Formulas + Brain Frames

Has everything for Module 5 of the June exam

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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
-- = +
negative number If you multiply or divide two negative
you add. numbers the answer is positive
Powers and roots
x 2 = x × x E.g. 52 = 5 × 5 = 25 x3 = x × x × x E.g. 23 = 2 × 2 × 2 = 8
Square root: 64 = 8 or - 8 Cube root: 3 27 = 3
Because 8 × 8 = 64 and -8 × -8 = 64 Because 3 × 3 × 3 = 27
Substitution into formulas
Replace the letters by the numbers given and workout:
E.g. Find 4x + 3y when x=5, y=-7
4x + 3y Remember 4x means 4×x
= 4 × 5 + 3 × -7
=20 ­21
=-1
Linear Equations
Move all the x-terms to one side, all the numbers to the other. Remember if you move a term from one
side of the = to the other you have to change the sign. (This is the effect of doing the same to both
sides).
E.g. E.g.
4x + 7 = 3 3 y - 11 = 9 - y
4x = 3-7 3 y + y = 9 + 11
4x = -4 4 y = 20
x= -1 y=5
gdw

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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 +3 +3
nth term here is 3n + 1
Expanding Brackets
(Multiplying out or removing brackets)
Single:
E.g. 3(x + 2) = 3x + 6 E.g.…read more

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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.…read more

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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 equal All 900 4-lines/order 4
Rectangle Opposite sides equal. All 900 2-lines/order 2
Parallelogram 2-pairs of equal and 2-pairs of equal None/order 2
parallel sides and opposite
angles.
Rhombus All equal.…read more

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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.…read more

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

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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 that multiply to give the end
number but add to give the middle number.
(x ­ 5)(x + 2)
Hard case ­ E.g.…read more

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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 ­ 4 ­ 5 The "a" will always be half the number in
(x + 2)2 ­ 9 front of the x.
(x + 2)2 would give x2 + 4x +4 so you need
the -4.…read more

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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 + 6 x + 9 4x + 2 + x2 + x
15 ( x + 1)(2 x + 1)
11x + 29
x2 + 5x + 2
15
( x + 1)(2 x +…read more

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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
Volumes must have 3 lengths multiplied together e.g. abc, r2h
You can only add lengths to lengths, areas to areas, volumes to volumes. (What meaning could adding
an area to a volume have?)
E.g.…read more

Comments

daviesg


A well written revision summary of formulae for foundation and higher.  Needs the title updating for linear Mathematics.

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