KS5 – Core Mathematics – England
KS5 – Core Mathematics
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| 1 | Adding indices when multiplying terms with the same bas… | Indices |
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| 2 | Subtracting indices when dividing terms with the same b… | Indices |
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| 3 | Multiplying indices when raising a power to a power | Indices |
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| 4 | Multiplying indices when raising to more than one term | Indices |
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| 5 | Terms raised to the power of zero | Indices |
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| 6 | Negative Indices | Indices |
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| 7 | Fractional indices | Indices |
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| 8 | Complex fractions as indices | Indices |
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| 9 | Introducing surds | Surds |
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| 10 | Some rules for the operations with surds | Surds |
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| 11 | Simplifying surds | Surds |
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| 12 | Creating entire surds | Surds |
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| 13 | Adding and subtracting like surds | Surds |
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| 14 | Expanding surds | Surds |
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| 15 | Conjugate binomials with surds | Surds |
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| 16 | Rationalising the denominator | Surds |
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| 17 | Rationalising binomial denominators | Surds |
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| 18 | Graphing irrational roots | Surds |
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| 19 | Simultaneous equations | Equations |
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| 20 | Elimination method | Equations |
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| 21 | Elimination method part 2 | Equations |
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| 22 | Applications of simultaneous equations | Equations |
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| 23 | Solving Inequalities. | Inequalities |
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| 24 | Simplifying algebraic fractions. | Simplifying |
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| 25 | Simplifying algebraic fractions using the index laws. | Simplifying |
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| 26 | Algebraic fractions resulting in negative indices. | Simplifying |
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| 27 | Cancelling binomial factors in algebraic fractions. | Simplifying |
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| 28 | Common factor and the difference of two squares | Factorising |
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| 29 | Factorising quadratic trinomials [monic] – Case 2. | Factorising |
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| 30 | Factorising quadratic trinomials [monic] – Case 3. | Factorising |
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| 31 | Factorising quadratic trinomials [monic] – Case 4. | Factorising |
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| 32 | Factorisation of non-monic quadratic trinomials | Factorising |
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| 33 | Factorisation of non-monic quadratic trinomials – moon … | Factorising |
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| 34 | Difference of two squares | Roots |
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| 35 | Quadratic equations with factorisation. | Roots |
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| 36 | Solving quadratic equations. | Roots |
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| 37 | Completing the square | Roots |
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| 38 | Solving quadratic equations by completing the square | Roots |
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| 39 | The quadratic formula | Roots |
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| 40 | Problem solving with quadratic equations | Roots |
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| 41 | Solving simultaneous quadratic equations graphically | Roots |
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| 42 | Quadratic polynomials of the form y = ax. + bx + c. | Graphs |
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| 43 | Graphing perfect squares: y=(a-x) squared | Graphs |
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| 44 | Solve by graphing | Graphs |
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| 45 | Graphing complex polynomials: quadratics with no real r… | Graphs |
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| 46 | General equation of a circle: determine and graph the e… | Graphs |
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| 47 | Graphing cubic curves | Graphs |
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| 48 | Graphs of polynomials | Graphs |
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| 49 | Introduction to polynomials | Polynomials |
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| 50 | The sum, difference and product of two polynomials. | Polynomials |
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| 51 | Polynomials and long division. | Polynomials |
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| 52 | Polynomial equations | Polynomials |
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| 53 | The factor theorem | Factor theorem |
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| 54 | More on the factor theorem | Factor theorem |
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| 55 | Complete factorisations using the factor theorem | Factor theorem |
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| 56 | Expansions leading to the difference of two squares | Factorising |
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| 57 | The remainder theorem. | Remainder theorem |
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| 58 | More on remainder theorem | Remainder theorem |
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| 59 | Absolute value equations | Modulus |
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| 60 | Sum and difference of two cubes. | Roots |
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| 61 | Sum and product of roots of quadratic equations | Roots |
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| 62 | Sum and product of roots of cubic and quartic equations | Roots |
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| 63 | Methods of approximating roots | Roots |
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| 64 | Inductive and deductive reasoning | Proofs |
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| 65 | Definition and use of counter examples | Proofs |
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| 66 | Indirect proofs | Proofs |
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| 67 | Mathematical induction | Proofs |
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| 68 | Conditional statements (converse, inverse and contrapos… | Proofs |
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| 69 | Use grids to enlarge/reduce 2D shapes | Transformations |
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| 70 | Special transformations – reflections, rotations and en… | Transformations |
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| 71 | Transformations – reflections | Transformations |
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| 72 | The definition and concept of combined transformations … | Transformations |
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| 73 | Distance formula. | Coordinate geometry |
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| 74 | Mid-point formula | Coordinate geometry |
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| 75 | Gradient | Coordinate geometry |
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| 76 | Gradient formula. | Coordinate geometry |
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| 77 | The straight line. | Coordinate geometry |
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| 78 | Lines through the origin. | Coordinate geometry |
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| 79 | General form of a line and the x and y Intercepts. | Coordinate geometry |
