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• NUMBER

Definitions

Integer, sum, product, factor, prime, HCF, LCF, prime factor, square number

• Definition to term 
• Term to definition 

Fractions: equivalent, mixed, improper, proper, numerator, denominator, common denom, reciprocal

• Definition to term 
• Term to definition 

Decimals: recurring, terminating, irrational, rational, surd, dps, sig figs, standard form

• Definition to term 
• Term to definition 

Misc. number terms

• Definition to term 
• Term to definition 

Tables practice

Multiplication tables

• 10×
• 11×
• 12×
• 0× to 5×
• 6× to 9×
• 0× to 10×

Four operations - basic

• Addition (+ve to 10)
• Addition (±ve to 10)

Subtraction

• (+ve to 10)
• (±ve to 10)
• (2-digit)
• (3-digit)
• (4-digit)

Multiplication

• (+ve to 10)
• (±ve to 10)

Division

• Division (+ve to 10)
• Division (±ve to 10)

Multiplication methods

Integer multiplication - any method

• 2 digit x 2 digit
• 3 digit x 2 digit
• 4 digit x 2 digit
• 3 digit x 3 digit
• 4 digit x 3 digit

Decimal multiplication - any method

• 2 digit x 2 digit
• 3 digit x 2 digit
• 4 digit x 2 digit
• 3 digit x 3 digit
• 4 digit x 3 digit

Long multiplication

• 2 digit x 2 digit
• 3 digit x 2 digit
• 4 digit x 2 digit
• 3 digit x 3 digit
• 4 digit x 3 digit

Lattice multiplication - integers

• 2 digit x 2 digit
• 3 digit x 2 digit
• 4 digit x 2 digit
• 3 digit x 3 digit
• 4 digit x 3 digit
• 5 digit x 3 digit
• 4 digit x 4 digit
• 5 digit x 4 digit
• 6 digit x 4 digit
• Misc to 3x3 digits
• Misc over 3x3 digits

Lattice multiplication - decimals

• 2 digit x 2 digit
• 3 digit x 2 digit
• 4 digit x 2 digit
• 3 digit x 3 digit
• 4 digit x 3 digit
• 5 digit x 3 digit
• 4 digit x 4 digit
• 5 digit x 4 digit
• 6 digit x 4 digit
• Misc to 3x3 digits
• Misc over 3x3 digits

Grid multiplication - integers

• 2 digit x 1 digit
• 3 digit x 1 digit
• 2 digit x 2 digit
• 3 digit x 2 digit

Divisibility tests

Basic

• Divisibility by 2
• Divisibility by 3
• Divisibility by 4
• Divisibility by 5
• Divisibility by 6
• Divisibility by 9
• Divisibility by 10
• Divisibility by 2,5,10
• Divisibility by 2,3,4,5,6,9,10

Medium

• Divisibility by 8
• Divisibility by 11
• Divisibility by 12
• Divisibility by 15
• Divisibility by 18
• Divisibility by 25
• Divisibility by 8,11,12,15,18,25

Division methods

Integer short division - no remainder

• 3 digit ÷ 2-5
• 3 digit ÷ 6-9
• 3 digit ÷ 2-9
• 4 digit ÷ 2-5
• 4 digit ÷ 6-9
• 4 digit ÷ 2-9
• 5 digit ÷ 2-5
• 5 digit ÷ 6-9
• 5 digit ÷ 2-9
• 6 digit ÷ 2-5
• 6 digit ÷ 6-9
• 6 digit ÷ 2-9

Decimal short division

• 3 digit ÷ 2-5
• 3 digit ÷ 6-9
• 3 digit ÷ 2-9
• 4 digit ÷ 2-5
• 4 digit ÷ 6-9
• 4 digit ÷ 2-9
• 5 digit ÷ 2-5
• 5 digit ÷ 6-9
• 5 digit ÷ 2-9
• 6 digit ÷ 2-5
• 6 digit ÷ 6-9
• 6 digit ÷ 2-9

BIDMAS and Factors

BIDMAS

• Add/subtract +ve numbers
• Add/subtract ±ve numbers
• Multiply/divide +ve numbers
• Multiply/divide ±ve numbers
• Combined operations 1: +ve numbers
• Combined operations 1: ±ve numbers
• Combined operations 2: +ve numbers
• Combined operations 2: ±ve numbers

Factors

• List all factors
• Express as product of primes
• HCF
• LCM

Fractions

Cancelling down fractions

• Easy
• Medium
• Hard
• Misc

Equivalent fractions

• Easy

Converting fractions

• Top-heavy to mixed
• Mixed to top-heavy
• Misc

• Addition: ³/₇ + ²/₇
• Subtraction: ³/₇ - ²/₇
• Add/Sub: ³/₇ ± ²/₇
• Addition: ³/₇ + ²/₂₁
• Subtraction: ³/₇ - ²/₂₁
• Add/Sub: ³/₇ ± ²/₂₁
• Addition: ¹/₂ + ²/₇
• Subtraction: ¹/₂ - ²/₇
• Add/Sub: ¹/₂ ± ²/₇
• Addition: 4³/₇ + 1²/₂₁
• Subtraction: 4³/₇ - 1²/₂₁
• Add/Sub: 4³/₇ ± 1²/₂₁
• Addition: 4¹/₂ + 1²/₇
• Subtraction: 4¹/₂ - 1²/₇
• Add/Sub: 4¹/₂ ± 1²/₇

Multiplying/dividing fractions

• Multiplication: ¹/₂ × ³/₇
• Division: ¹/₂ ÷ ³/₇
• Mult/Div: ¹/₂ ×/÷ ³/₇
• Multiplication: 3¹/₂ × ³/₇
• Division: 3¹/₂ ÷ ³/₇
• Mult/Div: 3¹/₂ ×/÷ ³/₇
• Multiplication: 3¹/₂ × 2³/₇
• Division: 3¹/₂ ÷ 2³/₇
• Mult/Div: 3¹/₂ ×/÷ 2³/₇

'Show that' fractions + -

• Addition: ³/₇ + ²/₂₁
• Subtraction: ³/₇ - ²/₂₁
• Add/Sub: ³/₇ ± ²/₂₁
• Addition: ¹/₂ + ²/₇
• Subtraction: ¹/₂ - ²/₇
• Add/Sub: ¹/₂ ± ²/₇
• Addition: 4³/₇ + 1²/₂₁
• Subtraction: 4³/₇ - 1²/₂₁
• Add/Sub: 4³/₇ ± 1²/₂₁
• Addition: 4¹/₂ + 1²/₇
• Subtraction: 4¹/₂ - 1²/₇
• Add/Sub: 4¹/₂ ± 1²/₇

'Show that' fractions × ÷

• Multiplication: ¹/₂ × ³/₇
• Division: ¹/₂ ÷ ³/₇
• Mult/Div: ¹/₂ ×/÷ ³/₇
• Multiplication: 3¹/₂ x ³/₇
• Division: 3¹/₂ ÷ ³/₇
• Mult/Div: 3¹/₂ ×/÷ ³/₇
• Multiplication: 3¹/₂ x 2³/₇
• Division: 3¹/₂ ÷ 2³/₇
• Mult/Div: 3¹/₂ ×/÷ 2³/₇

Decimals

Ordering decimals

• Easy ascending
• Easy descending
• Medium ascending
• Medium descending

Converting

• Recurring decimal to fraction: 0.222222...
• Recurring decimal to fraction: 0.232323...
• Recurring decimal to fraction: 0.234234...
• Recurring decimal to fraction: 0.9222222...
• Recurring decimal to fraction: 0.9232323...
• Recurring decimal to fraction: 0.9234234...

