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• NUMBER

Definitions



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


  • Definition to term [9]
  • Term to definition [9]

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


  • Definition to term [8]
  • Term to definition [8]

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


  • Definition to term [8]
  • Term to definition [8]

   Misc. number terms


  • Definition to term [25]
  • Term to definition [25]

Tables practice



   Multiplication tables


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

Four operations - basic



   Addition


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

   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

   Adding/subtracting fractions


  • 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
  • Addition
  • Subtraction
  • Addition/subtraction
  • Misc. calculations

Electronic Calculators



   Evaluating expressions


  • +ve numbers
  • ±ve numbers

• ALGEBRA

Definitions



   Equation, expression, identity, formula, inequality


  • Definition to term [5]
  • Term to definition [5]

   Expand, simplify, factorise, solve, evaluate


  • Definition to term [5]
  • Term to definition [5]

   Term, coefficient, constant, variable, index


  • Definition to term [5]
  • Term to definition [5]

   Misc. algebra terms


  • Definition to term [15]
  • Term to definition [15]

   Sequences: Arithmetic, quadratic, geometric, Fibonacci


  • Definition to term [4]
  • Term to definition [4]

   Function, domain, range, inverse, composite


  • Definition to term [5]
  • Term to definition [5]

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


  • Definition to term [5]
  • Term to definition [5]

   Graphs: parabola, cubic, linear, reciprocal, exponential


  • Definition to term [5]
  • Term to definition [5]

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


  • Definition to term [4]
  • Term to definition [4]

Formulae



   Quadratic formula


  • Definition to term [1]
  • Term to definition [1]

   Equation of a circle


  • Definition to term [1]
  • Term to definition [1]

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

Quadratic Algebraic Manipulation



   Expanding quadratics


  • 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

   Factorising quadratics


  • 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)

Quadratic Equations



   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

   Solving simultaneous linear/quadratic


  • 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

   Quadratic inequalities


  • 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. [5]
  • 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 [3]
  • 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 [3]
  • 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 [3]
  • 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


  • Gradient of radius
  • 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 [3]
  • y=1/x, 1/x² [2]
  • y=x, x², x³, 1/x, 1/x² [5]
  • y=√x, ³√x [2]
  • y=k^x: 01 [2]
  • Non-trig graph [9]
  • y=sinx, cosx, tanx [3]
  • y=cosecx, secx, cotx [3]
  • Trig graph [6]
  • y=sin⁻¹x, cos⁻¹x, tan⁻¹x [3]

   Sketch a graph


  • y=x, x², x³ [3]
  • y=1/x, 1/x² [2]
  • y=x, x², x³, 1/x, 1/x² [5]
  • y=√x, ³√x [2]
  • y=k^x: 01 [2]
  • Non-trig graph [9]
  • y=sinx, cosx, tanx [3]
  • y=cosecx, secx, cotx [3]
  • Trig graph [6]
  • y=sin⁻¹x, cos⁻¹x, tan⁻¹x [3]

• MEASUREMENT and GEOMETRY

Definitions



   Acute, right, obtuse, reflex


  • Definition to term [4]
  • Term to definition [4]

   Bearing, elevation, depression, perpendicular


  • Definition to term [4]
  • Term to definition [4]

   Polygons: 3-6 sides


  • Definition to term [4]
  • Term to definition [4]

   Polygons: 7-10 sides


  • Definition to term [4]
  • Term to definition [4]

   Polygon, regular, interior, exterior


  • Definition to term [4]
  • Term to definition [4]

   Equilateral, isosceles, right-angled, scalene


  • Definition to term [4]
  • Term to definition [4]

   Square, rhombus, parallelogram, trapezium, rectangle, kite


  • Definition to term [6]
  • Term to definition [6]

   Radius, diameter, circumference, chord


  • Definition to term [4]
  • Term to definition [4]

   Arc, sector, tangent, segment


  • Definition to term [4]
  • Term to definition [4]

   Pressure, speed, density, acceleration


  • Definition to term [4]
  • Term to definition [4]

   Vector, scalar, magnitude, resultant


  • Definition to term [4]
  • Term to definition [4]

   Translation, rotation, reflection, enlargement


  • Definition to term [4]
  • Term to definition [4]

Formulae



   Pythagoras


  • Definition to term [1]
  • Term to definition [1]

   Sin, Cos, Tan ratios


  • Definition to term [3]
  • Term to definition [3]

   Sine, Cosine rules and Area of triangle


  • Definition to term [5]
  • Term to definition [5]

   Area of trapezium, volume of prism


  • Definition to term [2]
  • Term to definition [2]

   Circumference and area of circle


  • Definition to term [2]
  • Term to definition [2]

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°)

   Quadrilaterals


  • 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) [1]
  • Equilateral triangle from baseline (big) [1]
  • Square from baseline (small) [1]
  • Square from baseline (big) [1]
  • Regular hexagon from baseline (small) [1]
  • Regular hexagon from baseline (big) [1]
  • Misc regular polygon from baseline (small) [3]
  • Misc regular polygon from baseline (big) [3]

   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
  • Cyclic quadrilaterals
  • 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° [5]
  • cos 0, 30, 45, 60, 90° [5]
  • tan 0, 30, 45, 60, 90° [5]
  • sin/cos/tan 0, 30, 45, 60, 90°
  • sin 120-360° [12]
  • cos 120-360° [12]
  • tan 120-360° [12]
  • 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


  • Addition
  • 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 [4]
  • Term to definition [4]

   Histogram, freq density, class width, grouped freq table


  • Definition to term [4]
  • Term to definition [4]

   Mean, median, mode, range


  • Definition to term [4]
  • Term to definition [4]

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 [4]
  • Term to definition [4]

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


  • Definition to term [4]
  • Term to definition [4]

   Mutually exclusive, independent, AND rule, OR rule


  • Definition to term [4]
  • Term to definition [4]

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


  • Definition to term [7]
  • Term to definition [7]

Probability



   Probability basics


  • Identify valid probabilities
  • Name probabilities [7]
  • 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 [7]
  • 2 dice [7]
  • 2 coins [6]
  • 3 coins [9]
  • 4 coins [12]

   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 [5]
  • Term to definition [5]

Polynomials



   Polynomial expressions


  • Order
  • Add cubics
  • Subtract cubics
  • Multiply linear by quadratic
  • Multiply linear by cubic
  • Multiply quadratic by quadratic
  • 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,