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| 80 | Slope intercept form of a line. | Coordinate geometry |
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| 81 | Point slope form of a line | Coordinate geometry |
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| 82 | Two point formula: equation of a line which joins a pai… | Coordinate geometry |
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| 83 | Intercept form of a straight line: find the equation wh… | Coordinate geometry |
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| 84 | Parallel lines: identify equation of a line parallel to… | Coordinate geometry |
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| 85 | Perpendicular lines. | Coordinate geometry |
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| 86 | Perpendicular distance | Coordinate geometry |
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| 87 | Line through intersection of two given lines | Coordinate geometry |
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| 88 | Angles between two lines | Coordinate geometry |
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| 89 | Internal and external division of an interval | Coordinate geometry |
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| 90 | Triangle inequality theorem | Co-ordinate Geometry |
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| 91 | The equation of a circle: to find radii of circles | Circles |
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| 92 | The semicircle: to select the equation given the semi c… | Circles |
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| 93 | Binomial expansions | Surds |
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| 94 | Binomial products. | Binomial |
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| 95 | Binomial products with negative multiplier | Binomial |
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| 96 | Binomial products [non-monic]. | Binomial |
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| 97 | Squaring a binomial. [monic] | Binomial |
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| 98 | Squaring a binomial [non-monic]. | Binomial |
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| 99 | Binomial Theorem – Pascal’s Triangle | Probability |
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| 100 | Differentiation from first principles. | Differentiation |
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| 101 | Differentiation of y = x to the power of n. | Differentiation |
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| 102 | Meaning of dy over dx – equations of tangents and norma… | Differentiation |
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| 103 | Function of a function rule, product rule, quotient rul… | Differentiation |
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| 104 | Increasing, decreasing and stationary functions. | Differentiation |
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| 105 | First Derivative – turning points and curve sketching | Differentiation |
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| 106 | The second derivative – concavity. | Differentiation |
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| 107 | Curve sketching | Differentiation |
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| 108 | Practical applications of maxima and minima | Differentiation |
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| 109 | Limits | Differentiation |
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| 110 | Integration – anti-differentiation, primitive function | Integration |
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| 111 | Computation of an area | Integration |
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| 112 | Computation of volumes of revolution | Integration |
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| 113 | The Trapezium rule and Simpson’s rule | Integration |
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| 114 | The arithmetic progression | Series and sequences |
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| 115 | Finding the position of a term in an A.P. | Series and sequences |
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| 116 | Given two terms of A.P., find the sequence. | Series and sequences |
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| 117 | Arithmetic means | Series and sequences |
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| 118 | The sum to n terms of an A.P. | Series and sequences |
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| 119 | The geometric progression. | Series and sequences |
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| 120 | Finding the position of a term in a G.P. | Series and sequences |
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| 121 | Given two terms of G.P., find the sequence. | Series and sequences |
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| 122 | Geometric means. | Series and sequences |
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| 123 | The sum to n terms of a G.P. | Series and sequences |
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| 124 | Sigma notation | Series and sequences |
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| 125 | Limiting sum or sum to infinity. | Series and sequences |
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| 126 | Recurring decimals and the infinite G.P. | Series and sequences |
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| 127 | Superannuation. | Series and sequences |
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| 128 | Time payments. | Series and sequences |
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| 129 | Applications of arithmetic sequences | Series and sequences |
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| 130 | Graphing the trigonometric ratios – I Sine curve. | Trigonometry |
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| 131 | Graphing the trigonometric ratios – II Cosine curve. | Trigonometry |
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| 132 | Graphing the trigonometric ratios – III Tangent curve. | Trigonometry |
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| 133 | Graphing the trigonometric ratios – IV Reciprocal ratio… | Trigonometry |
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| 134 | Trigonometric ratios. | Trigonometry |
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| 135 | Using the calculator. | Trigonometry |
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| 136 | Using the trigonometric ratios to find unknown length. … | Trigonometry |
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| 137 | Using the trigonometric ratios to find unknown length. … | Trigonometry |
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| 138 | Using the trigonometric ratios to find unknown length. … | Trigonometry |
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| 139 | Unknown in the denominator. [Case 4]. | Trigonometry |
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| 140 | Angles of elevation and depression. | Trigonometry |
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| 141 | Trigonometric ratios in practical situations. | Trigonometry |
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| 142 | Using the calculator to find an angle given a trigonome… | Trigonometry |
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| 143 | Using the trigonometric ratios to find an angle in a ri… | Trigonometry |
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| 144 | Trigonometric ratios of 30., 45. and 60. – exact ratios… | Trigonometry |
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| 145 | The cosine rule to find an unknown side. [Case 1 SAS]. | Trigonometry |
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| 146 | The cosine rule to find an unknown angle. [Case 2 SSS]. | Trigonometry |
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| 147 | The sine rule to find an unknown side. Case 1. | Trigonometry |
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| 148 | The sine rule to find an unknown angle. Case 2. | Trigonometry |
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| 149 | The area formula | Trigonometry |
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| 150 | Reciprocal ratios. | Trigonometry |
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| 151 | Trigonometric identities | Trigonometry |
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| 152 | Angles of any magnitude | Trigonometry |
