A16 recognise and use the equation of a circle with centre at the origin Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. The equation of a circle with centre at the origin and radius r is

   • x^2 + y^2 = r^2
   • x^2 - y^2 = r^2
   • (x - r)^2 + y^2 = 1
   • x + y = r

2. The radius of the circle x^2 + y^2 = 49 is

   • 49
   • -7
   • 24.5
   • 7

3. How does a circle's tangent relate to the radius at the point of contact?

   • Equal length
   • Parallel
   • Perpendicular
   • Bisecting

4. Which point lies on the circle x^2 + y^2 = 25?

   • (5, 5)
   • (3, 4)
   • (3, 3)
   • (2, 2)

5. A circle with centre at the origin passes through (0, 6). Its radius is

   • 6
   • 12
   • 36
   • 3

6. The point (1, 2) relative to the circle x^2 + y^2 = 10 is

   • at the centre
   • inside the circle
   • on the circle
   • outside the circle

7. Which equation describes a circle with centre at the origin?

   • (x - 1)^2 + y^2 = 16
   • x^2 + (y + 2)^2 = 4
   • x^2 + y = 16
   • x^2 + y^2 = 16

8. A tangent to a circle meets the circle at

   • no points
   • the centre
   • exactly one point
   • two points

9. The point (-5, 12) lies on a circle centred at the origin. The radius is

   • 17
   • 13
   • 7
   • 169

10. A circle centred at the origin passes through (6, -8). Its radius is

    • 100
    • 14
    • 10
    • 48

11. The point (4, y) with y > 0 lies on x^2 + y^2 = 25. Then y =

    • 3
    • 4
    • 9
    • 21

12. Which point lies on the circle x^2 + y^2 = 50?

    • (6, 6)
    • (1, 7)
    • (5, 6)
    • (4, 5)

13. The point (2, p) with p > 0 lies on x^2 + y^2 = 13. Then p =

    • 9
    • 11
    • 3
    • 5

14. The gradient of the radius from the origin to (3, 4) is

    • 4/3
    • 7
    • -4/3
    • 3/4

15. The gradient of the tangent to x^2 + y^2 = 25 at (3, 4) is

    • -4/3
    • -3/4
    • 3/4
    • 4/3

16. The tangent to x^2 + y^2 = 25 at (0, 5) is

    • x = 0
    • x = 5
    • y = 5
    • y = 0

17. The equation of the tangent to x^2 + y^2 = 25 at (3, 4) is

    • 3x + 4y = 5
    • 3x + 4y = 25
    • 3x - 4y = 25
    • 4x + 3y = 25

18. The line y = x + 5 and the circle x^2 + y^2 = 25 share how many points?

    • one
    • none
    • two
    • infinitely many

19. The points where x^2 + y^2 = 25 meets the x-axis have x =

    • x = 12.5
    • x = 0 only
    • x = 25
    • x = 5 or x = -5

20. What are the x-coordinates where y = 2x meets x^2 + y^2 = 20?

    • 10 and -10
    • sqrt(20) and -sqrt(20)
    • 4 and -4
    • 2 and -2

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