| 1 |
Initial Assessment |
Initial Assessment |
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| 2 |
N
Indices |
Adding indices when multiplying terms with the same bas… |
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| 3 |
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Indices |
Subtracting indices when dividing terms with the same b… |
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| 4 |
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Indices |
Multiplying indices when raising a power to a power |
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| 5 |
N
Indices |
Multiplying indices when raising to more than one term |
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| 6 |
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Indices |
Terms raised to the power of zero |
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| 7 |
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Indices |
Negative Indices |
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| 8 |
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Indices |
Fractional indices |
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| 9 |
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Indices |
Complex fractions as indices |
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| 10 |
N
Surds |
Introducing surds |
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| 11 |
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Surds |
Some rules for the operations with surds |
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| 12 |
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Surds |
Simplifying surds |
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| 13 |
N
Surds |
Creating entire surds |
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| 14 |
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Surds |
Adding and subtracting like surds |
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| 15 |
N
Surds |
Expanding surds |
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| 16 |
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Surds |
Conjugate binomials with surds |
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| 17 |
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Surds |
Rationalising the denominator |
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| 18 |
N
Surds |
Rationalising binomial denominators |
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| 19 |
N
Surds |
Graphing irrational roots |
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| 20 |
A
Equations |
Simultaneous equations |
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| 21 |
A
Equations |
Elimination method |
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| 22 |
A
Equations |
Elimination method part 2 |
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| 23 |
A
Equations |
Applications of simultaneous equations |
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| 24 |
A
Inequalities |
Solving Inequalities. |
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| 25 |
A
Simplifying |
Simplifying algebraic fractions. |
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| 26 |
A
Simplifying |
Simplifying algebraic fractions using the index laws. |
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| 27 |
A
Simplifying |
Algebraic fractions resulting in negative indices. |
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| 28 |
A
Simplifying |
Cancelling binomial factors in algebraic fractions. |
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| 29 |
A
Factorising |
Common factor and the difference of two squares |
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| 30 |
A
Factorising |
Factorising quadratic trinomials [monic] – Case 2. |
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| 31 |
A
Factorising |
Factorising quadratic trinomials [monic] – Case 3. |
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| 32 |
A
Factorising |
Factorising quadratic trinomials [monic] – Case 4. |
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| 33 |
A
Factorising |
Factorisation of non-monic quadratic trinomials |
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| 34 |
A
Factorising |
Factorisation of non-monic quadratic trinomials – moon … |
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| 35 |
A
Roots |
Difference of two squares |
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| 36 |
A
Roots |
Quadratic equations with factorisation. |
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| 37 |
A
Roots |
Solving quadratic equations. |
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| 38 |
A
Roots |
Completing the square |
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| 39 |
A
Roots |
Solving quadratic equations by completing the square |
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| 40 |
A
Roots |
The quadratic formula |
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| 41 |
A
Roots |
Problem solving with quadratic equations |
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| 42 |
A
Roots |
Solving simultaneous quadratic equations graphically |
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| 43 |
A
Graphs |
Quadratic polynomials of the form y = ax. + bx + c. |
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| 44 |
A
Graphs |
Graphing perfect squares: y=(a-x) squared |
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| 45 |
A
Graphs |
Solve by graphing |
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| 46 |
A
Graphs |
Graphing complex polynomials: quadratics with no real r… |
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| 47 |
A
Graphs |
General equation of a circle: determine and graph the e… |
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| 48 |
A
Graphs |
Graphing cubic curves |
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| 49 |
A
Graphs |
Graphs of polynomials |
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| 50 |
A
Polynomials |
Introduction to polynomials |
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| 51 |
A
Polynomials |
The sum, difference and product of two polynomials. |
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| 52 |
A
Polynomials |
Polynomials and long division. |
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| 53 |
A
Polynomials |
Polynomial equations |
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| 54 |
A
Factor theorem |
The factor theorem |
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| 55 |
A
Factor theorem |
More on the factor theorem |
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| 56 |
A
Factor theorem |
Complete factorisations using the factor theorem |
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| 57 |
A
Factorising |
Expansions leading to the difference of two squares |
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| 58 |
A
Remainder theorem |
The remainder theorem. |
