Numbers and Proportional Reasoning
1. Multiples, factors and primes.
2. Rules of divisibility.
3. Find the prime factor decomposition of numbers.
4. Use LCM and HCF.
5. Add and subtract fractions by writing them with a common denominator.
6. Multiply and divide and integer by a fraction.
7. Add, subtract, multiply and divide fractions
8. Use the equivalence of F.D.P (fraction – decimal – percentage) to compare proportions, calculate percentages and calculate the result of a percentage increase or decrease.
9. Solve problems involving percentage change.
10. Understand the relationship between ratio and proportion.
11. Reduce a ratio to its simples form.
12. Divide a quantity in a given ratio.
13. Unitary method to solve problems.
14. Extend knowledge of integer powers of 10, multiply and divide by any power of 10.
15. Write numbers in standard form.
16. Round decimals to whole, 1 or 2 decimal places.
17. Round to significant figures (whole numbers and decimals).
18. Understand upper and lower bound (exercises and problems).
Algebra and Sequences
19. Understand the meaning of the words: Equation, Formulae, Identity, and Expression.
20. Simplify linear expression by collecting like terms.
21. Substitute numbers into expressions and formulae.
22. Construct and solve linear equations.
23. Solve linear equations with integer coefficients, unknown in both sides, using brackets and using negatives.
24. Construct and solve linear inequalities in one variable.
25. Represent the solution set on a number line and as an interval.
26. Use squares, positive and negative square roots, and index notation for small integer powers.
27. Use index notation for rational powers and apply index laws (addition of indexes, subtraction of indexes, multiplication of indexes, negative index, zero index, and fractional indexes; multiplication of two single terms – monomial times monomial).
28. Expand the product of two simple linear expressions and simplify the corresponding quadratic expression [multiplication of linear binomials; e.g.: (2x + 3)(x – 5), (a – 2b)(-3a + 4b); and multiplication of special binomials; e.g.: (a + 3)(a + 3), (4x – 7)(4x + 7)]
29. Factorise algebraic expressions (common factor).
30. Add simple algebraic fractions.
31. Generate sequences, begin to use linear expression to describe the nth term.
32. Write an expression for the nth term of an arithmetic sequence.
33. Recognise that equations of the form y = mx + c are straight line graphs.
34. Plot graphs given values for m and c, find m and c given the equation.
35. Investigate the gradients of parallel lines.
36. Link a graphical representation to a simultaneous solution.
37. Solve a pair of simultaneous linear equations by eliminating one variable.
38. Understand and use measures related to speed.
39. Solve problems involving average speed.
40. Interpret graphs arising from real situations – distance time graphs.
Geometry and Mensuration
41. Know the sum of angles at a point, on a straight line and in a triangle.
42. Identify parallel and perpendicular lines.
43. Identify angles inside parallel lines.
44. Solve problems using angles, parallel and intersecting lines, triangles and polygons.
45. Find and use interior and exterior angles of regular polygons.
46. Understand and apply Pythagoras theorem in all cases.
47. Use trigonometry ratios to calculate sides and angles.
48. Use and interpret bearings.
49. Know that congruence means corresponding sides and angles are equal.
50. Definition and use of similarity.
51. Enlarge 2D given a centre and a fractional or negative scale factor.
52. Know translations, reflections, and rotations.
53. Problems about perimeter.