Powers and Roots

Simplifying surds

• Easy square factor, eg: √20
• Harder square factor, eg: √108
• Rationalise denominator, eg: 2/√6
• Easy add, eg: √45 + √20
• Easy subtract, eg: √45 - √20
• Easy add/subtract, eg: √45 ± √20
• Easy multiply, eg: √15 × √5
• Easy divide, eg: √15 ÷ √5
• Easy multiply/divide, eg: √15 ×/÷ √5
• Misc
• Simplify (a + √b)²

Evaluating

• Exact roots
• +ve integer powers
• zero integer powers
• -ve integer powers
• +ve and zero integer powers
• ±ve integer powers
• -ve and zero integer powers
• ±ve and zero integer powers
• +ve unit fractional powers
• -ve unit fractional powers
• ±ve unit fractional powers
• +ve non-unit fractional powers
• -ve non-unit fractional powers
• ±ve non-unit fractional powers
• Misc powers of integers
• Fraction to +ve integer power
• Fraction to -ve integer power
• Fraction to ±ve integer power
• Fraction to +ve fractional power
• Fraction to -ve fractional power
• Fraction to ±ve fractional power
• Misc powers of fractions

Laws of indices

• Multiplication
• Division
• Brackets
• Misc

Percentages

Converting

• Percentage to decimal, eg 17%
• Decimal to percentage, eg 0.17
• Misc. between % and decimal, eg 17%
• Percentage to decimal, eg 1.7%
• Decimal to percentage, eg 0.017
• Misc. between % and decimal, eg 1.7%
• Percentage to fraction, eg 60%
• Fraction to percentage, eg 3/5
• Misc. between % and fraction, eg 60%
• Percentage to fraction, eg 32%
• Fraction to percentage, eg 8/25
• Misc. between % and fraction, eg 32%
• Percentage to fraction, eg 37.5%
• Fraction to percentage, eg 3/8
• Misc. between % and fraction, eg 37.5%
• Arrange %, decimal and fraction into order

Find P% of Y

• eg: find 40% of 60
• eg: find 32% of 70
• eg: find 13.5% of 5.8

Find X as a percentage of Y

• eg: find 24 as a % of 60
• eg: find 22.4 as a % of 70
• eg: find 0.783 as a % of 5.8

Find a number so that P% of it gives X

• eg: 40% of Y = 24; find Y
• eg: 32% of Y = 22.4; find Y
• eg: 13.5% of Y = 0.783; find Y

Increase/decrease by percentage

• eg: increase 60 by 40%
• eg: increase 70 by 32%
• eg: increase 5.8 by 13.5%
• eg: decrease 60 by 40%
• eg: decrease 70 by 32%
• eg: decrease 5.8 by 13.5%
• eg: increase/decrease 60 by 40%
• eg: increase/decrease 70 by 32%
• eg: increase/decrease 5.8 by 13.5%

Find percentage increase/decrease

• Find % increase (easy)
• Find % increase (medium)
• Find % increase (hard)
• Find % decrease (easy)
• Find % decrease (medium)
• Find % decrease (hard)
• Find % increase/decrease (easy)
• Find % increase/decrease (medium)
• Find % increase/decrease (hard)

Compound interest/depreciation

• Compound interest: new value
• Compound interest: interest
• Compound interest: misc
• Depreciation: remaining value
• Depreciation: loss
• Depreciation: misc
• Compound interest/depreciation

Reverse percentage problem

• Reverse % problem - pre-sale

Ratios

Manipulation of ratios

• Cancel down a:b
• Cancel down a:b:c

Using ratios

• Sharing 2 ways
• Sharing 3 ways
• Sharing 2 or 3 ways
• Increase
• Decrease
• Increase/decrease
• Increase/decrease/share

Accuracy

Identifying Accuracy

• Count decimal places
• Count significant figures

Rounding

• Round to decimal places
• Round to significant figures
• Round to dec places/sig figs

Lower and upper bounds

• Lower bound
• Upper bound
• Lower or upper bound
• Lower and upper bounds
• Lower bound, nearest 2 or 5
• Upper bound, nearest 2 or 5
• Lower or upper bound, nearest 2 or 5
• Lower and upper bounds, nearest 2 or 5
• Give min or max values of calculations

Standard Form

Standard form

• Verify
• Convert from [exponent ≥ 0]
• Convert to [exponent ≥ 0]
• Convert from [exponent < 0]
• Convert to [exponent < 0]
• Convert from [any exponent]
• Convert to [any exponent]
• Multiplication
• Division
• Multiplication/division
• Subtraction
• Misc. calculations

Electronic Calculators

Evaluating expressions

• +ve numbers
• ±ve numbers

• ALGEBRA

Definitions

Equation, expression, identity, formula, inequality

• Definition to term 
• Term to definition 

Expand, simplify, factorise, solve, evaluate

• Definition to term 
• Term to definition 

Term, coefficient, constant, variable, index

• Definition to term 
• Term to definition 

Misc. algebra terms

• Definition to term 
• Term to definition 

Sequences: Arithmetic, quadratic, geometric, Fibonacci

• Definition to term 
• Term to definition 

Function, domain, range, inverse, composite

• Definition to term 
• Term to definition 

Gradient, y-intercept, y=mx+c, parallel, perpendicular

• Definition to term 
• Term to definition 

Graphs: parabola, cubic, linear, reciprocal, exponential

• Definition to term 
• Term to definition 

Transformations of graphs: y=-f(x), y=f(-x), y=f(x)+a, y=f(x+a)

• Definition to term 
• Term to definition 

Formulae

• Definition to term 
• Term to definition 

Equation of a circle

• Definition to term 
• Term to definition 

Converting words to algebra

Expressions in one variable

• Single operation: add/subtract/multiply/divide
• Single operation: variable combined with itself
• Single operation: powers/roots/reciprocal/negation
• Two operations: add/subtract/multiply/divide

Use of symbols

Indices

• eg: a×a×a
• eg: a²×a³
• eg: a³÷a²
• eg: (a³)²
• eg: a×a³/a²
• +ve integer indices
• eg: 1/(a×a×a)
• eg: a²×a⁻³ =
• eg: a³÷a⁻² =
• eg: (a⁻³)² =
• eg: a×a⁻³/a²
• ±ve integer indices
• eg: 6a²×3a
• eg: 6a²/3a
• eg: (2a²)³
• Mixed indices
• eg: 6a²b³×3ab²
• eg: 6a²b³/3ab²
• eg: (2ab²)³
• Mixed indices
• eg: 4ⁿ = 16
• eg: 4ⁿ = 1
• eg: 4ⁿ = 1/16
• eg: 4ⁿ = 2
• eg: 4ⁿ = 1/2
• Misc Aⁿ = B

Basic Algebraic Manipulation

Collecting like +ve terms

• eg: x+x+x+x
• eg: 3x + 5x
• eg: 2x + 4y + 3x + y
• eg: 2x + 4 + 3x + 1
• eg: 2x + 4y + 6 + 3x + y + 5
• Misc. collecting +ve terms 1
• eg: 2x² + 4x + 3x² + x
• eg: 2x² + 4x + 6 + 3x² + x + 5
• eg: 2xy + 4x + 3yx + x
• Misc. collecting +ve terms 2

Collecting like ±ve terms

• eg: 3x - 5x
• eg: 2x + 4y - 3x + y
• eg: 2x + 4 - 3x + 1
• eg: 2x + 4y + 6 - 3x + y - 5
• Misc. collecting ±ve terms 1
• eg: 2x² + 4x - 3x² + x
• eg: 2x² + 4x + 6 - 3x² + x - 5
• eg: 2xy + 4x + 3yx + x
• Misc. collecting ±ve terms 2

Expanding over one bracket

• eg: 2(3x+4)
• eg: 2(3x+4) + 4(7x+1)
• eg: 2(3x+4) - 4(7x+1)
• eg: 2(3x+4) ± 4(7x+1)
• eg: 2(±3x±4)
• eg: -2(±3x±4)
• eg: ±2(±3x±4)
• eg: 2(3x±4) + 4(7x±1)
• eg: 2(3x±4) - 4(7x±1)
• eg: 2(3x±4) ± 4(7x±1)
• eg: ±2(±3x±4) ± 4(±7x±1)
• Misc. linear expanding
• eg: 2x(3x-4)
• eg: 2x(3x-4y)

