GED Algebra Practice Questions, Set 4

This is set 4 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

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A line passes through (2, 9) and (6, 1). What is its y-intercept?

Algebra practice set 4: 22 questions with answers

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

  1. 1.A line passes through (2, 9) and (6, 1). What is its y-intercept?

    1. A.13
    2. B.−2
    3. C.9
    4. D.5
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    Answer: A. 13

    The slope is (1 − 9) ÷ (6 − 2) = −2. Then 9 = −2(2) + b, so b = 13. Choice 5 uses a slope of +2 by mistake.

  1. 2.Which equation describes the line through (0, 4) that is perpendicular to 2x − 3y = 6?

    1. A.y = (2/3)x + 4
    2. B.y = −(3/2)x + 4
    3. C.y = (3/2)x + 4
    4. D.y = −(2/3)x + 4
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    Answer: B. y = −(3/2)x + 4

    Solving 2x − 3y = 6 for y gives y = (2/3)x − 2, so its slope is 2/3. A perpendicular slope is the negative reciprocal, −3/2, and the intercept is 4. Choice y = (2/3)x + 4 is parallel, not perpendicular.

  1. 3.If f(x) = 10 − 3x, what is f(−4)?

    1. A.−2
    2. B.2
    3. C.22
    4. D.−22
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    Answer: C. 22

    f(−4) = 10 − 3(−4) = 10 + 12 = 22. Choice −2 treats −3(−4) as −12.

  1. 4.The table shows a linear function. x: 2, 4, 6, 8 y: 7, 13, 19, 25 Which equation fits every pair in the table?

    1. A.y = 3x + 1
    2. B.y = 6x − 5
    3. C.y = 2x + 3
    4. D.y = 3x + 7
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    Answer: A. y = 3x + 1

    y rises 6 when x rises 2, so the slope is 3, and 7 = 3(2) + b gives b = 1. The equation y = 2x + 3 works for (2, 7) but gives 11, not 13, when x = 4.

  1. 5.Solve for x: 1.5x − 4 = 0.5x + 6

    1. A.x = 5
    2. B.x = 1
    3. C.x = 2.5
    4. D.x = 10
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    Answer: D. x = 10

    Subtract 0.5x from both sides and add 4 to get x = 10. Check: 1.5(10) − 4 = 11 and 0.5(10) + 6 = 11. Choice x = 5 divides 10 by 2 after the x terms already combined to 1x.

  1. 6.Factor completely: 3x² − 12x − 15

    1. A.3(x + 5)(x − 1)
    2. B.3(x − 3)(x + 5)
    3. C.3(x − 5)(x + 1)
    4. D.(3x − 5)(x + 3)
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    Answer: C. 3(x − 5)(x + 1)

    Factor out 3 to get 3(x² − 4x − 5). Then −5 and 1 multiply to −5 and add to −4, so the answer is 3(x − 5)(x + 1). Choice 3(x + 5)(x − 1) gives a middle term of +12x.

  1. 7.Multiply: (x + 4)(2x − 3)

    1. A.2x² + 11x − 12
    2. B.2x² − 5x − 12
    3. C.2x² − 12
    4. D.2x² + 5x − 12
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    Answer: D. 2x² + 5x − 12

    Multiply each pair: 2x², −3x, +8x, and −12. Combining −3x + 8x = 5x gives 2x² + 5x − 12. Choice 2x² − 12 multiplies only the first terms and the last terms.

  1. 8.A hiker starts at an elevation of 2,300 feet and climbs at a steady 450 feet per hour. Which equation gives the elevation E after h hours?

    1. A.E = 2,300 + 450h
    2. B.E = 450 + 2,300h
    3. C.E = 2,300 − 450h
    4. D.E = 2,750h
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    Answer: A. E = 2,300 + 450h

    The starting elevation is the constant, 2,300, and the climb adds 450 feet each hour, so E = 2,300 + 450h. Choice E = 2,300 − 450h describes a hiker going downhill.

  1. 9.A coffee shop mixes beans that cost $9 per pound with beans that cost $14 per pound to make 20 pounds of a blend worth $11 per pound. How many pounds of the $9 beans are used?

    1. A.8
    2. B.12
    3. C.15
    4. D.10
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    Answer: B. 12

    Write 9x + 14(20 − x) = 11 × 20, which gives 280 − 5x = 220, so x = 12. Choice 8 is the pounds of the $14 beans.

  1. 10.A hotel bill for 2 nights and 3 meals is $315. A bill for 1 night and 5 meals is $210. What is the cost of one night?

    1. A.$15
    2. B.$120
    3. C.$135
    4. D.$150
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    Answer: C. $135

    From n + 5m = 210, n = 210 − 5m. Then 2(210 − 5m) + 3m = 315 gives 7m = 105, so m = 15 and n = 135. Choice $15 is the price of one meal.

