2.13 Drawing and sketching of functions; interpretation of graphs Quiz: AQA Further Maths, Unit 2

The 20 questions

1. What is the y-intercept of y = x^2 − 5x + 6?

   • (0, −5)
   • (5, 0)
   • (6, 0)
   • (0, 6)

2. Where does y = x^2 − 5x + 6 cross the x-axis?

   • (−2, 0) and (−3, 0)
   • (2, 0) only
   • (0, 2) and (0, 3)
   • (2, 0) and (3, 0)

3. What is the shape of the graph of y = −x² + 4?

   • Exponential curve
   • Upright parabola
   • Inverted parabola
   • Straight line

4. What is the y-intercept of y = 3x − 2?

   • 2
   • −2
   • 3
   • −3

5. Which point does the graph of y = 2^x pass through?

   • (0, 2)
   • (0, 1)
   • (2, 0)
   • (1, 0)

6. Which lines are the asymptotes of y = 1/x?

   • x = 1 and y = 1
   • y = x and y = −x
   • y = 0 only
   • x = 0 and y = 0

7. How many points does y = x^2 − 4 share with the x-axis?

   • 0
   • 4
   • 1
   • 2

8. The graph of y = ab^x passes through (0, 3) and (2, 12), with b > 0. What is b?

   • 3
   • 2
   • 1.5
   • 4

9. Where does y = x^2 meet the line y = x, other than at the origin?

   • (2, 2)
   • (1, 1)
   • (−1, −1)
   • (1, −1)

10. A function is f(x) = x^2 for 0 ≤ x < 1, f(x) = 1 for 1 ≤ x < 2, and f(x) = 3 − x for 2 ≤ x < 3. What is f(2.5)?

    • 2.5
    • 0.25
    • 1
    • 0.5

11. A function is f(x) = x^2 for 0 ≤ x < 1, f(x) = 1 for 1 ≤ x < 2, and f(x) = 3 − x for 2 ≤ x < 3. What is the range of f(x) on 0 ≤ x < 3?

    • 0 ≤ f(x) < 3
    • 0 ≤ f(x) ≤ 1
    • 0 ≤ f(x) ≤ 3
    • 0 < f(x) ≤ 1

12. On a distance–time graph, what does the gradient represent?

    • Distance
    • Speed
    • Acceleration
    • Time

13. A straight line has the equation y = 20 − 4x. What is y when x = 3?

    • 4
    • 17
    • 12
    • 8

14. The cost of hiring is C = 5n + 20 pounds for n hours. How many hours cost £70?

    • 8
    • 10
    • 12
    • 50

15. A ball's height is h = −t^2 + 6t metres after t seconds. At what time is the height greatest?

    • 9 seconds
    • 1.5 seconds
    • 3 seconds
    • 6 seconds

16. What is the minimum value of y = (x − 1)(x + 3)?

    • −3
    • −1
    • 4
    • −4

17. How many points of intersection do y = x^2 and y = 2x − 2 have?

    • 0
    • 2
    • 3
    • 1

18. As x tends to −∞, what value does y = 2^x approach?

    • 0
    • −∞
    • 1
    • +∞

19. What are the coordinates of the vertex of y = (x − 2)^2 + 3?

    • (2, 3)
    • (2, −3)
    • (3, 2)
    • (−2, 3)

20. At which x-values do y = x^3 and y = 4x intersect?

    • 0, 4 and −4
    • ±2 only
    • 0 and 2 only
    • 0, 2 and −2

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