Taking out a common factor

• eg: 6x - 8
• eg: -6x - 8
• eg: ±6x - 8
• eg: 6x² - 8x
• eg: 6x² - 8xy
• Misc. common factor

• eg: (x+4)(x+5)
• eg: (x-4)(x-5)
• eg: (x+4)(x-5) or (x-4)(x+5)
• eg: (x-4)(x+4)
• Misc (x±A)(x±B)
• eg: (x-4)²
• eg: (3x-7)(-5x+8)
• eg: (3x-7)²

• eg: x² + 4x
• eg: x² + 5x + 6
• eg: x² - 5x + 6
• eg: x² ± 5x - 6
• eg: x² ± 5x ± 6
• eg: x² ± 10x + 25
• eg: x² - 25
• Misc x² ± Ax ± B
• eg: 3x² - 7x + 2

Completing the square

• Complete the square (x+p)²+q
• Complete the square a(x+p)²+q
• Find line of symmetry (x+p)²+q
• Find line of symmetry a(x+p)²+q
• Find min/max value (x+p)²+q
• Find min/max value a(x+p)²+q
• Find co-ordinates of vertex (x+p)²+q
• Find co-ordinates of vertex a(x+p)²+q

Cubic Algebraic Manipulation

Expanding three brackets

• x(x±A)(x±B)
• x(x±A)(Bx±C)
• x(Ax±B)(Cx±D)
• Misc up to x(Ax±B)(Cx±D)
• (x±A)(x±B)(x±C)
• (x±A)(x±B)(Cx±D)
• (x±A)(Bx±C)(Dx±E)
• (Ax±B)(Cx±D)(Ex±F)
• Misc up to (Ax±B)(Cx±D)(Ex±F)
• x(x±A)²
• x(Ax±B)²
• Misc up to x(Ax±B)²
• (x±A)²(x±B)
• (x±A)²(Bx±C)
• (Ax±B)²(x±C)
• (Ax±B)²(Cx±D)
• Misc up to (Ax±B)²(Cx±D)
• (x±A)³
• (Ax±B)³
• Misc up to (Ax±B)³
• Misc (x±A)(x±B)(x±C)
• Misc (x±A)(x±B)(Cx±D)
• Misc (x±A)(Bx±C)(Dx±E)
• Misc (Ax±B)(Cx±D)(Ex±F)

Algebraic Fractions

Algebraic fractions - simplify

• eg: 2x/6
• eg: 2(x+2)/6
• eg: (2x+4)/6
• eg: (2x+4)/6x
• eg: (2x+4)/(6x-2)
• Numeric common factor
• eg: x(x+2)/6x
• eg: (x²+2x)/6x
• eg: x(x+2)/x(x-3)
• eg: (x²+2x)/(x²-3x)
• eg: (2x²+4x)/(4x²-12x)
• Algebraic common factor 1
• eg: (x+2)(x+1)/(x+2)
• eg: (x²+3x+2)/(x+2)
• eg: (x²-4)/(x±2)
• eg: (x²-4)/(x²±2x)
• eg: (x+2)(x+1)/(x+3)(x+2)
• eg: (x²+3x+2)/(x²+5x+6)
• Algebraic common factor 2

Algebraic fractions - add/subtract

• eg: 2x/3 ± x/6
• eg: 2x/3 ± x/4
• eg: 2x/3 ± 3(x+1)/4
• eg: (x-1)/3 ± 2/5
• eg: 2(x-3)/3 ± 3(2x+1)/4
• eg: 2/3x ± 1/6x
• eg: 2/x ± 3/(x+1)
• eg: 2/(x+1) ± 3/(x+2)
• eg: 2x/(2x+1) - x/(x-2)
• eg: (x+3)/(x+1) - (x-3)/(x-2)

Algebraic fractions - multiply/divide 1

• eg: 2x/3 × 6/7x
• eg: 2x/3 ÷ 7x/6
• eg: 2x/3 × 6/7x [or divide]
• eg: (2x+1)/3 × 4x/(6x+3)
• eg: (2x+1)/3 ÷ (6x+3)/4x
• eg: (2x+1)/3 × 4x/(6x+3) [or divide]
• eg: (2x²+x)/3x × 4x/(6x+3)
• eg: (2x²+x)/3x ÷ (6x+3)/4x
• eg: (2x²+x)/3x × 4x/(6x+3) [or divide]
• Misc multiplication
• Misc division
• Misc mult/division

Algebraic fractions - multiply/divide 2

• eg: (x²+3x+2)/3 × 4/(x+2)
• eg: (x²+3x+2)/3 ÷ (x+2)/4
• eg: (x²+3x+2)/3 × 4/(x+2) [or divide]
• eg: (x²+3x+2)/3x × 4x/(x+2)
• eg: (x²+3x+2)/3x ÷ (x+2)/4x
• eg: (x²+3x+2)/3x × 4x/(x+2) [or divide]
• eg: (x²+3x+2)/3 × 4/(x²+5x+6)
• eg: (x²+3x+2)/3 ÷ (x²+5x+6)/4
• eg: (x²+3x+2)/3 × 4/(x²+5x+6) [or divide]
• eg: (x²+3x+2)/3 × 4x/(x²+5x+6)
• eg: (x²+3x+2)/3 ÷ (x²+5x+6)/4x
• eg: (x²+3x+2)/3 × 4x/(x²+5x+6) [or divide]
• eg: (x²+3x+2)/(x²+5x+6) × (x²+2x-3)/(x²-3x+2)
• eg: (x²+3x+2)/(x²+5x+6) ÷ (x²-3x+2)/(x²+2x-3)
• eg: (x²+3x+2)/(x²+5x+6) × (x²+2x-3)/(x²-3x+2) [or divide]
• Misc multiplication
• Misc division
• Misc mult/division

Expressions and Formulae

Substituting

• +ve integers
• ±ve integers

Rearranging formulae

• Variable occurs once (easy)
• Variable occurs once (medium)
• Variable occurs once (harder)
• Variable occurs twice

Linear Equations

One-step linear equations

• x ± b = c, (+ve x)
• x ± b = c, (-ve x)
• x ± b = c, (±ve x)
• ax = c, (+ve x)
• ax = c, (-ve x)
• ax = c, (±ve x)
• x/d = c, (+ve x)
• x/d = c, (-ve x)
• x/d = c, (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Two-step linear equations (1)

• ax ± b = c, (+ve x)
• ax ± b = c, (-ve x)
• ax ± b = c, (±ve x)
• x/d ± b = c, (+ve x)
• x/d ± b = c, (-ve x)
• x/d ± b = c, (±ve x)
• a(x ± b) = c, (+ve x)
• a(x ± b) = c, (-ve x)
• a(x ± b) = c, (±ve x)
• (x ± b)/d = c, (+ve x)
• (x ± b)/d = c, (-ve x)
• (x ± b)/d = c, (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Two-step linear equations (2)

• b - ax = c, (+ve x)
• b - ax = c, (-ve x)
• b - ax = c, (±ve x)
• b - x/d = c, (+ve x)
• b - x/d = c, (-ve x)
• b - x/d = c, (±ve x)
• a/x ± b = c, (+ve x)
• a/x ± b = c, (-ve x)
• a/x ± b = c, (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Repeated variable

• ax = cx ± d, (+ve x)
• ax = cx ± d, (-ve x)
• ax = cx ± d, (±ve x)
• ax ± b = cx ± d, (+ve x)
• ax ± b = cx ± d, (-ve x)
• ax ± b = cx ± d, (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Repeated variable and brackets

• a(x ± b) = cx ± d, (+ve x)
• a(x ± b) = cx ± d, (-ve x)
• a(x ± b) = cx ± d, (±ve x)
• a(x ± b) = c(x ± d), (+ve x)
• a(x ± b) = c(x ± d), (-ve x)
• a(x ± b) = c(x ± d), (±ve x)
• a(x ± b) + c(x ± d) = e, (+ve x)
• a(x ± b) + c(x ± d) = e, (-ve x)
• a(x ± b) + c(x ± d) = e, (±ve x)
• a(x ± b) - c(x ± d) = e, (+ve x)
• a(x ± b) - c(x ± d) = e, (-ve x)
• a(x ± b) - c(x ± d) = e, (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Repeated variable and division

