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

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= 1 4 𝑐𝑜𝑠𝜃=−2 (no solutions) 𝜃=−75.5°, 75.5° CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

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 – (-1 2 3 ) = 10 2 3 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

3 ai + bj is a vector of magnitude of 10 the direction of 2i – 4j 2𝑖 −4𝑗 = 2 2 + 4 2 = 20 2 5 𝑖−4 5 j CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

4 Solve e3x-2 = 20ex giving your answer correct to 3 decimal places 𝑒 2𝑥−2 =20 2x – 2 = ln 20 x = ln 20 +2 2 x = 2.498 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

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 = 1 y + 2 = x – 2 y = x - 4 CLICK FOR SOLUTION CLICK FOR SOLUTION www.mathsbox.org.uk

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