GED Algebra Practice Questions, Set 2

This is set 2 of 4 for GED Algebra, with 22 practice questions that are not part of any full practice test. If a question type feels unfamiliar, review the Algebra study guide first, then check each answer below.

Question 1 of 22

0 answered

Which line is perpendicular to y = (2/5)x − 1?

Algebra practice set 2: 22 questions with answers

Work each question on paper first, then open the answer to check your reasoning.

  1. 1.Which line is perpendicular to y = (2/5)x − 1?

    1. A.y = (5/2)x + 3
    2. B.y = (2/5)x + 3
    3. C.y = −(2/5)x + 3
    4. D.y = −(5/2)x + 3
    Show answer

    Answer: D. y = −(5/2)x + 3

    Perpendicular slopes are negative reciprocals, so flip 2/5 to 5/2 and change the sign. Choice y = (5/2)x + 3 flips the fraction but keeps the positive sign.

  1. 2.The graph of a savings balance is a line through (0, 500) and (8, 1,300), where x is months and y is dollars. What is the slope of the line?

    1. A.100
    2. B.800
    3. C.162.5
    4. D.0.01
    Show answer

    Answer: A. 100

    Slope = (1,300 − 500) ÷ (8 − 0) = 800 ÷ 8 = 100, so the balance grows $100 per month. Choice 162.5 divides the final balance by 8 and ignores the $500 start.

  1. 3.If f(x) = 4x + 1, what is f(a + 2)?

    1. A.4a + 9
    2. B.4a + 12
    3. C.4a + 6
    4. D.4a + 3
    Show answer

    Answer: A. 4a + 9

    Replace x with (a + 2): 4(a + 2) + 1 = 4a + 8 + 1 = 4a + 9. Choice 4a + 3 multiplies only the a by 4, not the 2.

  1. 4.A function is given as a set of pairs: (−2, 3), (0, −1), (1, −3), (4, −9). Which equation describes the function?

    1. A.y = 2x − 1
    2. B.y = −2x − 1
    3. C.y = −x − 1
    4. D.y = −2x + 1
    Show answer

    Answer: B. y = −2x − 1

    The pair (0, −1) gives the y-intercept −1, and y drops 2 each time x rises 1, so y = −2x − 1. Check: −2(4) − 1 = −9. Choice y = −2x + 1 has the right slope but the wrong intercept.

  1. 5.The function d(t) = 55t gives the distance in miles a truck travels in t hours. What is d(3.5), and what does it mean?

    1. A.3.5; hours needed to drive 55 miles
    2. B.192.5; hours to drive 3.5 miles
    3. C.192.5; miles driven in 3.5 hours
    4. D.15.7; miles driven in each hour
    Show answer

    Answer: C. 192.5; miles driven in 3.5 hours

    d(3.5) = 55 × 3.5 = 192.5, and since the input is hours, the output is the miles driven in 3.5 hours. The choice reading 192.5 as hours mixes up the input and the output.

  1. 6.Solve for x: 7 − 2(x + 3) = 5x − 13

    1. A.−2
    2. B.26/7
    3. C.2
    4. D.4
    Show answer

    Answer: C. 2

    Distribute −2 to get 7 − 2x − 6 = 5x − 13, which is 1 − 2x = 5x − 13. Add 2x and 13 to get 14 = 7x, so x = 2. Choice 26/7 comes from writing −2 × 3 as +6.

  1. 7.Solve for x: (x − 4)/5 = (x + 2)/3

    1. A.−11
    2. B.−7
    3. C.11
    4. D.−13
    Show answer

    Answer: A. −11

    Cross multiply: 3(x − 4) = 5(x + 2), so 3x − 12 = 5x + 10, which gives −22 = 2x and x = −11. Choice 11 loses the negative sign when dividing.

  1. 8.Multiply: (2x − 3)²

    1. A.4x² − 12x + 9
    2. B.4x² + 9
    3. C.4x² − 9
    4. D.2x² − 12x + 9
    Show answer

    Answer: A. 4x² − 12x + 9

    (2x − 3)² means (2x − 3)(2x − 3) = 4x² − 6x − 6x + 9 = 4x² − 12x + 9. Choice 4x² + 9 squares each term and leaves out the middle term.

  1. 9.Simplify: (8x⁵ − 12x³) ÷ 4x²

    1. A.2x³ − 12x³
    2. B.2x⁷ − 3x⁵
    3. C.4x³ − 8x
    4. D.2x³ − 3x
    Show answer

    Answer: D. 2x³ − 3x

    Divide each term by 4x²: 8x⁵ ÷ 4x² = 2x³ and 12x³ ÷ 4x² = 3x. Choice 2x⁷ − 3x⁵ adds the exponents instead of subtracting them.

  1. 10.A 40-gallon water heater starts at 55°F and heats at a steady rate, reaching 115°F after 30 minutes. Which equation gives the temperature T after m minutes, for m from 0 to 30?

    1. A.T = 2 + 55m
    2. B.T = 55 + 4m
    3. C.T = 115 − 2m
    4. D.T = 55 + 2m
    Show answer

    Answer: D. T = 55 + 2m

    The temperature rose 115 − 55 = 60 degrees in 30 minutes, which is 2 degrees per minute, starting at 55. Choice T = 2 + 55m swaps the starting value and the rate.

  1. 11.How many solutions does the system 2x + y = 5 and 4x + 2y = 10 have?

