GED Mathematical Reasoning Preparation Course: Graphs, lines and functions

1. Question 1 of 16

   In which quadrant is the point (−3, 4)?

   • AQuadrant IV
   • BQuadrant III
   • CQuadrant II
   • DQuadrant I
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   Answer: C. Quadrant II

   x is negative (left) and y is positive (up), so the point is in Quadrant II, the upper left.

2. Question 2 of 16

   What is the slope of the line through (2, 3) and (6, 11)?

   • A8
   • B2
   • C−2
   • D1/2
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   Answer: B. 2

   Slope = (y₂ − y₁) ÷ (x₂ − x₁) = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.

3. Question 3 of 16

   What is the slope of the line y = −3x + 7?

   • A−3
   • B7
   • C3
   • D−7
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   Answer: A. −3

   In y = mx + b, m is the slope. Here m = −3.

4. Question 4 of 16

   What is the y-intercept of the line 2x + y = 6?

   • A2
   • B3
   • C−2
   • D6
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   Answer: D. 6

   Solve for y: y = −2x + 6. The y-intercept is b = 6, the point (0, 6). The x-intercept is 3.

5. Question 5 of 16

   The table shows a worker's pay. The points lie on a line. What does the slope of the line mean?

   Hours worked	Pay
   1	$18
   2	$36
   3	$54
   4	$72

   • AThe worker works 18 hours
   • BThe worker started with $18
   • CPay goes up $72 each hour
   • DThe worker earns $18 per hour
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   Answer: D. The worker earns $18 per hour

   Slope = change in pay ÷ change in hours = $18 ÷ 1 hour. The slope is the unit rate: $18 per hour.

6. Question 6 of 16

   Which equation is the line through (1, 5) and (3, 9)?

   • Ay = (1/2)x + 4.5
   • By = 4x + 1
   • Cy = 2x + 3
   • Dy = 2x + 5
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   Answer: C. y = 2x + 3

   Slope = (9 − 5) ÷ (3 − 1) = 2. Use (1, 5): 5 = 2(1) + b, so b = 3. The line is y = 2x + 3.

7. Question 7 of 16

   A line has a slope of −4 and passes through (2, −1). What is its equation?

   • Ay = −4x + 7
   • By = −4x + 9
   • Cy = 4x − 9
   • Dy = −4x − 9
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   Answer: A. y = −4x + 7

   Point-slope form: y − (−1) = −4(x − 2), so y + 1 = −4x + 8 and y = −4x + 7.

8. Question 8 of 16

   Which line is parallel to y = 5x − 2?

   • Ay = −5x − 2
   • By = −(1/5)x + 3
   • Cy = 5x + 8
   • Dy = (1/5)x − 2
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   Answer: C. y = 5x + 8

   Parallel lines have the same slope. Only y = 5x + 8 has a slope of 5.

9. Question 9 of 16

   A line has the equation y = (2/3)x + 1. What is the slope of a line perpendicular to it?

   • A2/3
   • B−3/2
   • C−2/3
   • D3/2
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   Answer: B. −3/2

   Perpendicular slopes are negative reciprocals. Flip 2/3 to 3/2 and change the sign: −3/2.

10. Question 10 of 16

    Which set of ordered pairs is a function?

    • A(5, 5), (6, 1), (5, 2)
    • B(2, 1), (2, 4), (3, 5)
    • C(0, 1), (4, 2), (0, 3)
    • D(1, 3), (2, 3), (3, 5)
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    Answer: D. (1, 3), (2, 3), (3, 5)

    In a function, each input (x) has only one output (y). The other sets repeat an x with a different y. Two inputs may share an output.

11. Question 11 of 16

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

    • A28
    • B16
    • C−2
    • D10
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    Answer: D. 10

    Replace x with 3: 2(9) − 3(3) + 1 = 18 − 9 + 1 = 10. Square 3 first, then multiply by 2.

12. Question 12 of 16

    Car A goes 210 miles in 3.5 hours. Car B's distance is d = 58t, where t is hours. Which car is faster, and by how much?

    • ACar A, by 152 mph
    • BCar B, by 2 mph
    • CThey go the same speed
    • DCar A, by 2 mph
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    Answer: D. Car A, by 2 mph

    Car A's rate is 210 ÷ 3.5 = 60 mph. Car B's rate is the slope, 58 mph. 60 − 58 = 2 mph.

13. Question 13 of 16

    Function f is f(x) = 3x + 2. Function g is shown in the table. Which statement is true?

    x	g(x)
    0	5
    1	7
    2	9
    3	11

    • Af has the greater rate of change
    • Bg has the smaller y-intercept
    • CThey have the same rate of change
    • Dg has the greater rate of change
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    Answer: A. f has the greater rate of change

    f has slope 3 and y-intercept 2. In the table, g goes up 2 for each 1 in x, so its slope is 2, and its y-intercept is 5.

14. Question 14 of 16

    Where does the graph of y = x² − 4 cross the x-axis?

    • AAt x = 4 and x = −4
    • BOnly at x = 2
    • CAt x = 2 and x = −2
    • DOnly at (0, −4)
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    Answer: C. At x = 2 and x = −2

    The graph crosses the x-axis where y = 0: x² − 4 = 0, so x² = 4 and x = 2 or −2. (0, −4) is the y-intercept and lowest point.

15. Question 15 of 16

    A ball's height in feet after t seconds is h = −16t² + 64t. After how many seconds is it highest?

    • A1 second
    • B2 seconds
    • C64 seconds
    • D4 seconds
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    Answer: B. 2 seconds

    The highest point of y = ax² + bx + c is at x = −b ÷ (2a) = −64 ÷ (−32) = 2 seconds. Its height then is 64 feet.

16. Question 16 of 16

    A car is worth $24,000 when new and loses $3,000 in value each year. Which equation gives its value v after x years?

    • Av = 3,000x + 24,000
    • Bv = −24,000x + 3,000
    • Cv = 24,000 − 3,000
    • Dv = −3,000x + 24,000
    Show answer

    Answer: D. v = −3,000x + 24,000

    The value starts at $24,000 (the y-intercept) and drops $3,000 a year (a slope of −3,000).

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The real test: 145 on each GED subject