3.2 Know the relationship between the gradients of parallel and perpendicular lines Quiz: AQA Further Maths, Unit 3

The 20 questions

1. What is the relationship between the gradients of two parallel lines?

   • They sum to 0
   • They multiply to 1
   • They are equal
   • They multiply to -1

2. What is the product of the gradients of two non-vertical perpendicular lines?

   • 1
   • 0
   • -1
   • 0.5

3. A line has gradient 3. What is the gradient of a line perpendicular to it?

   • 3
   • 1/3
   • -1/3
   • -3

4. A line has gradient -2/5. What is the gradient of a parallel line?

   • 5/2
   • -2/5
   • 2
   • 2/5

5. What gradient does a line perpendicular to y = 0.5x + 1 have?

   • -0.5
   • 0.5
   • 2
   • -2

6. Line L has gradient 4. Which gradient belongs to a line perpendicular to L?

   • -1/4
   • 4
   • -4
   • 1/4

7. Which line is parallel to y = 2x + 5?

   • y = 2x - 3
   • y = -2x + 5
   • y = x/2 + 5
   • y = -x/2 + 1

8. Which pair of gradients belongs to two perpendicular lines?

   • 5 and 5
   • 5 and -5
   • 5 and -1/5
   • 5 and 1/5

9. In triangle ABC with vertices A(0, 2), B(4, 6) and C(10, 0), which angle is a right angle?

   • Angle ACB
   • Angle CAB
   • Angle ABC
   • Angle BAC

10. A(1, 1) and B(3, 5) lie on a line of gradient 2. What is the gradient of a line perpendicular to AB?

    • -2
    • -1/2
    • 1/2
    • 2

11. Which line is perpendicular to 3x + 2y = 6?

    • 2x + 3y = 1
    • 3x + 2y = 1
    • 3x - 2y = 6
    • 2x - 3y = 1

12. Lines y = mx + 1 and y = 4x - 7 are perpendicular. Find m.

    • -4
    • -1/4
    • 1/4
    • 4

13. The line through (0, 0) and (2, k) is perpendicular to a line of gradient 2. Find k.

    • 1
    • -1
    • -4
    • 4

14. How are a horizontal line and a vertical line geometrically related?

    • They are identical
    • They never intersect
    • They are parallel
    • They are perpendicular

15. Line AB has gradient 0.75 and line CD has gradient -4/3. How are they related?

    • They are perpendicular
    • They are parallel
    • They are identical
    • They intersect at 45°

16. A line passes through (2, 5) and is parallel to y = -3x + 1. Which equation describes it?

    • y = -3x + 11
    • y = -3x - 1
    • y = -x/3 + 11
    • y = 3x + 11

17. A line through (-1, 4) is perpendicular to y = 2x. Where does it cross the y-axis?

    • 2
    • -0.5
    • 3.5
    • 4

18. Triangle P(0, 0), Q(4, 0), R(a, 3) has a right angle at Q. Find a.

    • -4
    • 3
    • 0
    • 4

19. The line through (0, 1) and (2, 5) is L1. Line L2 is perpendicular to L1 and passes through (0, 1). Where does L2 cross the x-axis?

    • x = 0.5
    • x = 2
    • x = 1
    • x = -2

20. A line with gradient 3/4 passes through (-4, 1). Which point lies on the perpendicular line through the origin?

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

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