1. Week 6 If sin θ= 5 13 and θ is acute, find the value of cos θ
Solve for n log 4 𝑛 log 4 𝑛 =2
Simplify − 1 1− 2
Find the coordinates of the local minimum point of
y = x3 + 3x2 + 72
If 𝑑𝑦 𝑑𝑥 = 𝑥 and the curve y = f(x) passes through the point (1,1), find f(x)

2. 1
If sin θ= and θ is acute, find the value of cos θ
13 2 − 5 2 = 𝑐𝑜𝑠𝜃=
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3. 2 Solve for n log 4 𝑛+6 + log 4 𝑛 =2 log 4 𝑛(𝑛+6 ) = log 4 16
n2 + 6n = 16
n2 + 6n – 16 = 0
(n + 8)(n – 2) = 0
n = -8 (no solution)
n = 2
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4. 3
Simplify − 1 1− 2
(3+ 2 )( 2 −1) ( 2 +1)( 2 −1) − −
− −1− 2
=3 2
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5. 4 Find the coordinates of the local minimum point of y = x3 + 3x2 + 72
𝑑𝑦 𝑑𝑥 =3 𝑥 2 +6𝑥 𝑑 2 𝑦 𝑑 𝑥 2 =6𝑥+6
3 𝑥 2 +6𝑥=0
3𝑥 𝑥+2 =0
x = 0 or x = -2 x = 𝑑 2 𝑦 𝑑 𝑥 2 > 0 minimum
(0, 72)
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SOLUTION
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6. 5
If 𝑑𝑦 𝑑𝑥 = 𝑥 and the curve y = f(x) passes through the point (1,1), find f(x)
𝑦= 𝑥 4 𝑑𝑥 = 3𝑥 − 4 𝑥 3 +𝑐
x = 1 , y = 1 3− 4 1 +𝑐 = 1
c = 2
𝑓 𝑥 =3𝑥 − 4 𝑥 3 +2
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SOLUTION
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SOLUTION

7. Week 6 If sin θ= 5 13 and θ is acute, find the value of cos θ
12 13
Solve for n log 4 𝑛 log 4 𝑛 =2
n = 2
Simplify − 1 1− 2
3 2
Find the coordinates of the local minimum point of
y = x3 + 3x2 + 72
(0, 72)
If 𝑑𝑦 𝑑𝑥 = 𝑥 and the curve y = f(x) passes through the point (1,1), find f(x)
𝑓 𝑥 =3𝑥 − 4 𝑥 3 +2