KS5 - Core Maths - Wales

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	Solving quadratic equations.
38	A Roots	Completing the square
39	A Roots	Solving quadratic equations by completing the square
40	A Roots	The quadratic formula
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	Gradient
77	G Coordinate geometry	Gradient formula.
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

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KS5 – Core Mathematics – Wales

KS5 – Core Mathematics

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