• x ± b = (cx ± d)/a, (+ve x)
• x ± b = (cx ± d)/a, (-ve x)
• x ± b = (cx ± d)/a, (±ve x)
• (x ± b)/a = (x ± d)/c, (+ve x)
• (x ± b)/a = (x ± d)/c, (-ve x)
• (x ± b)/a = (x ± d)/c, (±ve x)
• a/(x ± b) = c/(x ± d), (+ve x)
• a/(x ± b) = c/(x ± d), (-ve x)
• a/(x ± b) = c/(x ± d), (±ve x)
• Misc (+ve x)
• Misc (-ve x)
• Misc (±ve x)

Proportion

Finding k

• Direct proportion
• Inverse proportion
• Misc proportion

Finding equation

• Direct proportion
• Inverse proportion
• Misc proportion

Solving

• Direct proportion
• Inverse proportion
• Misc proportion

Linear Simultaneous Equations

Algebraic solution of simultaneous

• eg: 3x+2y=7, 3x+4y=11 (+ve x,y)
• eg: 3x+2y=7, 3x+4y=11 (±ve x,y)
• eg: 3x+2y=7, 6x-y=4 (+ve x,y)
• eg: 3x+2y=7, 6x-y=4 (±ve x,y)
• eg: 3x+2y=7, 4x+3y=10 (+ve x,y)
• eg: 3x+2y=7, 4x+3y=10 (±ve x,y)

Solving quadratics by factorising

• eg: (x+2)(x+3)=0
• eg: x(x+4)=0
• eg: x²+4x=0
• eg: x²+5x+6=0
• eg: x²-5x+6=0
• eg: x²±5x-6=0
• eg: x²±5x±6=0
• eg: x²+10x+25=0
• eg: x²-25=0
• Misc x²±Ax±B=0
• eg: 3x²-7x+2=0

Rearrange quadratics and solve by factorising

• eg: (x-1)(x+2) = 4
• eg: x + 6/x = 5, etc.
• eg: x - 4/(x+2) = 1, etc.
• eg: 3/(x+7) - 3/(x+9) = 2, etc.

Solving quadratics by completing the square

• Completing the square (a=1)
• Completing the square (a<>1)

Solving quadratics by formula

• eg: x²+x-5=0, surd form
• eg: x²+x-5=0, 3 sig figs
• eg: 2x²+x-5=0, surd form
• eg: 2x²+x-5=0, 3 sig figs

• eg: y=x², y=2x+3
• eg: y=x²+7x+9, y=2x+3
• eg: x²+y²=25, 2x+y=1
• eg: x²+y²=25, 3x+5y=2
• Misc

Inequalities

Inequalities on number lines

• Plotting x < 3, x > -2
• Plotting x ≤ 3, x ≥ -2
• Plotting x /≥ -2
• Plotting -4 < x ≤ 3
• Plotting x ≤ -4 or x > 3
• Plotting misc
• Reading off x < 3, x > -2
• Reading off x ≤ 3, x ≥ -2
• Reading off x /≥ -2
• Reading off -4 < x ≤ 3
• Reading off x ≤ -4 or x > 3
• Reading off misc

Solving linear inequalities (+ve x coeff)

• x ± b < c, x ± b > c
• ax < c, ax > c
• ax ± b < c, ax ± b > c
• a(x ± b) < c, a(x ± b) > c
• Misc

Solving linear inequalities (-ve x coeff)

• -x ± b < c, -x ± b > c
• -ax < c, -ax > c
• -ax ± b < c, -ax ± b > c
• -a(x ± b) < c, -a(x ± b) > c
• Misc

Solving linear inequalities (±ve x coeff)

• ±x ± b < c, ±x ± b > c
• ±ax < c, ±ax > c
• ±ax ± b < c, ±ax ± b > c
• ±a(x ± b) < c, ±a(x ± b) > c
• Misc

Solving linear inequalities and plotting (+ve x coeff)

• x ± b < c, x ± b > c
• ax < c, ax > c
• ax ± b < c, ax ± b > c
• a(x ± b) < c, a(x ± b) > c
• Misc

Solving linear inequalities and plotting (-ve x coeff)

• -x ± b < c, -x ± b > c
• -ax < c, -ax > c
• -ax ± b < c, -ax ± b > c
• -a(x ± b) < c, -a(x ± b) > c
• Misc

Solving linear inequalities and plotting (±ve x coeff)

• ±x ± b < c, ±x ± b > c
• ±ax < c, ±ax > c
• ±ax ± b < c, ±ax ± b > c
• ±a(x ± b) < c, ±a(x ± b) > c
• Misc

Regions on (x,y) plane

• Shade out a region yc
• Identify an inequality yc
• Shade out a region xc
• Identify an inequality xc
• Shade out a region y<>mx+c (integer m)
• Identify an inequality y<>mx+c (integer m)
• Shade out a region y<>mx+c (integer m) or x<>c or y<>c
• Identify an inequality y<>mx+c (integer m) or x<>c or y<>c
• Shade out a region y<>mx+c (rational m)
• Identify an inequality y<>mx+c (rational m)
• Misc shade out a region
• Misc identify a shaded region
• Shade out two inequalities x<>c y<>d
• Identify two inequalities x<>c y<>d
• Shade out two inequalities y<>mx+c x/y<>d
• Identify two inequalities y<>mx+c x/y<>d

• Solve algebraically, eg x² > 4
• Solve algebraically, eg 2x²+4 < 22
• Solve and show on number line, eg x² > 4
• Solve and show on number line, eg 2x²+4 < 22
• List integer solutions, eg x² > 4
• List integer solutions, eg 2x²+4 < 22

Sequences

Find the next terms

• Linear sequence, +ve terms
• Linear sequence, ±ve terms
• Linear sequence, ±ve decimal terms
• Quadratic sequence, +ve terms
• Quadratic sequence, ±ve terms
• Geometric sequence, integer terms
• Geometric sequence, incl. fractional terms
• Squares, primes, etc. 
• Misc

Use term-to-term rule

• Add a constant (+ve terms)
• Add a constant (-ve terms)
• Add a constant (±ve terms)
• Subtract a constant (+ve terms)
• Subtract a constant (-ve terms)
• Subtract a constant (±ve terms)
• Multiply by a fixed ratio (+ve terms)
• Multiply by a fixed ratio (-ve terms)
• Multiply by a fixed ratio (±ve terms)
• Multiply then add/subtract (+ve terms)
• Multiply then add/subtract (-ve terms)
• Multiply then add/subtract (±ve terms)
• Add/subtract then multiply (+ve terms)
• Add/subtract then multiply (-ve terms)
• Add/subtract then multiply (±ve terms)
• Misc add/subtract/multiply (+ve terms)
• Misc add/subtract/multiply (-ve terms)
• Misc add/subtract/multiply (±ve terms)
• Square then add/subtract
• Add/subtract then square
• Misc add/subtract/multiply/square (±ve terms)

Use position-to-term formula

• Linear sequence, +ve terms
• Linear sequence, ±ve terms
• Quadratic sequence, +ve terms
• Quadratic sequence, ±ve terms
• Geometric sequence, integer terms
• Geometric sequence, incl. fractional terms
• Squares, cubes, triangle 
• Misc

Solve position-to-term formula

• Linear sequence, +ve terms
• Linear sequence, ±ve terms
• Quadratic sequence, +ve terms
• Quadratic sequence, ±ve terms
• Geometric sequence, integer terms
• Geometric sequence, incl. fractional terms
• Squares, cubes, triangle 
• Misc

Find the position-to-term formula

• Linear sequence, +ve terms
• Linear sequence, ±ve terms
• Linear sequence, ±ve decimal terms
• Quadratic sequence, +ve terms
• Quadratic sequence, ±ve terms
• Geometric sequence, integer terms
• Geometric sequence, incl. fractional terms
• Squares, cubes, triangle 
• Misc

Functions

Evaluate f(a)