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| 59 |
A
Remainder theorem |
More on remainder theorem |
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| 60 |
A
Modulus |
Absolute value equations |
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| 61 |
A
Roots |
Sum and difference of two cubes. |
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| 62 |
A
Roots |
Sum and product of roots of quadratic equations |
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| 63 |
A
Roots |
Sum and product of roots of cubic and quartic equations |
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| 64 |
A
Roots |
Methods of approximating roots |
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| 65 |
A
Proofs |
Inductive and deductive reasoning |
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| 66 |
A
Proofs |
Definition and use of counter examples |
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| 67 |
A
Proofs |
Indirect proofs |
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| 68 |
A
Proofs |
Mathematical induction |
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| 69 |
A
Proofs |
Conditional statements (converse, inverse and contrapos… |
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| 70 |
G
Transformations |
Use grids to enlarge/reduce 2D shapes |
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| 71 |
G
Transformations |
Special transformations – reflections, rotations and en… |
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| 72 |
G
Transformations |
Transformations – reflections |
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| 73 |
G
Transformations |
The definition and concept of combined transformations … |
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| 74 |
G
Coordinate geometry |
Distance formula. |
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| 75 |
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Coordinate geometry |
Mid-point formula |
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| 76 |
G
Coordinate geometry |
Gradient |
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| 77 |
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Coordinate geometry |
Gradient formula. |
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| 78 |
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Coordinate geometry |
The straight line. |
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| 79 |
G
Coordinate geometry |
Lines through the origin. |
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| 80 |
G
Coordinate geometry |
General form of a line and the x and y Intercepts. |
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| 81 |
G
Coordinate geometry |
Slope intercept form of a line. |
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| 82 |
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Coordinate geometry |
Point slope form of a line |
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| 83 |
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Coordinate geometry |
Two point formula: equation of a line which joins a pai… |
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| 84 |
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Coordinate geometry |
Intercept form of a straight line: find the equation wh… |
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| 85 |
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Coordinate geometry |
Parallel lines: identify equation of a line parallel to… |
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| 86 |
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Coordinate geometry |
Perpendicular lines. |
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| 87 |
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Coordinate geometry |
Perpendicular distance |
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| 88 |
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Coordinate geometry |
Line through intersection of two given lines |
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| 89 |
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Coordinate geometry |
Angles between two lines |
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| 90 |
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Coordinate geometry |
Internal and external division of an interval |
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| 91 |
G
Co-ordinate Geometry |
Triangle inequality theorem |
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| 92 |
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Circles |
The equation of a circle: to find radii of circles |
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| 93 |
G
Circles |
The semicircle: to select the equation given the semi c… |
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| 94 |
N
Surds |
Binomial expansions |
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| 95 |
N
Binomial |
Binomial products. |
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| 96 |
N
Binomial |
Binomial products with negative multiplier |
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| 97 |
N
Binomial |
Binomial products [non-monic]. |
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| 98 |
N
Binomial |
Squaring a binomial. [monic] |
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| 99 |
N
Binomial |
Squaring a binomial [non-monic]. |
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| 100 |
N
Probability |
Binomial Theorem – Pascal’s Triangle |
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| 101 |
AC
Differentiation |
Differentiation from first principles. |
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| 102 |
AC
Differentiation |
Differentiation of y = x to the power of n. |
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| 103 |
AC
Differentiation |
Meaning of dy over dx – equations of tangents and norma… |
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| 104 |
AC
Differentiation |
Function of a function rule, product rule, quotient rul… |
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| 105 |
AC
Differentiation |
Increasing, decreasing and stationary functions. |
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| 106 |
AC
Differentiation |
First Derivative – turning points and curve sketching |
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| 107 |
AC
Differentiation |
The second derivative – concavity. |
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| 108 |
AC
Differentiation |
Curve sketching |
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| 109 |
AC
Differentiation |
Practical applications of maxima and minima |
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| 110 |
AC
Differentiation |
Limits |
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| 111 |
AC
Integration |
Integration – anti-differentiation, primitive function |
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| 112 |
AC
Integration |