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| 153 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | Trigonometry |
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| 154 | Using one ratio to find another. | Trigonometry |
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| 155 | Solving trigonometric equations – Type I. | Trigonometry |
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| 156 | Solving trigonometric equations – Type II. | Trigonometry |
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| 157 | Solving trigonometric equations – Type III. | Trigonometry |
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| 158 | Plotting polar coordinates and converting polar to rect… | Trigonometry |
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| 159 | Converting rectangular coordinates to polar form | Trigonometry |
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| 160 | Write and graph points in polar form with negative vect… | Trigonometry |
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| 161 | Sin(A+B) etc sum and difference identities (Stage 2) | Trigonometry |
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| 162 | Double angle formulas (Stage 2) | Trigonometry |
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| 163 | Half angle identities (Stage 2) | Trigonometry |
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| 164 | t Formulas (Stage 2) | Trigonometry |
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| 165 | The exponential function. | Exponentials |
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| 166 | Logarithmic functions. | Logarithms |
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| 167 | Powers of 2. | Logarithms |
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| 168 | Equations of type log x to the base 3 = 4. | Logarithms |
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| 169 | Equations of type log 32 to the base x = 5. | Logarithms |
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| 170 | Laws of logarithms. | Logarithms |
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| 171 | Using the log laws to expand logarithmic expressions. | Logarithms |
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| 172 | Using the log laws to simplify expressions involving lo… | Logarithms |
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| 173 | Using the log laws to find the logarithms of numbers. | Logarithms |
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| 174 | Equations involving logarithms. | Logarithms |
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| 175 | Using logarithms to solve equations. | Logarithms |
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| 176 | Change of base formula | Logarithms |
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| 177 | The graph of the logarithmic curve | Logarithms |
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| 178 | Working with log curves. | Logarithms |
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| 179 | Definition, domain and range | Functions |
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| 180 | Notation and evaluations | Functions |
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| 181 | More on domain and range | Functions |
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| 182 | Domain and range from graphical representations | Functions |
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| 183 | Evaluating and graphing piecewise functions | Functions |
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| 184 | Functions combinations | Functions |
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| 185 | Composition of functions | Functions |
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| 186 | Inverse functions | Functions |
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| 187 | Rational functions Part 1 | Functions |
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| 188 | Rational functions Part 2 | Functions |
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| 189 | Parametric equations (Stage 2) | Functions |
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| 190 | Polynomial addition etc in combining and simplifying fu… | Functions |
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| 191 | Parametric functions (Stage 2) | Functions |
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| 192 | Vectors | Matrices |
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| 193 | Average speed | Speed |
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| 194 | Using subscripted variables | Speed |
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| 195 | Uniform motion with equal distances | Speed |
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| 196 | Uniform motion adding the distances | Speed |
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| 197 | Uniform motion with unequal distances | Speed |
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| 198 | Uniform motion of all types | Speed |
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| 199 | Motion under gravity – objects in vertical motion | Speed |
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| 200 | Introducing initial velocity | Speed |
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| 201 | Newton’s method of approximation | Approximation |
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| 202 | Imaginary numbers and standard form | Complex numbers |
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| 203 | Complex numbers – multiplication and division | Complex numbers |
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| 204 | Plotting complex number and graphical representation | Complex numbers |
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| 205 | Absolute value | Complex numbers |
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| 206 | Trigonometric form of a complex number | Complex numbers |
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| 207 | Multiplication and division of complex numbers in trig … | Complex numbers |
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| 208 | DeMoivre’s theorem (Stage 2) | Complex numbers |
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| 209 | The nth root of real and complex numbers (Stage 2) | Complex numbers |
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| 210 | Fundamental theorem of algebra (Stage 2) | Complex numbers |
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| 211 | Basic concepts – Matrices | Matrices |
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| 212 | Addition and subtraction of matrices | Matrices |
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| 213 | Scalar matrix multiplication | Matrices |
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| 214 | Multiplication of one matrix by another matrix | Matrices |
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| 215 | Translation in the number plane | Matrices |
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| 216 | Translation by matrix multiplication | Matrices |
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| 217 | Number of solutions (Stage 2) | Matrices |
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| 218 | 2 vector addition in 2 and 3D (stage 2) | Matrices |
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| 219 | Optimal solutions (Stage 2) – Vectors | Matrices |
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| 220 | Linear systems with matrices (Stage 2) | Matrices |
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| 221 | Row-echelon form (Stage 2) | Matrices |
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| 222 | Gauss Jordan elimination method (Stage 2) | Matrices |
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| 223 | The parabola: to describe properties of a parabola from… | Parabola |
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| 224 | The rectangular hyperbola. | Conic sections |
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| 225 | Introduction to conic sections and their general equati… | Conic sections |
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| 226 | The parabola x. = 4ay | Conic sections |
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| 227 | Circles | Conic sections |
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| 228 | Ellipses | Conic sections |
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| 229 | Hyperbola | Conic sections |
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| 230 | Exam – KS5 – Maths – Core | Review of all course work |
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