• Find f(a) (easy 1)
• Find f(a) (medium 2)
• Find f(a) (medium 3)
• Find f(a) (medium 2/3)
• Find f(a) (hard 4)
• Find f(a) (hard 5)
• Find f(a) (hard 4/5)

Solve f(x)=a

• Solve f(x)=a (easy 1)
• Solve f(x)=a (medium 2)
• Solve f(x)=a (medium 3)
• Solve f(x)=a (medium 2/3)
• Solve f(x)=a (hard 4)
• Solve f(x)=a (hard 5)
• Solve f(x)=a (hard 4/5)

Inverse: evaluate f⁻¹(a)

• Find f⁻¹(a) (easy 1)
• Find f⁻¹(a) (medium 2)
• Find f⁻¹(a) (medium 3)
• Find f⁻¹(a) (medium 2/3)
• Find f⁻¹(a) (hard 4)
• Find f⁻¹(a) (hard 5)
• Find f⁻¹(a) (hard 4/5)

Inverse: find f⁻¹(x)

• Find f⁻¹(x) (easy)
• Find f⁻¹(x) (medium)
• Find f⁻¹(x) (hard)
• Find f⁻¹(x) (misc)

Domain and range

• Domain: reciprocal f(x)
• Domain: square root f(x)
• Domain: misc f(x)
• Domain exclusions: reciprocal f(x)
• Domain exclusions: square root f(x)
• Domain exclusions: misc f(x)

Composition: find ff⁻¹(x), fg(x)

• Find ff⁻¹(a)
• Find fg(a) (linear)
• Find fg(a) (quadratic)
• Find fg(a) (linear/quadratic)
• Find ff⁻¹(x)
• Find fg(x) (linear)
• Find fg(x) (quadratic)
• Find fg(x) (linear/quadratic)

Co-ordinates

Basic 2D Co-ordinates

• Plot in one quadrant
• Identify in one quadrant
• Plot in four quadrants (large)
• Identify in four quadrants (large)
• Plot in four quadrants (small)
• Identify in four quadrants (small)

Find missing vertices

• Identify the missing vertex in a square (1)
• Identify the missing vertex in a square (2)
• Identify two missing vertices in a square (adjacent)
• Identify two missing vertices in a square (diagonal)

Linear graphs

Line segments

• Gradient of a line segment
• Mid-point of a line segment
• Gradient and mid-point of a line segment
• Length of a line segment
• Gradient and length of a line segment
• Mid-point and length of a line segment
• Gradient, mid-point & length of a line segment

Straight line graphs

• Identify x=... or y=...
• Sketch x=... or y=...
• Identify y=mx+c (+ve integer m)
• Sketch y=mx+c (+ve integer m)
• Identify y=mx+c (-ve integer m)
• Sketch y=mx+c (-ve integer m)
• Identify y=mx+c (±ve integer m)
• Sketch y=mx+c (±ve integer m)
• Identify y=mx+c (±ve integer m) or x=c, y=c
• Sketch y=mx+c (±ve integer m) or x=c, y=c
• Identify y=mx+c (+ve rational m)
• Sketch y=mx+c (+ve rational m)
• Identify y=mx+c (-ve rational m)
• Sketch y=mx+c (-ve rational m)
• Identify y=mx+c (±ve rational m)
• Sketch y=mx+c (±ve rational m)
• Identify misc straight line graph
• Sketch misc straight line graph

Circle equation and tangent

Give the equation of a circle

• Centre O, radius r
• Centre (a, b), radius r
• Centre O passing through (c, d)
• With diameter (c, d), (e, f)

Give information about a circle

• Radius of a circle centre O
• Radius and centre of a circle

Radius of a circle

• Equation of radius

Tangent to a circle

• Gradient of tangent
• Equation of tangent

Plot and solve xⁿ graphs

Plot a graph from a table of values

• Linear graph
• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph from values
• ±ve quadratic graphs
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph from values

Complete a table of values

• Linear function
• +ve quadratic function
• +ve cubic function
• +ve reciprocal function
• +ve reciprocal squared function
• Misc +ve function
• ±ve quadratic function
• ±ve cubic function
• ±ve reciprocal function
• ±ve reciprocal squared function
• Misc ±ve function

Complete a table and plot a graph

• Linear function
• +ve quadratic function
• +ve cubic function
• +ve reciprocal function
• +ve reciprocal squared function
• Misc +ve function
• ±ve quadratic function
• ±ve cubic function
• ±ve reciprocal function
• ±ve reciprocal squared function
• Misc ±ve function

Find gradient of a given graph using a tangent

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Plot a graph and find gradient using a tangent

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Solve f(x)=k using a given graph

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc ±ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Plot a graph and solve f(x)=k

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Solve f(x)=mx+c using a given graph

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Solve f(x)=mx+c (rearranged) using a given graph

• +ve quadratic graph
• +ve cubic graph
• +ve reciprocal graph
• +ve reciprocal squared graph
• Misc +ve graph
• ±ve quadratic graph
• ±ve cubic graph
• ±ve reciprocal graph
• ±ve reciprocal squared graph
• Misc ±ve graph

Sketch graphs

Identify a graph

• y=x, x², x³ 
• y=1/x, 1/x² 
• y=x, x², x³, 1/x, 1/x² 
• y=√x, ³√x 
• y=k^x: 01 
• Non-trig graph 
• y=sinx, cosx, tanx 
• y=cosecx, secx, cotx 
• Trig graph 
• y=sin⁻¹x, cos⁻¹x, tan⁻¹x 

Sketch a graph

• y=x, x², x³ 
• y=1/x, 1/x² 
• y=x, x², x³, 1/x, 1/x² 
• y=√x, ³√x 
• y=k^x: 01 
• Non-trig graph 
• y=sinx, cosx, tanx 
• y=cosecx, secx, cotx 
• Trig graph 
• y=sin⁻¹x, cos⁻¹x, tan⁻¹x 

• MEASUREMENT and GEOMETRY

Definitions

Acute, right, obtuse, reflex

• Definition to term 
• Term to definition 

Bearing, elevation, depression, perpendicular

• Definition to term 
• Term to definition 

Polygons: 3-6 sides

• Definition to term 
• Term to definition 

Polygons: 7-10 sides

• Definition to term 
• Term to definition 

Polygon, regular, interior, exterior

• Definition to term 
• Term to definition 

Equilateral, isosceles, right-angled, scalene

• Definition to term 
• Term to definition 

Square, rhombus, parallelogram, trapezium, rectangle, kite

• Definition to term 
• Term to definition 

Radius, diameter, circumference, chord

• Definition to term 
• Term to definition 

Arc, sector, tangent, segment

• Definition to term 
• Term to definition 

Pressure, speed, density, acceleration

• Definition to term 
• Term to definition 

Vector, scalar, magnitude, resultant

• Definition to term 
• Term to definition 

Translation, rotation, reflection, enlargement

• Definition to term 
• Term to definition 

Formulae

Pythagoras

• Definition to term 
• Term to definition 

Sin, Cos, Tan ratios

• Definition to term 
• Term to definition 

Sine, Cosine rules and Area of triangle

• Definition to term 
• Term to definition 

Area of trapezium, volume of prism

• Definition to term 
• Term to definition 

Circumference and area of circle

• Definition to term 
• Term to definition 

Angles and Bearings

Measure and draw angles

• Estimate size (nearest 45°)
• Estimate size (nearest 15°)
• Measure size (0-90°)
• Measure size (90-180°)
• Measure size (180-360°)
• Measure size (0-180°)
• Measure size (0-360°)
• Draw (0-90°)
• Draw (90-180°)
• Draw (180-360°)
• Draw (0-180°)
• Draw (0-360°)

Angles on a straight line

• Find angle (10°) - 1 of 2
• Find angle (1°) - 1 of 2
• Find angle (10°) - 1 of 3
• Find angle (1°) - 1 of 3
• Find angle (10°) - 1 of 4
• Find angle (1°) - 1 of 4
• Find angle (10°) - misc
• Find angle (1°) - misc
• Find 2 angles algebraically (1)
• Find 2 angles algebraically (2)
• Find 3 angles algebraically (1)
• Find 3 angles algebraically (2)

