1.1 Unit 1 revision Q 1 What is the perpendicular bisector of a line ?

Answer to Unit 1 revision Q 1 A line which cuts the given line in half at 90 o

1.1 Unit 1 revision Q 2 How do you find the median AM of triangle ABC ?

Answer to Unit 1 revision Q 2 (i)find the mid point of BC. Call it M (ii)find the gradient of AM (iii)use y-b = m(x-a) A BC M

1.1 Unit 1 revision Q 3 What is the gradient of a vertical line ?

Answer to Unit 1 revision Q 3 undefined x y

1.1 Unit 1 revision Q 4 How do you find where two lines intersect ?

Answer to Unit 1 revision Q 4 Simultaneous equations

1.1 Unit 1 revision Q 5 What two things do you require in order to find the equation of a straight line ?

Answer to Unit 1 revision Q 5 The gradient of the line and a point on the line x y (a,b) m 1

1.1 Unit 1 revision Q 6 What is the general equation of a straight line passing through (a,b) with gradient m ? x y (a,b)

Answer to Unit 1 revision Q 6 y – b = m(x – a) x y (a,b)

1.1 Unit 1 revision Q 7 How do you find the gradient of a line, given the angle the line makes with the positive direction of the x-axis ?

Answer to Unit 1 revision Q 7 m = tan Θ x yΘ

1.1 Unit 1 revision Q 8 What is the gradient of a horizontal line ?

Answer to Unit 1 revision Q 8 0 x y

1.1 Unit 1 revision Q 9 What is an altitude of a triangle ?

Answer to Unit 1 revision Q 9 A line from a vertex, perpendicular to the opposite side

1.2 Unit 1 revision Q 10 How do you change from degrees to radians ?

Answer to Unit 1 revision Q 10 Divide by 180 and multiply by π

1.2 Unit 1 revision Q 11 What is an equivalent expression for y = a x using logs ?

Answer to Unit 1 revision Q 11 x = log a y

1.2 Unit 1 revision Q 12 How do you solve an equation like 3sinx+1 = 0 ?

Answer to Unit 1 revision Q 12 (i) rearrange to sinx = (ii) decide on 2 quadrants (iii) ignore any –ve and press INV sin to get angle (iv) work out two answers

1.2 Unit 1 revision Q 13 How do you draw the graph of 3+f(x) given the graph of f(x) ?

Answer to Unit 1 revision Q 13 move graph up 3

1.2 Unit 1 revision Q 14 How do you find the exact values of sin x or tan x given cos x = a ? b

Answer to Unit 1 revision Q 14 (i) draw triangle (ii) use Pythagoras to fill in missing side (iii) read values off triangle using SOHCAHTOA a b x

1.2 Unit 1 revision Q 15 How do you draw the graph of –f(x) given the graph of f(x) ?

Answer to Unit 1 revision Q 15 Reflect the graph in the x-axis

1.2 Unit 1 revision Q 16 Which two points does the graph of y = log a x always pass through ?

Answer to Unit 1 revision Q 16 (1,0) and (a,1)

1.3 Unit 1 revision Q 17 If f(x) = x n then what is f ’ (x) ?

Answer to Unit 1 revision Q 17 nx n-1

1.3 Unit 1 revision Q 18 How do you show that a curve is always decreasing?

Answer to Unit 1 revision Q 18 (i) differentiate (ii) show that f’(x) is always negative e.g. –(x+a) 2, x = a

1.3 Unit 1 revision Q 19 For a curve, how do you find the stationary points and their nature ?

Answer to Unit 1 revision Q 19 (i)differentiate (ii)let f’(x) = 0 (iii)solve to find stationary points (iv)find y-coordinates (v)draw nature table

1.4 Unit 1 revision Q 20 How do you know when a recurrence relation of the form u n+1 = au n + b converges ?

Answer to Unit 1 revision Q < a < 1