Computation of an area |
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| 113 |
AC
Integration |
Computation of volumes of revolution |
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| 114 |
AC
Integration |
The Trapezium rule and Simpson’s rule |
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| 115 |
AS
Series and sequences |
The arithmetic progression |
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| 116 |
AS
Series and sequences |
Finding the position of a term in an A.P. |
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| 117 |
AS
Series and sequences |
Given two terms of A.P., find the sequence. |
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| 118 |
AS
Series and sequences |
Arithmetic means |
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| 119 |
AS
Series and sequences |
The sum to n terms of an A.P. |
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| 120 |
AS
Series and sequences |
The geometric progression. |
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| 121 |
AS
Series and sequences |
Finding the position of a term in a G.P. |
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| 122 |
AS
Series and sequences |
Given two terms of G.P., find the sequence. |
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| 123 |
AS
Series and sequences |
Geometric means. |
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| 124 |
AS
Series and sequences |
The sum to n terms of a G.P. |
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| 125 |
AS
Series and sequences |
Sigma notation |
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| 126 |
AS
Series and sequences |
Limiting sum or sum to infinity. |
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| 127 |
AS
Series and sequences |
Recurring decimals and the infinite G.P. |
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| 128 |
AS
Series and sequences |
Superannuation. |
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| 129 |
AS
Series and sequences |
Time payments. |
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| 130 |
AS
Series and sequences |
Applications of arithmetic sequences |
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| 131 |
G
Trigonometry |
Graphing the trigonometric ratios – I Sine curve. |
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| 132 |
G
Trigonometry |
Graphing the trigonometric ratios – II Cosine curve. |
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| 133 |
G
Trigonometry |
Graphing the trigonometric ratios – III Tangent curve. |
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| 134 |
G
Trigonometry |
Graphing the trigonometric ratios – IV Reciprocal ratio… |
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| 135 |
G
Trigonometry |
Trigonometric ratios. |
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| 136 |
G
Trigonometry |
Using the calculator. |
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| 137 |
G
Trigonometry |
Using the trigonometric ratios to find unknown length. … |
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| 138 |
G
Trigonometry |
Using the trigonometric ratios to find unknown length. … |
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| 139 |
G
Trigonometry |
Using the trigonometric ratios to find unknown length. … |
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| 140 |
G
Trigonometry |
Unknown in the denominator. [Case 4]. |
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| 141 |
G
Trigonometry |
Angles of elevation and depression. |
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| 142 |
G
Trigonometry |
Trigonometric ratios in practical situations. |
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| 143 |
G
Trigonometry |
Using the calculator to find an angle given a trigonome… |
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| 144 |
G
Trigonometry |
Using the trigonometric ratios to find an angle in a ri… |
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| 145 |
G
Trigonometry |
Trigonometric ratios of 30., 45. and 60. – exact ratios… |
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| 146 |
G
Trigonometry |
The cosine rule to find an unknown side. [Case 1 SAS]. |
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| 147 |
G
Trigonometry |
The cosine rule to find an unknown angle. [Case 2 SSS]. |
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| 148 |
G
Trigonometry |
The sine rule to find an unknown side. Case 1. |
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| 149 |
G
Trigonometry |
The sine rule to find an unknown angle. Case 2. |
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| 150 |
G
Trigonometry |
The area formula |
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| 151 |
G
Trigonometry |
Reciprocal ratios. |
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| 152 |
G
Trigonometry |
Trigonometric identities |
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| 153 |
G
Trigonometry |
Angles of any magnitude |
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| 154 |
G
Trigonometry |
Trigonometric ratios of 0°, 90°, 180°, 270° and 360° |
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| 155 |
G
Trigonometry |
Using one ratio to find another. |
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| 156 |
G
Trigonometry |
Solving trigonometric equations – Type I. |
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| 157 |
G
Trigonometry |
Solving trigonometric equations – Type II. |
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| 158 |
G
Trigonometry |
Solving trigonometric equations – Type III. |
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| 159 |
G
Trigonometry |
Plotting polar coordinates and converting polar to rect… |
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| 160 |
G
Trigonometry |
Converting rectangular coordinates to polar form |
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| 161 |
G
Trigonometry |
Write and graph points in polar form with negative vect… |
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| 162 |
G
Trigonometry |
Sin(A+B) etc sum and difference identities (Stage 2) |
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| 163 |
G
Trigonometry |
Double angle formulas (Stage 2) |
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| 164 |
G
Trigonometry |
Half angle identities (Stage 2) |
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| 165 |
G
Trigonometry |
t Formulas (Stage 2) |
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| 166 |
AL
Exponentials |
The exponential function. |
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| 167 |
AL
Logarithms |
Logarithmic functions. |
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| 168 |
AL
Logarithms |
Powers of 2. |
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| 169 |
AL
Logarithms |
Equations of type log x to the base 3 = 4. |
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| 170 |
