# Formulas + Brain Frames

Has everything for Module 5 of the June exam

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- Created by: elliott miller
- Created on: 10-04-11 13:29

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## Pages in this set

### Page 1

Formulas and Methods for AQA Module 5/Unit 3, Grades E, D and C.

Algebra

Negative Numbers

Adding/Subtracting Multiplying Dividing

5++3=8 In brief +×+=+ +÷+=+

5+-3=2 ++ = + +×-=- +÷ -=-

5-+3=2 +- = - -×+=- -÷ +=-

5--3=8 -+ = - -×-=+ -÷ -=+

If you subtract a

--…

Algebra

Negative Numbers

Adding/Subtracting Multiplying Dividing

5++3=8 In brief +×+=+ +÷+=+

5+-3=2 ++ = + +×-=- +÷ -=-

5-+3=2 +- = - -×+=- -÷ +=-

5--3=8 -+ = - -×-=+ -÷ -=+

If you subtract a

--…

### Page 2

Finding nth terms

E.g. 4, 7, 10, 13,...

Add Positions 1 2 3 4 n

4 7 10 13 ... ?

Find differences +3 +3 +3

nth term will be 3n ± number

To find the number go back one term:

1 4 7 10 13 ... ?

-3 +3…

E.g. 4, 7, 10, 13,...

Add Positions 1 2 3 4 n

4 7 10 13 ... ?

Find differences +3 +3 +3

nth term will be 3n ± number

To find the number go back one term:

1 4 7 10 13 ... ?

-3 +3…

### Page 3

Formulas and Methods for AQA Module 5/Unit, Grades E, D and C.

Shape and Space

Area and Perimeter

Shape Diagram Area Perimeter

Rectangle A=ab P = 2a +2b

a

b Area=length × width Twice length +

twice width.

Triangle A=½bh

h

Area=half base × height

b

Parallelogram A=bh

h

Area=…

Shape and Space

Area and Perimeter

Shape Diagram Area Perimeter

Rectangle A=ab P = 2a +2b

a

b Area=length × width Twice length +

twice width.

Triangle A=½bh

h

Area=half base × height

b

Parallelogram A=bh

h

Area=…

### Page 4

Volume

Shape Diagram Formula

Cuboid

V = lwh

h

Volume = length × width × height.

l w

Cylinder

r

V=r2h

h Volume = area of circular base ×

height

Prism

Volume = area of circular base ×

height

Properties of Quadrilaterals

Shape Diagram Sides Angles Symmetries

(Reflection/Rotation)

Square All…

Shape Diagram Formula

Cuboid

V = lwh

h

Volume = length × width × height.

l w

Cylinder

r

V=r2h

h Volume = area of circular base ×

height

Prism

Volume = area of circular base ×

height

Properties of Quadrilaterals

Shape Diagram Sides Angles Symmetries

(Reflection/Rotation)

Square All…

### Page 5

Angles in Polygons

ext int

int ext

int ext

Interior Interior, Regular. Exterior, Regular

(Angles inside add up to) (Each angle) (Each angle)

Triangles: add to180o. 60o 120o

Quadrilaterals: add to 360o. 900 900

Polygon with n-sides: add to 180(n 2)o. 180(n -2) 360

n n

Angles and Parallel Lines…

ext int

int ext

int ext

Interior Interior, Regular. Exterior, Regular

(Angles inside add up to) (Each angle) (Each angle)

Triangles: add to180o. 60o 120o

Quadrilaterals: add to 360o. 900 900

Polygon with n-sides: add to 180(n 2)o. 180(n -2) 360

n n

Angles and Parallel Lines…

### Page 6

Formulas and Methods for AQA Module 5/Unit 3 Grades B, A and A*.

Algebra

Rules of Indices (powers)

m+n

a 2 × a 3 = (a × a) × (a × a × a ) = a 5 Generally a × a = a

m n

(When multiplying add the…

Algebra

Rules of Indices (powers)

m+n

a 2 × a 3 = (a × a) × (a × a × a ) = a 5 Generally a × a = a

m n

(When multiplying add the…

### Page 7

Shapes of graphs

y = mx + c y= x2 y= -x2

c

m = gradient = change in y

change in x

c = intercept.

y= x3 y= -x3 1

y=

x

Factorising Quadratics (Double Brackets)

Easy case just x2 E.g. x2 3x -10 Find 2 numbers…

y = mx + c y= x2 y= -x2

c

m = gradient = change in y

change in x

c = intercept.

y= x3 y= -x3 1

y=

x

Factorising Quadratics (Double Brackets)

Easy case just x2 E.g. x2 3x -10 Find 2 numbers…

### Page 8

Completing the square

E.g. (a) Write x2 + 4x 5 in the form (x + a)2 + b

(b) Solve the equation x2 + 4x 5 = 0

(c) Find the coordinates of the minimum value of the

curve y = x2 + 4x 5

(a) (x + 2)2 …

E.g. (a) Write x2 + 4x 5 in the form (x + a)2 + b

(b) Solve the equation x2 + 4x 5 = 0

(c) Find the coordinates of the minimum value of the

curve y = x2 + 4x 5

(a) (x + 2)2 …

### Page 9

Algebraic Fractions

Simplifying

Examples x + 4 2x + 3 2 x

+ +

3 5 x +1 2x +1

5( x + 4) + 3(2 x + 3) 2(2 x + 1) + x( x + 1)

15 ( x + 1)(2 x + 1)

5 x + 20…

Simplifying

Examples x + 4 2x + 3 2 x

+ +

3 5 x +1 2x +1

5( x + 4) + 3(2 x + 3) 2(2 x + 1) + x( x + 1)

15 ( x + 1)(2 x + 1)

5 x + 20…

### Page 10

Formulas and Methods for AQA Module 5/Unit 3 Grades B, A and A*.

Shape and Space

Dimensions

By looking at the dimensions of a formula you can workout whether it could be a length, area, volume

or inconsistent with these.

Areas must have 2 lengths multiplied together e.g. ab, r2…

Shape and Space

Dimensions

By looking at the dimensions of a formula you can workout whether it could be a length, area, volume

or inconsistent with these.

Areas must have 2 lengths multiplied together e.g. ab, r2…

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