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### KS5 – Core Mathematics

# TOPIC TITLE
1 Initial Assessment Initial Assessment

2 N

Indices
Adding indices when multiplying terms with the same bas…

3 N

Indices
Subtracting indices when dividing terms with the same b…

4 N

Indices
Multiplying indices when raising a power to a power

5 N

Indices
Multiplying indices when raising to more than one term

6 N

Indices
Terms raised to the power of zero

7 N

Indices
Negative Indices

8 N

Indices
Fractional indices

9 N

Indices
Complex fractions as indices

10 N

Surds
Introducing surds

11 N

Surds
Some rules for the operations with surds

12 N

Surds
Simplifying surds

13 N

Surds
Creating entire surds

14 N

Surds
Adding and subtracting like surds

15 N

Surds
Expanding surds

16 N

Surds
Conjugate binomials with surds

17 N

Surds
Rationalising the denominator

18 N

Surds
Rationalising binomial denominators

19 N

Surds
Graphing irrational roots

20 A

Equations
Simultaneous equations

21 A

Equations
Elimination method

22 A

Equations
Elimination method part 2

23 A

Equations
Applications of simultaneous equations

24 A

Inequalities
Solving Inequalities.

25 A

Simplifying
Simplifying algebraic fractions.

26 A

Simplifying
Simplifying algebraic fractions using the index laws.

27 A

Simplifying
Algebraic fractions resulting in negative indices.

28 A

Simplifying
Cancelling binomial factors in algebraic fractions.

29 A

Factorising
Common factor and the difference of two squares

30 A

Factorising
Factorising quadratic trinomials [monic] – Case 2.

31 A

Factorising
Factorising quadratic trinomials [monic] – Case 3.

32 A

Factorising
Factorising quadratic trinomials [monic] – Case 4.

33 A

Factorising
Factorisation of non-monic quadratic trinomials

34 A

Factorising
Factorisation of non-monic quadratic trinomials – moon …

35 A

Roots
Difference of two squares

36 A

Roots
Quadratic equations with factorisation.

37 A

Roots

38 A

Roots
Completing the square

39 A

Roots
Solving quadratic equations by completing the square

40 A

Roots

41 A

Roots
Problem solving with quadratic equations

42 A

Roots
Solving simultaneous quadratic equations graphically

43 A

Graphs
Quadratic polynomials of the form y = ax. + bx + c.

44 A

Graphs
Graphing perfect squares: y=(a-x) squared

45 A

Graphs
Solve by graphing

46 A

Graphs
Graphing complex polynomials: quadratics with no real r…

47 A

Graphs
General equation of a circle: determine and graph the e…

48 A

Graphs
Graphing cubic curves

49 A

Graphs
Graphs of polynomials

50 A

Polynomials
Introduction to polynomials

51 A

Polynomials
The sum, difference and product of two polynomials.

52 A

Polynomials
Polynomials and long division.

53 A

Polynomials
Polynomial equations

54 A

Factor theorem
The factor theorem

55 A

Factor theorem
More on the factor theorem

56 A

Factor theorem
Complete factorisations using the factor theorem

57 A

Factorising
Expansions leading to the difference of two squares

58 A

Remainder theorem
The remainder theorem.

59 A

Remainder theorem
More on remainder theorem

60 A

Modulus
Absolute value equations

61 A

Roots
Sum and difference of two cubes.

62 A

Roots
Sum and product of roots of quadratic equations

63 A

Roots
Sum and product of roots of cubic and quartic equations

64 A

Roots
Methods of approximating roots

65 A

Proofs
Inductive and deductive reasoning

66 A

Proofs
Definition and use of counter examples

67 A

Proofs
Indirect proofs

68 A

Proofs
Mathematical induction

69 A

Proofs
Conditional statements (converse, inverse and contrapos…

70 G

Transformations
Use grids to enlarge/reduce 2D shapes

71 G

Transformations
Special transformations – reflections, rotations and en…

72 G

Transformations
Transformations – reflections

73 G

Transformations
The definition and concept of combined transformations …

74 G

Coordinate geometry
Distance formula.

75 G

Coordinate geometry
Mid-point formula

76 G

Coordinate geometry

77 G

Coordinate geometry

78 G

Coordinate geometry
The straight line.

79 G

Coordinate geometry
Lines through the origin.

80 G

Coordinate geometry
General form of a line and the x and y Intercepts.

81 G

Coordinate geometry
Slope intercept form of a line.