AL
Logarithms |
Equations of type log 32 to the base x = 5. |
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| 171 |
AL
Logarithms |
Laws of logarithms. |
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| 172 |
AL
Logarithms |
Using the log laws to expand logarithmic expressions. |
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| 173 |
AL
Logarithms |
Using the log laws to simplify expressions involving lo… |
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| 174 |
AL
Logarithms |
Using the log laws to find the logarithms of numbers. |
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| 175 |
AL
Logarithms |
Equations involving logarithms. |
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| 176 |
AL
Logarithms |
Using logarithms to solve equations. |
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| 177 |
AL
Logarithms |
Change of base formula |
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| 178 |
AL
Logarithms |
The graph of the logarithmic curve |
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| 179 |
AL
Logarithms |
Working with log curves. |
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| 180 |
G
Functions |
Definition, domain and range |
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| 181 |
G
Functions |
Notation and evaluations |
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| 182 |
G
Functions |
More on domain and range |
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| 183 |
G
Functions |
Domain and range from graphical representations |
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| 184 |
G
Functions |
Evaluating and graphing piecewise functions |
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| 185 |
G
Functions |
Functions combinations |
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| 186 |
G
Functions |
Composition of functions |
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| 187 |
G
Functions |
Inverse functions |
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| 188 |
G
Functions |
Rational functions Part 1 |
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| 189 |
G
Functions |
Rational functions Part 2 |
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| 190 |
G
Functions |
Parametric equations (Stage 2) |
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| 191 |
G
Functions |
Polynomial addition etc in combining and simplifying fu… |
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| 192 |
G
Functions |
Parametric functions (Stage 2) |
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| 193 |
A
Matrices |
Vectors |
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| 194 |
N
Speed |
Average speed |
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| 195 |
N
Speed |
Using subscripted variables |
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| 196 |
N
Speed |
Uniform motion with equal distances |
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| 197 |
N
Speed |
Uniform motion adding the distances |
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| 198 |
N
Speed |
Uniform motion with unequal distances |
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| 199 |
N
Speed |
Uniform motion of all types |
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| 200 |
N
Speed |
Motion under gravity – objects in vertical motion |
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| 201 |
N
Speed |
Introducing initial velocity |
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| 202 |
N
Approximation |
Newton’s method of approximation |
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| 203 |
ACN
Complex numbers |
Imaginary numbers and standard form |
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| 204 |
ACN
Complex numbers |
Complex numbers – multiplication and division |
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| 205 |
ACN
Complex numbers |
Plotting complex number and graphical representation |
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| 206 |
ACN
Complex numbers |
Absolute value |
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| 207 |
ACN
Complex numbers |
Trigonometric form of a complex number |
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| 208 |
ACN
Complex numbers |
Multiplication and division of complex numbers in trig … |
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| 209 |
ACN
Complex numbers |
DeMoivre’s theorem (Stage 2) |
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| 210 |
ACN
Complex numbers |
The nth root of real and complex numbers (Stage 2) |
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| 211 |
ACN
Complex numbers |
Fundamental theorem of algebra (Stage 2) |
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| 212 |
G
Matrices |
Basic concepts – Matrices |
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| 213 |
G
Matrices |
Addition and subtraction of matrices |
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| 214 |
G
Matrices |
Scalar matrix multiplication |
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| 215 |
G
Matrices |
Multiplication of one matrix by another matrix |
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| 216 |
G
Matrices |
Translation in the number plane |
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| 217 |
G
Matrices |
Translation by matrix multiplication |
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| 218 |
G
Matrices |
Number of solutions (Stage 2) |
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| 219 |
G
Matrices |
2 vector addition in 2 and 3D (stage 2) |
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| 220 |
G
Matrices |
Optimal solutions (Stage 2) – Vectors |
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| 221 |
G
Matrices |
Linear systems with matrices (Stage 2) |
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| 222 |
G
Matrices |
Row-echelon form (Stage 2) |
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| 223 |
G
Matrices |
Gauss Jordan elimination method (Stage 2) |
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| 224 |
G
Parabola |
The parabola: to describe properties of a parabola from… |
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| 225 |
G
Conic sections |
The rectangular hyperbola. |
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| 226 |
G
Conic sections |
Introduction to conic sections and their general equati… |
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| 227 |
G
Conic sections |
The parabola x. = 4ay |
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| 228 |
G
Conic sections |
Circles |
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| 229 |
G
Conic sections |
Ellipses |
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| 230 |
G
Conic sections |
Hyperbola |
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| 231 |
End of Course Assessment |
End of Course Assessment |
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