1. Week 3 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
Differentiate with respect to x
(𝑥−3) 𝑥
Solve the equation
9x – 3(3x+1) = 0
Solve the equation for 0⁰ < x < 360⁰
sinx = 1 - 2cos2x
Find the area of the finite region enclosed by the curve
y = 4x – x2 and the x-axis

2. 1 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
4y = 6x y2 = 9x2 + 6x + 1
9x2 – 9x2 – 6x – 1 + 9x – 6x – 2 = 1
-3x = 4
x = − y = − 3 2
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SOLUTION
NEXT QUESTION

3. 2 Differentiate with respect to x (𝑥−3) 2 3 𝑥 𝑦= (𝑥−3) 2 3 𝑥
(𝑥−3) 𝑥
𝑦= (𝑥−3) 𝑥
= 𝑥 2 −6𝑥+9 3 𝑥
Y = 𝑥 − 2𝑥 𝑥 − 1 2
𝑑𝑦 𝑑𝑥 = 𝑥 − 1 𝑥 − 𝑥 3
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SOLUTION
NEXT QUESTION

4. 3 Solve the equation for 9x – 3(3x+1) = 0 9x – 3(3x+1) = 0
Let y = 3x y2 – 9y = 0
y(y – 9) = 0 y = 0 and y = 9
3x = 0 or 3x = 9
x = 2
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SOLUTION
NEXT QUESTION

5. 4 Solve the equation for 0⁰ < x < 360⁰ sinx = 1 - 2cos2x
sin x = 1 – 2(1 - sin2x)
2sin2x – sin x - 1 = 0
sin x = 1 or sin x = -½
x = 90⁰, 210⁰, 330⁰
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SOLUTION
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6. 5 Find the area of the finite region enclosed by the curve
y = 4x – x2 and the x-axis
4x – x2 = 0
x = 0 or x = 4
0 4 4𝑥− 𝑥 2 𝑑𝑥= 2 𝑥 2 − 1 3 𝑥 3 =
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SOLUTION
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SOLUTION

7. Week 3 Solve simultaneously 2y = 3x + 1 9x2 – 4y2 + 9x – 4y = 1
Differentiate with respect to x
(𝑥−3) 𝑥
1 2 𝑥 − 1 𝑥 − 𝑥 3
Solve the equation
9x – 3(3x+1) = 0
x = 2
Solve the equation for 0⁰ < x < 360⁰
sinx = 1 - 2cos2x
x = 90⁰, 210⁰, 330⁰
Find the area of the finite region enclosed by the curve
y = 4x – x2 and the x-axis
10 2 3