1. 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

2. 1
Solve the equation 𝑥 = 𝑥−1
( 2 −3 ) 2𝑥 = ( 2 4 ) 3𝑥−1
-6x = 4(3x -1)
x = 2 9
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SOLUTION
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3. 2 Calculate the area enclosed by the line y = 10 the curve y = x2 + 1
− − 𝑥 2 −1 𝑑𝑥 = 9𝑥 − 𝑥 3
= 36
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SOLUTION
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4. 3 Solve tan 2𝜃=−1 for 0° ≤ x < 360°
2θ = (-45⁰) , 135⁰ , 315⁰ , 495⁰, 675⁰
θ = 67.5⁰ , 157.5⁰ , 247.5⁰, 337.5⁰
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SOLUTION
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5. 4
Find the equation of the normal to the curve 𝑦= (𝑥+2) 2 𝑥 at the point where x = 1
𝑦=𝑥 𝑥 x = 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
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SOLUTION
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6. 5 Find the coefficient of the term x4 in the expansion of
(x – 4)(1 + 2x)7
x × 7C3 × (2x) × 7C4 × (2x)4
-1960 x4
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SOLUTION
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SOLUTION

7. 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