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

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 90o

1.1

Unit 1 revision Q 2

•How do you find the median AM of triangle ABC ?


•(i) find the mid pointof BC. Call it M

(ii) find the gradient of AM(iii) use y-b = m(x-a)

A

BCM

1.1

Unit 1 revision Q 3

•What is the gradient of a vertical line ?


•undefined

x

y

1.1

Unit 1 revision Q 4

•How do you find where two lines intersect ?


•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 ?


•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 thegeneral equationof a straightline passingthrough (a,b)with gradient m ?

x

y

(a,b)


•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 ?


•m = tan Θ

x

y

ΘΘ

1.1

Unit 1 revision Q 8

•What is the gradient of a horizontal line ?


•0

x

y

1.1

Unit 1 revision Q 9

•What is an altitude of a triangle ?


•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 ?


•Divide by 180 and multiply by π

1.2


•What is an equivalent expression fory = ax

using logs ?


•x = logay

1.2


•How do you solve an equation like3sinx+1 = 0 ?


•(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


•How do you draw the graph of 3+f(x) given the graph of f(x) ?


•move graph up 3

1.2


•How do you find the exact values of sin x or tan x givencos x = a ?

b


•(i) draw triangle(ii) use Pythagoras

to fill in missing side(iii) read values off triangle using SOHCAHTOA

a

b

xx

1.2


•How do you draw the graph of –f(x) given the graph of f(x) ?


•Reflect the graph in the x-axis

1.2


•Which two points does the graph of y = logax always pass through ?


•(1,0) and (a,1)

1.3


•If f(x) = xn

then what isf’(x) ?


•nxn-1

1.3


•How doyou showthat a curveis always decreasing?


• (i) differentiate(ii) show that f’(x)

is always negative e.g. –(x+a)2 , x = a

1.3


•For a curve, how do you find the stationary points and their nature ?


(i) differentiate(ii) let f’(x) = 0(iii) solve to find

stationary points(iv) find y-coordinates(v)draw nature table

1.4


•How do you know when a recurrence relation of the form un+1 = aun + b converges ?


•-1 < a < 1

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