Angles at a point

• Find angle (10°) - 1 of 2
• Find angle (1°) - 1 of 2
• Find angle (10°) - 1 of 3
• Find angle (1°) - 1 of 3
• Find angle (10°) - 1 of 4
• Find angle (1°) - 1 of 4
• Find angle (10°) - misc
• Find angle (1°) - misc
• Find 2 angles algebraically (1)
• Find 2 angles algebraically (2)
• Find 3 angles algebraically (1)
• Find 3 angles algebraically (2)

Bearings

• Measure
• Construct
• Measure off triangle
• Calculate back-bearings with a diagram
• Calculate back-bearings with no diagram

Polygons

Triangles

• Find interior angle (10°)
• Find interior angle (1°)
• Find exterior angle (10°)
• Find exterior angle (1°)
• Find algebraic interior angle (10°)
• Find algebraic interior angle (1°)

• Find interior angle (10°)
• Find interior angle (1°)
• Find exterior angle (10°)
• Find exterior angle (1°)
• Find algebraic interior angle (10°)
• Find algebraic interior angle (1°)

Regular Polygons (diagram)

• Interior angle (5-12)
• Exterior angle (5-12)
• Interior angle sum (5-12)
• Exterior angle sum (5-12)
• Misc angle (5-12)
• Misc angle sum (5-12)
• Misc angle or sum (5-12)

Regular Polygons (text)

• Interior angle (5-12)
• Exterior angle (5-12)
• Interior angle sum (5-12)
• Exterior angle sum (5-12)
• Misc angle (5-12)
• Misc angle sum (5-12)
• Misc angle or sum (5-12)
• Interior angle (15-72)
• Exterior angle (15-72)
• Interior angle sum (15-72)
• Exterior angle sum (15-72)
• Misc angle (15-72)
• Misc angle sum (15-72)
• Misc angle or sum (15-72)

Construction & Loci

Basic construction

• Perpendicular bisector (small)
• Perpendicular bisector (big)
• Angle bisector (small)
• Angle bisector (big)
• Perpendicular/angle bisector (small)
• Perpendicular/angle bisector (big)

Other constructions

• Perpendicular to line at point P (small)
• Perpendicular to line at point P (big)
• Perpendicular from point P to line (small)
• Perpendicular from point P to line (big)
• Equilateral triangle from baseline (small) 
• Equilateral triangle from baseline (big) 
• Square from baseline (small) 
• Square from baseline (big) 
• Regular hexagon from baseline (small) 
• Regular hexagon from baseline (big) 
• Misc regular polygon from baseline (small) 
• Misc regular polygon from baseline (big) 

Constructing triangles

• ASA triangle (small)
• ASA triangle (big)
• SAS triangle (small)
• SAS triangle (big)
• SSS triangle (small)
• SSS triangle (big)

Loci

• Equidistant from two points (small)
• Equidistant from two points (big)
• Equidistant from two lines (small)
• Equidistant from two lines (big)

Circle Properties

Circle Theorems

• Isosceles triangles
• Angles in same segment
• Angle at centre
• Angle in a semicircle
• Alternate segment theorem
• Tangent - radius
• Misc. 1-4
• Misc. 5-7
• Misc. 1-7

Trigonometry and Pythagoras

Pythagoras

• Integer sides - find hypotenuse
• Integer sides - find shorter side
• Integer sides - find any side
• Non-integer sides - find hypotenuse
• Non-integer sides - find shorter side
• Non-integer sides - find any side

Trigonometry - basics

• Names of triangle sides
• Sin ratio from triangle
• Cos ratio from triangle
• Tan ratio from triangle
• Sin/cos/tan ratios from triangle

Trigonometry - calculator usage

• Evaluate Sin x
• Evaluate Cos x
• Evaluate Tan x
• Evaluate Sin/Cos/Tan x
• Evaluate Sin⁻¹ x
• Evaluate Cos⁻¹ x
• Evaluate Tan⁻¹ x
• Evaluate Sin/Cos/Tan⁻¹ x

Trigonometry - exact values

• sin 0, 30, 45, 60, 90° 
• cos 0, 30, 45, 60, 90° 
• tan 0, 30, 45, 60, 90° 
• sin/cos/tan 0, 30, 45, 60, 90°
• sin 120-360° 
• cos 120-360° 
• tan 120-360° 
• sin/cos/tan 120-360°

Trigonometry - right-angled triangles

• Sin - find Opposite
• Sin - find Hypotenuse
• Sin - find Angle
• Sin - find Misc
• Cos - find Adjacent
• Cos - find Hypotenuse
• Cos - find Angle
• Cos - find Misc
• Tan - find Opposite
• Tan - find Adjacent
• Tan - find Angle
• Tan - find Misc
• Sin/cos/tan - find Numerator Side
• Sin/cos/tan - find Denominator Side
• Sin/cos/tan - find Side
• Sin/cos/tan - find Angle
• Sin/cos/tan - find Misc

Trigonometry - non-right-angled triangles

• Sine Rule - find Side
• Sine Rule - find Angle
• Sine Rule - find Misc
• Cosine Rule - find Side
• Cosine Rule - find Angle
• Cosine Rule - find Misc
• Sine/Cosine Rule - find Side
• Sine/Cosine Rule - find Angle
• Sine/Cosine Rule - find Misc
• Find area of triangle

Trigonometry - mixed questions

• Find misc side or angle (right-angled triangle)
• Find misc side or angle (any triangle)

Length, Area, Volume

Metric conversion

• Convert mm, cm, m, km
• Convert mm², cm², m², km²
• Convert mm³, cm³, m³, km³
• Convert metric length/area/volume
• Convert m/s, km/h
• Convert ml/litres, cm³/m³
• Convert mg, g, kg, tonnes
• Convert misc metric units

Metric/imperial conversion

• Convert inches, mm/cm/m
• Convert feet, mm/cm/m
• Convert miles, m/km
• Convert UK pints, litres
• Convert UK gallons, litres
• Convert UK lb, g/kg
• Convert misc metric/imperial

2D Perimeter, Area (no circles)

• Perimeter of triangle
• Area of triangle
• Perimeter of rectangle
• Area of rectangle
• Area of parallelogram
• Area of trapezium
• Perimeter of compound shape (no circles)
• Area of compound shape (no circles)

2D Perimeter, Area (with circles)

• Circumference of circle
• Area of circle
• Perimeter of ¼,½,¾ circle
• Area of ¼,½,¾ circle

3D Surface Area, Volume - Cuboid, Cube

• Cuboid: Surface area
• Cuboid: Volume
• Cube: Surface area
• Cube: Volume
• Cube: Side from surface area
• Cube: Side from volume

3D Surface Area, Volume - Cylinder

• Cylinder: Curved surface area from radius,height
• Cylinder: Total surface area from radius,height
• Cylinder: Misc surface area from radius,height
• Cylinder: Volume from radius,height
• Cylinder: Misc Area/Volume from radius,height
• Cylinder: Curved surface area from diameter,height
• Cylinder: Total surface area from diameter,height
• Cylinder: Misc surface area from diameter,height
• Cylinder: Volume from diameter,height
• Cylinder: Misc Area/Volume from diameter,height
• Cylinder: Misc surface area from radius/diameter,height
• Cylinder: Volume from radius/diameter,height
• Cylinder: Misc Area/Volume from radius/diameter,height

3D Surface Area, Volume - Sphere

• Sphere: Surface area from radius
• Sphere: Volume from radius
• Sphere: Misc Area/Volume from radius
• Sphere: Surface area from diameter
• Sphere: Volume from diameter
• Sphere: Misc Area/Volume from diameter
• Sphere: Surface area from radius/diameter
• Sphere: Volume from radius/diameter
• Sphere: Misc Area/Volume from radius/diameter
• Sphere: Radius from surface area
• Sphere: Radius from volume
• Sphere: Diameter from surface area
• Sphere: Diameter from volume
• Sphere: Misc Radius/Diameter from surface area/volume
• Sphere: Surface area from volume
• Sphere: Volume from surface area
• Sphere: Misc Volume/Area conversion

