# Core 1 - All you need to know

- Created by: lava-mite
- Created on: 17-10-12 19:53

First 270 words of the document:

ALL YOU NEED TO KNOW

CORE 1

1. Coordinate geometry

Always draw a diagram of the given coordinates; you will be able to

see if the gradient of a line is positive or negative so check your

calculations.

Midpoint is found by finding average of 2 x-values and 2 y-values.

To find the gradient = difference of y

difference of x

To find differences work from left to right point.

Parallel lines have same gradient.

Perpendicular gradient = -1/ gradient

Equation of line y = mx + c

Use simultaneous equations to find a point where 2 lines meet.

Lengths found using Pythagoras a2+b2 , may need to simplify surds.

Could find area of triangle if perpendicular lines, half base x height.

2. Surds

To simplify surds find the largest square number 150 25 6 5 6

Multiply by the bottom with opposite sign.

34

5 3

3 4 5 3

= the bottom is difference of squares

5 3 5 3

5 3 3 20 4 3 8 3 23

=

52 ( 3 ) 2 22

3. Completing the square

This will be in the form (x-a)2+b or a(x-b)2+c or b-(x-a)2

x 2 6x 5 (x 3) 2 32 5 (x 3) 2 14 Least value y - 14 when x -3

2x 16x 3 2[x 8x] 3 2[(x 4) 4 ] 3

2 2 2 2

2(x - 4) 2 32 3 2(x 4) 2 29 Least value y - 29 when x 4

8 10x - x 2 [x 2 10x] 8 [(x 5) 2 5 2 ] 8

- (x - 5) 2 25 8 - (x - 5) 2 33 Greatest value y 33 when x 5

Sketch the graph of the quadratic; make sure you mark the vertex (the 2

values from above) and where it cuts y axis (value from original

function).

If given 1/f(x) use y value from above.

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