3.1 Know and use the definition of a gradient Quiz: AQA Further Maths, Unit 3

The 20 questions

1. Which formula calculates the gradient of a straight line between two points?

   • (y2 + y1) / (x2 + x1)
   • (x2 - x1) / (y2 - y1)
   • (y2 - y1) / (x2 - x1)
   • (y2 - y1) * (x2 - x1)

2. Which expression gives the gradient of a line through (x1, y1) and (x2, y2)?

   • (y2 - y1) / (x2 - x1)
   • (y2 - x2) / (y1 - x1)
   • (y1 + y2) / (x1 + x2)
   • (x2 - x1) / (y2 - y1)

3. A line slopes upwards from left to right. What is the sign of its gradient?

   • Positive
   • Zero
   • Negative
   • Undefined

4. What is the gradient of a horizontal line?

   • 0
   • -1
   • Undefined
   • 1

5. What is the gradient of a vertical line?

   • Undefined
   • 1
   • 0
   • -1

6. Find the gradient of the line through (0, 3) and (4, 11).

   • 8
   • 2
   • 0.5
   • 3

7. Find the gradient of the line through (-2, 5) and (3, -5).

   • 2
   • -0.5
   • -2
   • -10

8. Find the gradient of the line through (2, -1) and (6, 3).

   • 1
   • 4
   • -1
   • 0.25

9. A ramp rises 3 m over a horizontal distance of 12 m. What is its gradient?

   • 4
   • 0.75
   • 0.25
   • 0.125

10. A line passes through (0, 0) and (3, -9). Find its gradient.

    • -3
    • -9
    • 3
    • -0.33

11. The gradient of a line is 4. How much does y change when x increases by 2?

    • 0.5
    • 6
    • 2
    • 8

12. How does the gradient of a straight line change along its entire length?

    • It decreases
    • It fluctuates
    • It stays constant
    • It increases

13. A line has gradient -3/4 and passes through the origin. Which other point lies on it?

    • (4, -3)
    • (-4, -3)
    • (3, 4)
    • (4, 3)

14. A line through A(2, k) and B(6, 10) has gradient 3. Find k.

    • 2
    • -2
    • 14
    • -6

15. Find the gradient of the line through (-1, -4) and (2, 5).

    • 9
    • 3
    • -3
    • 1/3

16. A straight line passes through (0, -2) and (5, 3). What is its gradient?

    • 5
    • 1
    • -1
    • 0.2

17. Points P(1, 2), Q(4, a) and R(7, 8) lie on one straight line. Find a.

    • 5
    • 4
    • 6
    • 3

18. The line through (3, p) and (9, 5) has gradient 1/2. Find p.

    • 8
    • 1
    • -2
    • 2

19. A line has gradient 2 and passes through (1, 4). What is the y-coordinate of the point on the line where x = 5?

    • 14
    • 12
    • 6
    • 10

20. The gradient of AB is 3, where A(-1, 2) and B(b, 14). Find b.

    • -3
    • 4
    • 11
    • 3

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