82 G

Coordinate geometry
Point slope form of a line

83 G

Coordinate geometry
Two point formula: equation of a line which joins a pai…

84 G

Coordinate geometry
Intercept form of a straight line: find the equation wh…

85 G

Coordinate geometry
Parallel lines: identify equation of a line parallel to…

86 G

Coordinate geometry
Perpendicular lines.

87 G

Coordinate geometry
Perpendicular distance

88 G

Coordinate geometry
Line through intersection of two given lines

89 G

Coordinate geometry
Angles between two lines

90 G

Coordinate geometry
Internal and external division of an interval

91 G

Co-ordinate Geometry
Triangle inequality theorem

92 G

Circles
The equation of a circle: to find radii of circles

93 G

Circles
The semicircle: to select the equation given the semi c…

94 N

Surds
Binomial expansions

95 N

Binomial
Binomial products.

96 N

Binomial
Binomial products with negative multiplier

97 N

Binomial
Binomial products [non-monic].

98 N

Binomial
Squaring a binomial. [monic]

99 N

Binomial
Squaring a binomial [non-monic].

100 N

Probability
Binomial Theorem – Pascal’s Triangle

101 AC

Differentiation
Differentiation from first principles.

102 AC

Differentiation
Differentiation of y = x to the power of n.

103 AC

Differentiation
Meaning of dy over dx – equations of tangents and norma…

104 AC

Differentiation
Function of a function rule, product rule, quotient rul…

105 AC

Differentiation
Increasing, decreasing and stationary functions.

106 AC

Differentiation
First Derivative – turning points and curve sketching

107 AC

Differentiation
The second derivative – concavity.

108 AC

Differentiation
Curve sketching

109 AC

Differentiation
Practical applications of maxima and minima

110 AC

Differentiation
Limits

111 AC

Integration
Integration – anti-differentiation, primitive function

112 AC

Integration
Computation of an area

113 AC

Integration
Computation of volumes of revolution

114 AC

Integration
The Trapezium rule and Simpson’s rule

115 AS

Series and sequences
The arithmetic progression

116 AS

Series and sequences
Finding the position of a term in an A.P.

117 AS

Series and sequences
Given two terms of A.P., find the sequence.

118 AS

Series and sequences
Arithmetic means

119 AS

Series and sequences
The sum to n terms of an A.P.

120 AS

Series and sequences
The geometric progression.

121 AS

Series and sequences
Finding the position of a term in a G.P.

122 AS

Series and sequences
Given two terms of G.P., find the sequence.

123 AS

Series and sequences
Geometric means.

124 AS

Series and sequences
The sum to n terms of a G.P.

125 AS

Series and sequences
Sigma notation

126 AS

Series and sequences
Limiting sum or sum to infinity.

127 AS

Series and sequences
Recurring decimals and the infinite G.P.

128 AS

Series and sequences
Superannuation.

129 AS

Series and sequences
Time payments.

130 AS

Series and sequences
Applications of arithmetic sequences

131 G

Trigonometry
Graphing the trigonometric ratios – I Sine curve.

132 G

Trigonometry
Graphing the trigonometric ratios – II Cosine curve.

133 G

Trigonometry
Graphing the trigonometric ratios – III Tangent curve.

134 G

Trigonometry
Graphing the trigonometric ratios – IV Reciprocal ratio…

135 G

Trigonometry
Trigonometric ratios.

136 G

Trigonometry
Using the calculator.

137 G

Trigonometry
Using the trigonometric ratios to find unknown length. …

138 G

Trigonometry
Using the trigonometric ratios to find unknown length. …

139 G

Trigonometry
Using the trigonometric ratios to find unknown length. …

140 G

Trigonometry
Unknown in the denominator. [Case 4].

141 G

Trigonometry
Angles of elevation and depression.

142 G

Trigonometry
Trigonometric ratios in practical situations.

143 G

Trigonometry
Using the calculator to find an angle given a trigonome…

144 G

Trigonometry
Using the trigonometric ratios to find an angle in a ri…

145 G

Trigonometry
Trigonometric ratios of 30., 45. and 60. – exact ratios…

146 G

Trigonometry
The cosine rule to find an unknown side. [Case 1 SAS].

147 G

Trigonometry
The cosine rule to find an unknown angle. [Case 2 SSS].

148 G

Trigonometry
The sine rule to find an unknown side. Case 1.

149 G

Trigonometry
The sine rule to find an unknown angle. Case 2.

150 G

Trigonometry
The area formula

151 G

Trigonometry
Reciprocal ratios.