3D Surface Area, Volume - Cone

• Cone: Curved surface area from radius,slant height
• Cone: Total surface area from radius,slant height
• Cone: Misc surface area from radius,slant height
• Cone: Volume from radius,vertical height
• Cone: Misc Area/Volume from radius,height
• Cone: Curved surface area from diameter,slant height
• Cone: Total surface area from diameter,slant height
• Cone: Misc surface area from diameter,slant height
• Cone: Volume from diameter,vertical height
• Cone: Misc Area/Volume from diameter,height
• Cone: Misc surface area from radius/diameter,slant height
• Cone: Volume from radius/diameter,vertical height
• Cone: Misc Area/Volume from radius/diameter,height

3D Surface Area, Volume - Misc shapes

• Cylinder/Sphere/Cone: Curved surface area from radius,height
• Cylinder/Sphere/Cone: Total surface area from radius,height
• Cylinder/Sphere/Cone: Misc surface area from radius,height
• Cylinder/Sphere/Cone: Volume from radius,height
• Cylinder/Sphere/Cone: Misc Area/Volume from radius,height
• Cylinder/Sphere/Cone: Curved surface area from diameter,height
• Cylinder/Sphere/Cone: Total surface area from diameter,height
• Cylinder/Sphere/Cone: Misc surface area from diameter,height
• Cylinder/Sphere/Cone: Volume from diameter,height
• Cylinder/Sphere/Cone: Misc Area/Volume from diameter,height
• Cylinder/Sphere/Cone: Misc surface area from radius/diameter,height
• Cylinder/Sphere/Cone: Volume from radius/diameter,height
• Cylinder/Sphere/Cone: Misc Area/Volume from radius/diameter,height

3D Surface Area, Volume - Compound solids

• Hemisphere: Curved surface area from radius
• Hemisphere: Total surface area from radius
• Hemisphere: Volume from radius
• Hemisphere on cylinder: Curved surface area from radius, height
• Hemisphere on cylinder: Total surface area from radius, height
• Hemisphere on cylinder: Volume from radius, height
• Cone on cylinder: Curved surface area from radius, heights
• Cone on cylinder: Total surface area from radius, heights
• Cone on cylinder: Volume from radius, heights
• Misc compound solid: Curved surface area from radius, height
• Misc compound solid: Total surface area from radius, height
• Misc compound solid: Volume from radius, height

Similarity

Are triangles similar?

• AAA with right angle
• AAA with no right angle
• SAS
• SAS vertically opposite
• SSS
• AAA/SAS/SSS

Distinct similar triangles

• Find linear scale factor
• Find a length
• Find two lengths

Similar shapes (word problems)

• Which 2D shapes are always similar?
• Which 3D shapes are always similar?
• Which 2D/3D shapes are always similar?
• Linear scale factor
• Linear to Area scale factor
• Linear to Volume scale factor
• Area to Linear scale factor
• Volume to Linear scale factor
• Area to Volume scale factor
• Volume to Area scale factor
• Misc. scale factor

Vectors

Column vectors

• Subtraction
• Scalar multiplication
• Misc
• Co-ordinates to vectors
• Parallel vectors
• Magnitude

Transformations

Rotation

• Rotate by 180
• Rotate by 90
• Rotate by 90 or 180
• Find centre of rotation (180)
• Find centre of rotation (90)
• Find centre of rotation (90 or 180)

Reflection

• Reflect in x=0 or y=0
• Reflect in y=±x
• Reflect in misc. line
• Find mirror line (x=0 or y=0)
• Find mirror line (y=±x)
• Find mirror line (misc)

Translation

• Translate by column vector (+ve quadrant)
• Find translation column vector (+ve quadrant)

Enlargement

• Enlarge by +ve scale factor
• Find enlargement (+ve scale factor)

Misc. transformations

• Identify (easy)
• Plot (easy)

• STATISTICS

Definitions

Cumulative freq, LQ, UQ, IQR

• Definition to term 
• Term to definition 

Histogram, freq density, class width, grouped freq table

• Definition to term 
• Term to definition 

Mean, median, mode, range

• Definition to term 
• Term to definition 

Presenting Data

Scatter diagrams

• Describe the correlation
• Plot a best fit line
• Plot a best fit line and read off

Pie charts

• Construct from angles (no protractor)
• Construct from angles with gap (no protractor)
• Read off angles (no protractor)
• Construct from data (no protractor)
• Construct from data with gap (no protractor)
• Read off data given total (no protractor)
• Read off data given one value (no protractor)
• Construct from data (with protractor)
• Construct from data with gap (with protractor)
• Read off data given total (with protractor)
• Read off data given one value (with protractor)

Cumulative frequency

• Fill a table
• Plot graph from given values
• Fill a table and plot a graph
• Read off median
• Read off lower quartile
• Read off upper quartile
• Read off lower or upper quartile
• Read off interquartile range
• Read off median or quartiles or IQR
• Read off median and IQR

Histograms

• Calculate frequency density
• Calculate frequency
• Calculate frequency OR density
• Plot histogram from frequency data
• Find frequency data from histogram
• Complete frequency data and histogram

Statistical Measures

Find average and spread from list

• Mean (from sorted list)
• Median (from sorted list)
• Mode (from sorted list)
• Range (from sorted list)
• Quartiles (from sorted list)
• IQR (from sorted list)
• Mean (from unsorted list)
• Median (from unsorted list)
• Mode (from unsorted list)
• Range (from unsorted list)
• Quartiles (from unsorted list)
• IQR (from unsorted list)

Problem-solving average and spread from list

• Find 2-3 numbers from mean, median, mode, range
• Find 3-5 numbers from mean, median, mode, range

Find average from table (discrete)

• Mean (from table)
• Median (from table)
• Mode (from table)
• Range (from table)
• Mean, median, mode and range (from table)

Find average from table (grouped discrete)

• Mean (from grouped table)
• Modal class (from grouped table)
• Mean, modal class (from table)

Find average from table (grouped continuous)

• Mean (from grouped table)
• Modal class (from grouped table)
• Mean, modal class (from table)

• PROBABILITY

Definitions

Probability, outcome, frequency, expected number

• Definition to term 
• Term to definition 

Equally likely outcomes, tree diagram, sample space, conditional prob

• Definition to term 
• Term to definition 

Mutually exclusive, independent, AND rule, OR rule

• Definition to term 
• Term to definition 

Sets: empty, universal, union, intersection, complement, element, subset

• Definition to term 
• Term to definition 

Probability

Probability basics

• Identify valid probabilities
• Name probabilities 
• Estimate probabilities of events
• Describe events with given likelihoods
• p(A): Pick an object out of a bag
• p(A): Select a letter from a word
• p(A): Outcome from die or spinner
• p(A): Pick a card from a pack
• p(A): Misc. equally likely outcomes
• p(A')=1-p(A): Basics
• p(A'): Pick an object out of a bag
• p(A'): Select a letter from a word
• p(A'): Outcome from die or spinner
• p(A'): Pick a card from a pack
• p(A'): Misc. equally likely outcomes
• p(A) & p(A'): Pick an object out of a bag
• p(A) & p(A'): Select a letter from a word
• p(A) & p(A'): Outcome from die or spinner
• p(A) & p(A'): Pick a card from a pack
• p(A) & p(A'): Misc. equally likely outcomes

Probability spinner tables

• Complete a probability table
• Probability table NOT RULE
• Probability table OR RULE
• Probability table AND RULE
• Expected frequency from total
• Total from expected frequency

Probability: mutually exclusive/independent

• Are events mutually exclusive?
• Test if mutually exclusive
• Are events independent?
• Test if independent

