# Formulas + Brain Frames

Has everything for Module 5 of the June exam

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### Page 1

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

Algebra

Negative Numbers

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…

### 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=…

### 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

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)
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

### 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

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 ­…

### 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…

### 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…