152 G

Trigonometry
Trigonometric identities

153 G

Trigonometry
Angles of any magnitude

154 G

Trigonometry
Trigonometric ratios of 0°, 90°, 180°, 270° and 360°

155 G

Trigonometry
Using one ratio to find another.

156 G

Trigonometry
Solving trigonometric equations – Type I.

157 G

Trigonometry
Solving trigonometric equations – Type II.

158 G

Trigonometry
Solving trigonometric equations – Type III.

159 G

Trigonometry
Plotting polar coordinates and converting polar to rect…

160 G

Trigonometry
Converting rectangular coordinates to polar form

161 G

Trigonometry
Write and graph points in polar form with negative vect…

162 G

Trigonometry
Sin(A+B) etc sum and difference identities (Stage 2)

163 G

Trigonometry
Double angle formulas (Stage 2)

164 G

Trigonometry
Half angle identities (Stage 2)

165 G

Trigonometry
t Formulas (Stage 2)

166 AL

Exponentials
The exponential function.

167 AL

Logarithms
Logarithmic functions.

168 AL

Logarithms
Powers of 2.

169 AL

Logarithms
Equations of type log x to the base 3 = 4.

170 AL

Logarithms
Equations of type log 32 to the base x = 5.

171 AL

Logarithms
Laws of logarithms.

172 AL

Logarithms
Using the log laws to expand logarithmic expressions.

173 AL

Logarithms
Using the log laws to simplify expressions involving lo…

174 AL

Logarithms
Using the log laws to find the logarithms of numbers.

175 AL

Logarithms
Equations involving logarithms.

176 AL

Logarithms
Using logarithms to solve equations.

177 AL

Logarithms
Change of base formula

178 AL

Logarithms
The graph of the logarithmic curve

179 AL

Logarithms
Working with log curves.

180 G

Functions
Definition, domain and range

181 G

Functions
Notation and evaluations

182 G

Functions
More on domain and range

183 G

Functions
Domain and range from graphical representations

184 G

Functions
Evaluating and graphing piecewise functions

185 G

Functions
Functions combinations

186 G

Functions
Composition of functions

187 G

Functions
Inverse functions

188 G

Functions
Rational functions Part 1

189 G

Functions
Rational functions Part 2

190 G

Functions
Parametric equations (Stage 2)

191 G

Functions
Polynomial addition etc in combining and simplifying fu…

192 G

Functions
Parametric functions (Stage 2)

193 A

Matrices
Vectors

194 N

Speed
Average speed

195 N

Speed
Using subscripted variables

196 N

Speed
Uniform motion with equal distances

197 N

Speed
Uniform motion adding the distances

198 N

Speed
Uniform motion with unequal distances

199 N

Speed
Uniform motion of all types

200 N

Speed
Motion under gravity – objects in vertical motion

201 N

Speed
Introducing initial velocity

202 N

Approximation
Newton’s method of approximation

203 ACN

Complex numbers
Imaginary numbers and standard form

204 ACN

Complex numbers
Complex numbers – multiplication and division

205 ACN

Complex numbers
Plotting complex number and graphical representation

206 ACN

Complex numbers
Absolute value

207 ACN

Complex numbers
Trigonometric form of a complex number

208 ACN

Complex numbers
Multiplication and division of complex numbers in trig …

209 ACN

Complex numbers
DeMoivre’s theorem (Stage 2)

210 ACN

Complex numbers
The nth root of real and complex numbers (Stage 2)

211 ACN

Complex numbers
Fundamental theorem of algebra (Stage 2)

212 G

Matrices
Basic concepts – Matrices

213 G

Matrices
Addition and subtraction of matrices

214 G

Matrices
Scalar matrix multiplication

215 G

Matrices
Multiplication of one matrix by another matrix

216 G

Matrices
Translation in the number plane

217 G

Matrices
Translation by matrix multiplication

218 G

Matrices
Number of solutions (Stage 2)

219 G

Matrices
2 vector addition in 2 and 3D (stage 2)

220 G

Matrices
Optimal solutions (Stage 2) – Vectors

221 G

Matrices
Linear systems with matrices (Stage 2)

222 G

Matrices
Row-echelon form (Stage 2)

223 G

Matrices
Gauss Jordan elimination method (Stage 2)

224 G

Parabola
The parabola: to describe properties of a parabola from…

225 G

Conic sections
The rectangular hyperbola.

226 G

Conic sections
Introduction to conic sections and their general equati…

227 G

Conic sections
The parabola x. = 4ay

228 G

Conic sections
Circles

229 G

Conic sections
Ellipses

230 G

Conic sections
Hyperbola

231 End of Course Assessment End of Course Assessment