1. Find the equation of the line parallel to the given line which passes through the given point. Give your answer in the form ay+bx=c
- 3x-4y=12 through (4,-1)
- 5y-2x=10 through (-4,2)
- 3x+5y=12 through (5,0)
- 4x+2y=5 through (1,1)
[8 marks]
2. Find the equation of the line perpendicular to the given line which passes through the given point. Give your answer in the form ay+bx+c=0
- 2x+3y=6 through (6,1)
- 3y-4x=5 through (-4,-3)
- 5y+3x=8 through (2,0)
- 4x-2y=3 through (1,0)
[8 marks]
3.
- Find the values of x for which the gradient is 0
- Draw a tangent line at x=1 and use this to estimate the gradient
[4 marks]
4.
- Find the value of x for which the gradient is 0
- Draw a tangent line at x=2 and use this to estimate the gradient
[4 marks]
5. Start by expanding (x+h)^2 and subsequently multiplying by (x+h) to find an expression for (x+h)^5. Use the result to find the gradient function for y=x^5
[5 marks]
6. Find the gradient funtion for y=x^2+x by looking at the limit of the following as h\rightarrow 0 \dfrac{(x+h)^2+(x+h)-(x^2+x)}{h}
[5 marks]
7. Can you conjecture a result about the gradient function for y=x^n? Can you prove this result?
[6 marks]
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