Week 5 Solve the equation 1 8 2𝑥 = 16 3𝑥−1 Calculate the area enclosed by the line y = 10 the curve y = x2 + 1 Solve tan 2𝜃=−1 for 0° ≤ x < 360° Find the equation of the normal to the curve 𝑦= (𝑥+2) 2 𝑥 at the point where x = 1 Find the coefficient of the term x4 in the expansion of (x – 4)(1 + 2x)7

1 Solve the equation 1 8 2𝑥 = 16 3𝑥−1 ( 2 −3 ) 2𝑥 = ( 2 4 ) 3𝑥−1 -6x = 4(3x -1) x = 2 9 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

2 Calculate the area enclosed by the line y = 10 the curve y = x2 + 1 −3 3 10 − 𝑥 2 −1 𝑑𝑥 = 9𝑥 − 1 3 𝑥 3 = 36 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

3 Solve tan 2𝜃=−1 for 0° ≤ x < 360° 2θ = (-45⁰) , 135⁰ , 315⁰ , 495⁰, 675⁰ θ = 67.5⁰ , 157.5⁰ , 247.5⁰, 337.5⁰ CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

4 Find the equation of the normal to the curve 𝑦= (𝑥+2) 2 𝑥 at the point where x = 1 𝑦=𝑥+4+ 4 𝑥 x = 1 y = 9 𝑑𝑦 𝑑𝑥 =1− 4 𝑥 2 Gradient of tangent = -3 Gradient of the normal = 1 3 y – 9 = 1 3 (x -1) 3y = x + 26 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

5 Find the coefficient of the term x4 in the expansion of (x – 4)(1 + 2x)7 x × 7C3 × (2x)3 - 4 × 7C4 × (2x)4 -1960 x4 CLICK FOR SOLUTION CLICK FOR SOLUTION www.mathsbox.org.uk

Week 5 Solve the equation 1 8 2𝑥 = 16 3𝑥−1 x = 2 9 Calculate the area enclosed by the line y = 10 the curve y = x2 + 1 = 36 Solve tan 2𝜃=−1 for 0° ≤ x < 360° θ = 67.5⁰ , 157.5⁰ , 247.5⁰, 337.5⁰ Find the equation of the normal to the curve 𝑦= (𝑥+2) 2 𝑥 at the point where x = 1 3y = x + 26 Find the coefficient of the term x4 in the expansion of (x – 4)(1 + 2x)7 -1960 x4