1. Week 7
Solve 4sin2θ - 2 = 7cos θ for -180° ≤ θ < 180° correct to 3 significant figures
Find the area enclosed by y = x2 + 2 and the line y = 2x + 5
ai + bj is a vector of magnitude of 10 the direction of 2i – 4j
Solve e3x-2 = 20ex giving your answer correct to 3 decimal places
P(2, -2) lies on the circle x2 + y2 + 4(x - y) = 24
Find the equation of the tangent to the circle of P

2. 1 4 1− 𝑐𝑜𝑠 2 𝜃 −2=7𝑐𝑜𝑠𝜃 2−4 𝑐𝑜𝑠 2 𝜃=7𝑐𝑜𝑠𝜃 4 𝑐𝑜𝑠 2 𝜃+7𝑐𝑜𝑠𝜃−2=0
Solve 4sin2θ - 2 = 7cos θ for -180° ≤ θ < 180° correct to 3 significant figures
4 1− 𝑐𝑜𝑠 2 𝜃 −2=7𝑐𝑜𝑠𝜃
2−4 𝑐𝑜𝑠 2 𝜃=7𝑐𝑜𝑠𝜃
4 𝑐𝑜𝑠 2 𝜃+7𝑐𝑜𝑠𝜃−2=0
𝑐𝑜𝑠𝜃= 𝑐𝑜𝑠𝜃=−2 (no solutions)
𝜃=−75.5°, 75.5°
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SOLUTION
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3. 2 Find the area enclosed by y = x2 + 2 and the line y = 2x + 5
x2 + 2 = 2x + 5
x2 - 2x - 3 = 0
(x – 3)(x + 1) = 0
x = -1 and x = 3
−1 3 2𝑥+5 − 𝑥 2 −2 𝑑𝑥 = 𝑥 2 +3𝑥 − 1 3 𝑥 3 = 9 – ( ) =
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4. 3
ai + bj is a vector of magnitude of 10 the direction of 2i – 4j
2𝑖 −4𝑗 =
= 20
2 5 𝑖−4 5 j
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SOLUTION
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5. 4
Solve e3x-2 = 20ex giving your answer correct to 3 decimal places
𝑒 2𝑥−2 =20
2x – 2 = ln 20
x = ln
x = 2.498
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SOLUTION
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6. 5 P(2, -2) lies on the circle x2 + y2 + 4(x - y) = 24
Find the equation of the tangent to the circle of P
(𝑥+2) 2 + (𝑦−2) 3 − 8=24
Centre of the circle (-2, 2)
Gradient of the normal = -1
Gradient of the tangent = y + 2 = x – 2
y = x - 4
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SOLUTION
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SOLUTION

7. Week 7
Solve 4sin2θ - 2 = 7cos θ for -180° ≤ θ < 180° correct to 3 significant figures
𝜃=−75.5°, 75.5°
Find the area enclosed by y = x2 + 2 and the line y = 2x + 5
10 2 3
ai + bj is a vector of magnitude of 10 the direction of 2i – 4j
2 5 𝑖−4 5 j
Solve e3x-2 = 20ex giving your answer correct to 3 decimal places
x = 2.498
P(2, -2) lies on the circle x2 + y2 + 4(x - y) = 24
Find the equation of the tangent to the circle of P
y = x - 4