Probability by listing outcomes

• 2 spinners 
• 2 dice 
• 2 coins 
• 3 coins 
• 4 coins 

Tree diagrams

• Use a 2x2 tree diagram (repeated)
• Complete and use a 2x2 tree diagram (repeated)
• Construct and use a 2x2 tree diagram (repeated)
• Use a 2x2 tree diagram (independent)
• Complete and use a 2x2 tree diagram (independent)
• Construct and use a 2x2 tree diagram (independent)
• Use a 2x2 tree diagram (conditional)
• Complete and use a 2x2 tree diagram (conditional)
• Construct and use a 2x2 tree diagram (conditional)
• Formulate and solve a quadratic 1 (independent)
• Formulate and solve a quadratic 2 (independent)
• Formulate and solve a quadratic 1 (conditional)
• Formulate and solve a quadratic 2 (conditional)

Sets

Venn diagrams

• Shade regions (2 sets)
• Identify regions (2 sets)

Set notation

• AUB, A∩B, A'
• n(A), n(AUB')

• ADVANCED PURE MATHS

Definitions

Differentiate, derivative, turning point, max, min

• Definition to term 
• Term to definition 

Polynomials

Polynomial expressions

• Order
• Subtract cubics
• Multiply linear by quadratic
• Multiply linear by cubic
• Multiply quadratic by cubic
• Multiply misc.
• Divide quadratic by linear
• Divide cubic by linear
• Is linear a factor of cubic?
• Factorise cubic into linears
• Remainder when cubic is divided by linear

Binomials

Binomial expansion

• Expand (1 + x)ⁿ
• Expand (1 + bx)ⁿ
• Expand (1 - bx)ⁿ
• Expand (1 ± bx)ⁿ
• Expand (a + bx)ⁿ
• Expand (a - bx)ⁿ
• Expand (a ± bx)ⁿ
• Expand (1 + x²)ⁿ, etc.
• Expand (x + y)ⁿ
• Expand (x + by)ⁿ
• Expand (x - by)ⁿ
• Expand (x ± by)ⁿ
• Expand (ax + by)ⁿ
• Expand (ax - by)ⁿ
• Expand (ax ± by)ⁿ

Calculus

Differentiation by rule

• y=xⁿ
• y=Axⁿ
• y=Ax⁻ⁿ
• y=A/xⁿ
• y=Axⁿ, y=Ax⁻ⁿ or y=A/xⁿ
• eg: y=5x³-3x²+6
• eg: y=5x³-3/x²

Applying differentiation

• Find gradient at a point, eg: y=5x³
• Find gradient at a point, eg: y=4/x
• Find gradient at a point, eg: y=5x³, y=4/x
• Find gradient at a point, eg: y=5x³-3x²+6
• Find gradient at a point, eg: y=5x³-3/x²
• Find where gradient = m, eg: y=5x³
• Find where gradient = m, eg: y=4/x
• Find where gradient = m, eg: y=5x³, y=4/x
• Find maximum/minimum (quadratics)
• Find maximum/minimum (cubics)
• Find maximum/minimum (misc)

Kinematics

• Find velocity given x=at³+bt²+ct+d
• Find acceleration given x=at³+bt²+ct+d
• Find acceleration given v=at³+bt²+ct+d
• Find vel or accel given x or v
• Find vel at t=k given x=at³+bt²+ct+d
• Find accel at t=k given x=at³+bt²+ct+d
• Find accel at t=k given v=at³+bt²+ct+d
• Find vel or accel at t=k given x or v

Further differentiation

• Chain rule (2x + 7)³
• Chain rule 4(2x + 7)³
• Chain rule (2x + 7)⁻³
• Chain rule 4(2x + 7)⁻³
• Chain rule 1/(2x + 7)³
• Chain rule 4/(2x + 7)³

Matrices

Basic operations (2x2)

• A + B
• A - B
• kA
• kA + lB
• kA - lB
• AB
• Det(A)
• Is A singular / Det(A)=0 ?
• A⁻¹

Solve matrix and vector equations (2x2)

• Solve AX = B for matrix X
• Solve XA = B for matrix X
• Solve Ar = b for vector r

Solving linear equations (2x2)

• Solve 2 linear equations by inverse matrix

Basic operations (3x3)

• A + B
• A - B
• kA
• kA + lB
• kA - lB
• AB
• Det(A)
• Is A singular / Det(A)=0 ?
• Cofactors of A
• Transpose of cofactors of A
• A⁻¹

Complex Numbers

Basic operations: a+bi

• Real part of a complex number
• Imaginary part of a complex number
• Add two complex numbers
• Subtract two complex numbers
• Multiply two complex numbers
• Square a complex number
• Conjugate of a complex number
• Multiply a complex number by its conjugate
• Reciprocal of a complex number
• Divide two complex numbers
• Modulus of a complex number
• Argument of a complex number

Quadratics with complex roots

• Solve z² + c = 0 (integer)
• Solve z² + c = 0 (surd)
• Solve z² = a + bi (complex z)
• Solve z² + bz + c = 0 (conjugate pair)
• Solve z² + bz + c = 0 (non conjugate pair)

Vectors

Scalar (dot) product

• Scalar product of two vectors
• Are two vectors perpendicular?
• Is angle ABC a right angle?
• Magnitude of a vector
• Angle between two vectors
• Acute angle between two vectors
• Angle ABC
• Make a perpendicular vector

Vector (cross) product

• Vector product of two vectors
• Unit normal vector

Area and Volume using vectors

• Area of parallelogram given 2 sides
• Area of parallelogram given 4 points
• Area of triangle given 2 sides
• Area of triangle given 3 points
• Volume of parallelepiped given 3 edges
• Volume of tetrahedron given 3 edges
• Volume of tetrahedron given 4 points

Lines in 3D

• Vector to Cartesian equation of a line (standard)
• Cartesian to vector equation of a line (standard)
• Vector to Cartesian equation of a line (harder)
• Cartesian to vector equation of a line (harder)
• Vector equation of a line through 2 points
• Cartesian equation of a line through 2 points
• Acute angle between two lines (vector/vector)
• Acute angle between two lines (vector/Cartesian)
• Acute angle between two lines (Cartesian/Cartesian)
• Does a point lie on a line (vector)?
• Does a point lie on a line (Cartesian)?
• Do three points lie on the same line?
• Perpendicular distance from a point to a line (vector)
• Perpendicular distance from a point to a line (Cartesian)
• Two lines (vector/vector): intersect/skew/parallel?
• Two lines (vector/Cartesian): intersect/skew/parallel?
• Two lines (Cartesian/Cartesian): intersect/skew/parallel?
• Shortest distance between two lines (vector)
• Shortest distance between two lines (Cartesian)

Planes in 3D

• Vector to Cartesian equation of a plane
• Vector equation of a plane through 3 points
• Cartesian equation of a plane through 3 points
• Vector equation of a plane containing a point and a line
• Cartesian equation of a plane containing a point and a line
• Acute angle between two planes (Cartesian)
• Acute angle between a plane (Cartesian) and a line
• Perpendicular distance of a plane (Cartesian) from the origin
• Perpendicular distance of a plane (Cartesian) from a point P
• Does a point lie in a plane (Cartesian)?
• Do four points lie in the same plane?
• Vector line of intersection of two planes (Cartesian)
• Point of intersection of a line (vector) with a plane (Cartesian)
• Point of intersection of a line (Cartesian) with a plane (Cartesian)

• NETWORKS and DECISION

Networks

Minimum Spanning Tree

• Prim
• Kruskal
• Matrix Prim

Shortest Route

• Dijkstra

Route Inspection

• Best pairing of 4 odd nodes
• Route Inspection - 4 odd nodes

Travelling Salesperson

• Nearest neighbour (single)
• Lower bound (single)
• Nearest neighbour (all nodes)
• Lower bound (all nodes)

Algorithms

Packing

• First fit
• First fit decreasing
• Full bin

Sorting

• Bubble sort
• Shuttle sort

Order of Algorithms

• Find order from efficiency
• Calculate using order

Linear Programming

LP Graphical Solution

• Terminology
• Definitions
• Solving from graph
• Solving from LP formulation

LP Simplex Method

• 2-variable simplex
• 3-variable simplex

MATHSprint © Transfinite Research,