    1. A.Exactly two
    2. B.Exactly one
    3. C.Infinitely many
    4. D.None
    Show answer

    Answer: C. Infinitely many

    Multiply the first equation by 2 and you get 4x + 2y = 10, which is the second equation. Both describe the same line, so every point on it is a solution. Choice None would be right only if the lines were parallel and separate.

  1. 12.A school paid $95 for 12 boxes of pens and 5 boxes of markers. A second order of 4 boxes of pens and 5 boxes of markers cost $55. What is the price of one box of markers?

    1. A.$5
    2. B.$11
    3. C.$8
    4. D.$7
    Show answer

    Answer: D. $7

    Subtract the second order from the first: 8 boxes of pens cost 95 − 55 = $40, so one box of pens is $5. Then 4(5) + 5m = 55 gives 5m = 35 and m = $7. Choice $5 is the price of the pens.

  1. 13.Factor completely: 2x² − 8x − 24

    1. A.2(x + 6)(x − 2)
    2. B.2(x − 6)(x + 2)
    3. C.(2x − 6)(x + 4)
    4. D.2(x − 4)(x + 3)
    Show answer

    Answer: B. 2(x − 6)(x + 2)

    Take out the common factor 2 to get 2(x² − 4x − 12). Then −6 and 2 multiply to −12 and add to −4, giving 2(x − 6)(x + 2). Choice 2(x + 6)(x − 2) has a middle term of +8x.

  1. 14.What are the solutions of x² = 9x?

    1. A.x = 0 and x = 9
    2. B.x = 3 and x = −3
    3. C.x = −9 and x = 0
    4. D.x = 9 only
    Show answer

    Answer: A. x = 0 and x = 9

    Move everything to one side: x² − 9x = 0, so x(x − 9) = 0, giving x = 0 or x = 9. Choice x = 9 only comes from dividing both sides by x, which loses the solution x = 0.

  1. 15.Which value of x is NOT a solution of 4x − 7 ≤ 2x + 5?

    1. A.−3
    2. B.7
    3. C.6
    4. D.0
    Show answer

    Answer: B. 7

    Subtract 2x and add 7 to get 2x ≤ 12, so x ≤ 6. Only 7 is greater than 6. Choice 6 is a solution because the symbol ≤ includes equality.

  1. 16.If f(x) = 2x² − 5, what is f(−3) + f(3)?

    1. A.13
    2. B.−10
    3. C.26
    4. D.0
    Show answer

    Answer: C. 26

    f(−3) = 2(9) − 5 = 13 and f(3) = 2(9) − 5 = 13, so the sum is 26. Choice 0 assumes the outputs are opposites, but squaring makes −3 and 3 give the same result.

  1. 17.The length of a rectangular parking lot is 15 meters less than 3 times its width. The perimeter is 290 meters. What is the width?

    1. A.105 meters
    2. B.45 meters
    3. C.40 meters
    4. D.32.5 meters
    Show answer

    Answer: C. 40 meters

    Length = 3w − 15, so 2(w + 3w − 15) = 290. Then 4w − 15 = 145, 4w = 160, and w = 40 meters. Choice 105 meters is the length.

  1. 18.Movie tickets cost $11 each and popcorn costs $6 per bag. A group buys t tickets and 2 fewer bags of popcorn than tickets. Which expression gives the total cost?

    1. A.11(t − 2) + 6t
    2. B.11t + 6(t − 2)
    3. C.11t + 6(2 − t)
    4. D.11t + 6t − 2
    Show answer

    Answer: B. 11t + 6(t − 2)

    Tickets cost 11t. The number of bags is t − 2, so popcorn costs 6(t − 2). Choice 11t + 6t − 2 subtracts $2 from the total instead of subtracting 2 bags.

  1. 19.Solve for x: 0.25x + 1.5 = 0.75x − 2.5

    1. A.x = 8
    2. B.x = −8
    3. C.x = 4
    4. D.x = 2
    Show answer

    Answer: A. x = 8

    Subtract 0.25x from both sides and add 2.5: 4 = 0.5x, so x = 8. Choice x = 2 comes from computing 2.5 − 1.5 = 1 instead of adding, which gives 0.5x = 1.

  1. 20.What is the x-intercept of the line y = 4x − 10?

    1. A.−10
    2. B.10
    3. C.2.5
    4. D.−2.5
    Show answer

    Answer: C. 2.5

    The x-intercept is where y = 0: 0 = 4x − 10, so 4x = 10 and x = 2.5. Choice −10 is the y-intercept, where x = 0.

  1. 21.Which line is the steepest?

    1. A.y = (1/2)x − 6
    2. B.y = 4x
    3. C.y = 3x + 8
    4. D.y = −5x + 1
    Show answer

    Answer: D. y = −5x + 1

    Steepness depends on the size of the slope, ignoring its sign, and −5 has the largest absolute value. Choice y = 4x has the greatest positive slope, but 5 is greater than 4.

  1. 22.Simplify: (x⁻³ · x⁷) ÷ x²

    1. A.x⁶
    2. B.x²
    3. C.x⁻²
    4. D.x¹²
    Show answer

    Answer: B. x²

    Add exponents when multiplying (−3 + 7 = 4), then subtract when dividing (4 − 2 = 2), giving x². Choice x⁶ adds the 2 instead of subtracting it.

More practice sets

Algebra has 4 practice sets. None of these questions appear in the full practice tests.