Year 11 Maths

What does a child learn in Year 11 maths?

Curriculum scope

1. KS4.N (our numbering) · Teaching content · checked against the act

   Number

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number

2. KS4.N.1 (our numbering) · Teaching content · checked against the act

   apply systematic listing strategies, {including use of the product rule for counting}

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.1

3. KS4.N.3 (our numbering) · Teaching content · checked against the act

   calculate with roots, and with integer {and fractional} indices

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.3

4. KS4.N.4 (our numbering) · Teaching content

   calculate exactly with fractions, {surds} and multiples of π; {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}

   our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.4

5. KS4.N.5 (our numbering) · Teaching content

   calculate with numbers in standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer

   our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.5

6. KS4.N.7 (our numbering) · Teaching content · checked against the act

   identify and work with fractions in ratio problems

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.7

7. KS4.N.8 (our numbering) · Teaching content · checked against the act

   apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}.

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Number, statutory requirement KS4.N.8

8. KS4.A (our numbering) · Teaching content · checked against the act

   Algebra

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra

9. KS4.A.1 (our numbering) · Teaching content · checked against the act

   simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by:

   National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1

10. KS4.A.2 (our numbering) · Teaching content · checked against the act

    know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.2

11. KS4.A.3 (our numbering) · Teaching content · checked against the act

    where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.3

12. KS4.A.4 (our numbering) · Teaching content

    use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.4

13. KS4.A.5 (our numbering) · Teaching content · checked against the act

    identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.5

14. KS4.A.6 (our numbering) · Teaching content

    recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, {the exponential function y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.6

15. KS4.A.8 (our numbering) · Teaching content · checked against the act

    plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.8

16. KS4.A.11 (our numbering) · Teaching content · checked against the act

    solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.11

17. KS4.A.12 (our numbering) · Teaching content · checked against the act

    solve two simultaneous equations in two variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.12

18. KS4.A.14 (our numbering) · Teaching content · checked against the act

    translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.14

19. KS4.A.15 (our numbering) · Teaching content · checked against the act

    solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in one variable}; represent the solution set on a number line, {using set notation and on a graph}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.15

20. KS4.A.16 (our numbering) · Teaching content

    recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rⁿ where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.16

21. KS4.A.17 (our numbering) · Teaching content · checked against the act

    deduce expressions to calculate the nth term of linear {and quadratic} sequences.

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.17

22. KS4.A.1.a (our numbering) · Teaching content

    factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; {factorising quadratic expressions of the form ax² + bx + c}

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1.a

23. KS4.A.1.b (our numbering) · Teaching content · checked against the act

    simplifying expressions involving sums, products and powers, including the laws of indices

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Algebra, statutory requirement KS4.A.1.b

24. KS4.R (our numbering) · Teaching content · checked against the act

    Ratio, proportion and rates of change

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change

25. KS4.R.1 (our numbering) · Teaching content · checked against the act

    compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios)

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.1

26. KS4.R.2 (our numbering) · Teaching content · checked against the act

    convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.2

27. KS4.R.3 (our numbering) · Teaching content

    understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; {construct and} interpret equations that describe direct and inverse proportion

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.3

28. KS4.R.4 (our numbering) · Teaching content · checked against the act

    interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.4

29. KS4.R.6 (our numbering) · Teaching content · checked against the act

    set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}.

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Ratio, proportion and rates of change, statutory requirement KS4.R.6

30. KS4.GM (our numbering) · Teaching content · checked against the act

    Geometry and measures

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures

31. KS4.GM.1 (our numbering) · Teaching content · checked against the act

    interpret and use fractional {and negative} scale factors for enlargements

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.1

32. KS4.GM.3 (our numbering) · Teaching content · checked against the act

    identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.3

33. KS4.GM.5 (our numbering) · Teaching content · checked against the act

    construct and interpret plans and elevations of 3D shapes

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.5

34. KS4.GM.6 (our numbering) · Teaching content · checked against the act

    interpret and use bearings

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.6

35. KS4.GM.7 (our numbering) · Teaching content · checked against the act

    calculate arc lengths, angles and areas of sectors of circles

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.7

36. KS4.GM.8 (our numbering) · Teaching content · checked against the act

    calculate surface areas and volumes of spheres, pyramids, cones and composite solids

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.8

37. KS4.GM.9 (our numbering) · Teaching content · checked against the act

    apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.9

38. KS4.GM.10 (our numbering) · Teaching content · checked against the act

    apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.10

39. KS4.GM.11 (our numbering) · Teaching content

    know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

    our summary of the point · National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.11

40. KS4.GM.14 (our numbering) · Teaching content · checked against the act

    describe translations as 2D vectors

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.14

41. KS4.GM.15 (our numbering) · Teaching content · checked against the act

    apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}.

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Geometry and measures, statutory requirement KS4.GM.15

42. KS4.P (our numbering) · Teaching content · checked against the act

    Probability

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability

43. KS4.P.1 (our numbering) · Teaching content · checked against the act

    apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.1

44. KS4.P.2 (our numbering) · Teaching content · checked against the act

    use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.2

45. KS4.P.3 (our numbering) · Teaching content · checked against the act

    calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Probability, statutory requirement KS4.P.3

46. KS4.S (our numbering) · Teaching content · checked against the act

    Statistics

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics

47. KS4.S.1 (our numbering) · Teaching content · checked against the act

    infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.1

48. KS4.S.2 (our numbering) · Teaching content · checked against the act

    interpret and construct tables and line graphs for time series data

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.2

49. KS4.S.4 (our numbering) · Teaching content · checked against the act

    interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4

50. KS4.S.5 (our numbering) · Teaching content · checked against the act

    apply statistics to describe a population

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.5

51. KS4.S.6 (our numbering) · Teaching content · checked against the act

    use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.6

52. KS4.S.4.a (our numbering) · Teaching content · checked against the act

    appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4.a

53. KS4.S.4.b (our numbering) · Teaching content · checked against the act

    appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}

    National Curriculum in England, mathematics, Key stage 4 (Years 10-11, GCSE), Statistics, statutory requirement KS4.S.4.b

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