1. Week 2
Given that the equation 4x2 – kx + k – 3 = 0, where k is a constant, has real roots find the range of values of k
Given that cos θ = 2 −1 find the value of sin2θ in the form a + b 2
A curve has equation 𝑦=𝑥+ 4 𝑥 . Point A on the curve has an x coordinate of 1. Find the x- coordinate of the point at which the normal to the curve at point A intersects the x- axis.
Solve for n
2 log 𝑎 𝑛 − log 𝑎 3−𝑛 = log 𝑎 4
Describe the transformation that maps the graph of y = 2x
on to 𝑦= 𝑥

2. 1
Given that the equation 4x2 – kx + k – 3 = 0, where k is a constant, has real roots find the range of values of k
−𝑘 2 −4×4× 𝑘−3 ≥0
𝑘 2 −16𝑘+48≥0
𝑘≤4 𝑜𝑟 𝑘≥12
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SOLUTION
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3. 2 Given that cos θ = 2 −1 find the value of sin2θ in the form a + b 2
𝑐𝑜𝑠 2 𝜃= 2 −1 2
= 3 −2 2
𝑠𝑖𝑛 2 𝜃=1 − 𝑐𝑜𝑠 2 𝜃
= 1− (3 −2 2 )
= −2
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SOLUTION
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4. 3
A curve has equation 𝑦=𝑥+ 4 𝑥 . Point A on the curve has an x coordinate of 1. Find the x- coordinate of the point at which the normal to the curve at point A intersects the x- axis.
𝑥=1 𝑦=5 𝐴 1, 5
𝑑𝑦 𝑑𝑥 =1− 4 𝑥 x = 1 𝑑𝑦 𝑑𝑥 = -3
Gradient of normal at A is 1 3
Equation of the normal (y - 5) = (x - 1)
3y = x + 14
y = x = -14
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SOLUTION
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5. 4 Solve for n 2 log 𝑎 𝑛 − log 𝑎 3−𝑛 = log 𝑎 4 log 𝑎 𝑛 2 3−𝑛 = log 𝑎 4
𝑛 2 3−𝑛 =4
n2 + 4n – 12 =0
n = 2 (n = -6 not possible)
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SOLUTION
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6. 5 Describe the transformation that maps the graph of y = 2x
on to 𝑦= 𝑥
1 2 𝑥 = 2 −𝑥
Reflection in the y - axis
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SOLUTION
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SOLUTION

7. Week 2
Given that the equation 4x2 – kx + k – 3 = 0, where k is a constant, has real roots find the range of values of k
𝑘≤4 𝑜𝑟 𝑘≥12
Given that cos θ = 2 −1 find the value of sin2θ in the form a + b 2
2 2 −2
A curve has equation 𝑦=𝑥+ 4 𝑥 . Point A on the curve has an x coordinate of 1. Find the x- coordinate of the point at which the normal to the curve at point A intersects the x- axis.
x = -14
Solve for n
2 log 𝑎 𝑛 − log 𝑎 3−𝑛 = log 𝑎 4
n = 2
Describe the transformation that maps the graph of y = 2x
on to 𝑦= 𝑥
Reflection in the y - axis