  1. 11.A phone repair shop finds its charge, in dollars, with f(h) = 45h + 30, where h is the hours of labor. What does the 30 represent?

    1. A.The charge for each hour of work
    2. B.The number of hours a repair takes
    3. C.The total cost of a one-hour job
    4. D.A flat fee charged on every repair
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    Answer: D. A flat fee charged on every repair

    The 30 is added once no matter how many hours are worked, so it is a flat fee. The charge for each hour is 45, the number multiplied by h.

  1. 12.A taxi company uses C(m) = 3.50 + 2.25m to find the fare, in dollars, for a ride of m miles. What is C(8)?

    1. A.$13.75
    2. B.$46.00
    3. C.$18.00
    4. D.$21.50
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    Answer: D. $21.50

    C(8) = 3.50 + 2.25 × 8 = 3.50 + 18 = 21.50. Choice $18.00 leaves out the $3.50 starting charge.

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

    1. A.12
    2. B.6
    3. C.10
    4. D.8
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    Answer: D. 8

    f(2) = 12 − 2 = 10 and f(1) = 3 − 1 = 2, so the difference is 8. Choice 10 is f(2) alone.

  1. 14.The sum of three consecutive odd integers is 87. What is the largest of the three?

    1. A.31
    2. B.27
    3. C.33
    4. D.29
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    Answer: A. 31

    Write n + (n + 2) + (n + 4) = 87, so 3n = 81 and n = 27. The integers are 27, 29, and 31. Choice 29 is the middle number, 87 ÷ 3.

  1. 15.Three shirts and a $12 belt cost $87 in total. Which equation can be used to find s, the price of one shirt?

    1. A.3(s + 12) = 87
    2. B.12s + 3 = 87
    3. C.3s + 12 = 87
    4. D.3s = 87 + 12
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    Answer: C. 3s + 12 = 87

    Three shirts cost 3s and the belt adds 12, so 3s + 12 = 87. Choice 3(s + 12) charges for a belt with every shirt.

  1. 16.A water tank holds 500 gallons and drains at 18 gallons per hour. Which expression gives the number of gallons left after h hours?

    1. A.518 − h
    2. B.500h − 18
    3. C.500 − 18h
    4. D.18h − 500
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    Answer: C. 500 − 18h

    The tank starts at 500 and loses 18 gallons each hour, so subtract 18h from 500. Choice 18h − 500 gives a negative amount at the start.

  1. 17.A number line shows an open circle at 3 with the shading going to the left. Which inequality does it show?

    1. A.x ≤ 3
    2. B.x < 3
    3. C.x > 3
    4. D.x ≥ 3
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    Answer: B. x < 3

    Shading to the left means values less than 3, and the open circle means 3 itself is not included. Choice x ≤ 3 would need a filled circle.

  1. 18.An elevator can carry at most 2,000 pounds. The operator weighs 180 pounds and each box weighs 45 pounds. Which inequality shows the number of boxes b that can ride with the operator?

    1. A.45 + 180b ≤ 2,000
    2. B.180 + 45b ≤ 2,000
    3. C.45b ≤ 2,000 + 180
    4. D.180 + 45b ≥ 2,000
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    Answer: B. 180 + 45b ≤ 2,000

    The total weight, 180 plus 45 for each box, must be at most 2,000, so use ≤. Choice 180 + 45b ≥ 2,000 reverses “at most.”

  1. 19.Simplify: (y²)⁴ ÷ y⁻³

    1. A.y⁵
    2. B.y¹¹
    3. C.y⁹
    4. D.y⁻²⁴
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    Answer: B. y¹¹

    A power raised to a power multiplies the exponents, so (y²)⁴ = y⁸. Dividing subtracts the exponents: 8 − (−3) = 11, giving y¹¹. Choice y⁵ subtracts 3 instead of subtracting −3.

  1. 20.What is the value of 2⁻³?

    1. A.1/8
    2. B.−6
    3. C.1/6
    4. D.−8
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    Answer: A. 1/8

    A negative exponent means a reciprocal: 2⁻³ = 1/2³ = 1/8. Choice −8 treats the negative exponent as a negative result.

  1. 21.What is the slope of a line perpendicular to y = −(2/5)x + 1?

    1. A.−5/2
    2. B.2/5
    3. C.5/2
    4. D.−2/5
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    Answer: C. 5/2

    A perpendicular slope is the negative reciprocal. The reciprocal of −2/5 is −5/2, and changing its sign gives 5/2. Choice −5/2 flips the fraction but keeps the sign.

  1. 22.Factor: 4x² − 25

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

    Answer: A. (2x − 5)(2x + 5)

    This is a difference of squares: (2x)² − 5² = (2x − 5)(2x + 5). Choice (2x − 5)² would expand to 4x² − 20x + 25.

More practice sets

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