5.6.1 Double angle and half angle formulae Quiz: Pearson Edexcel Maths, Unit 5

The 20 questions

1. What is the double angle formula for sin(2A)?

   • cos^2A - sin^2A
   • 2cos^2A - 1
   • 1 - 2sin^2A
   • 2sinAcosA

2. Which expression is NOT a valid form of cos(2A)?

   • 1 - 2sin^2A
   • 1 - 2cos^2A
   • cos^2A - sin^2A
   • 2cos^2A - 1

3. What is the double angle formula for tan(2A)?

   • 2tan^2A / (1 - tanA)
   • 2tanA / (1 + tan^2A)
   • tan^2A / (1 - tanA)
   • 2tanA / (1 - tan^2A)

4. Rewrite cos(2x) using only sine functions.

   • 2sin^2x - 1
   • cos^2x - sin^2x
   • 1 - 2sin^2x
   • 2cos^2x - 1

5. Rewrite cos(2θ) using only cosine functions.

   • 2cos^2θ + 1
   • 1 - 2cos^2θ
   • 2cos^2θ - 1
   • cos^2θ - sin^2θ

6. Express sin^2(x) in terms of cos(2x) using a half angle rearrangement.

   • (1 + cos(2x)) / 2
   • (1 - cos(2x)) / 2
   • 1 - cos(2x)
   • (1 - sin(2x)) / 2

7. Express cos^2(x) in terms of cos(2x) using a half angle identity.

   • (1 + sin(2x)) / 2
   • 1 + cos(2x)
   • (1 + cos(2x)) / 2
   • (1 - cos(2x)) / 2

8. What is the exact value of 2sin(22.5)cos(22.5)?

   • 1
   • 1 / 2
   • 1 / sqrt(2)
   • sqrt(3) / 2

9. Simplify cos^2(15) - sin^2(15) to an exact value.

   • 1 / sqrt(2)
   • 1 / 2
   • sqrt(3) / 2
   • sqrt(3)

10. Evaluate (2tan(22.5)) / (1 - tan^2(22.5)).

    • sqrt(3)
    • 1
    • 1 / sqrt(2)
    • 0

11. What is the maximum value of the expression 4cos(2x)?

    • 4
    • 1
    • 8
    • 2

12. Solve 2sin(x)cos(x) = 1/2 for 0 <= x < 90 in degrees.

    • 30
    • 45
    • 15
    • 75

13. Solve cos^2(x) - sin^2(x) = 1/2 for 0 <= x < 90 in degrees.

    • 15
    • 30
    • 45
    • 60

14. Find the exact integral of cos^2(x) with respect to x using a double angle identity.

    • sin(2x)/2 + C
    • x/2 - sin(2x)/4 + C
    • x/2 + sin(2x)/4 + C
    • sin^3(x)/3 + C

15. What substitution is used to integrate sin^2(x)?

    • (1 + cos(2x)) / 2
    • 1 - sin^2(x)
    • (1 - cos(2x)) / 2
    • 2sin(x)cos(x)

16. Express cos(4θ) in terms of double angles using cos(2A).

    • 2cos^2(2θ) - 1
    • 1 - 2sin^2(4θ)
    • cos^2(2θ) - sin^2(2θ)
    • 4cos^2(θ) - 2

17. Which identity helps express sin(3θ) using sin(θ)?

    • Factor theorem
    • Half angle
    • Compound angle
    • Pythagorean

18. Find the minimum value of 3 - 2cos(2x).

    • 5
    • 1
    • 3
    • -1

19. Express sin(2x) in terms of tan(x) using the appropriate identity.

    • 2tan(x) / (1 - tan^2(x))
    • 2tan(x) / (1 + tan^2(x))
    • 2tan^2(x) / (1 + tan(x))
    • tan(x) / (1 + tan^2(x))

20. What is the exact value of cos^2(75) - sin^2(75) in surd form?

    • sqrt(3)/2
    • 1/2
    • -sqrt(3)/2
    • -1/2

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