Core Curriculum
1.1 Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square and cube numbers, common factors and common multiples, rational and irrational numbers (e.g. π, √2 ), real numbers, reciprocals.
1.2 Use language, notation and Venn diagrams to describe sets and represent relationships between sets. Definition of sets e.g. A = {x: x is a natural number} B = {(x, y): y = mx + c} C = {x: a ⩽ x ⩽ b} D = {a, b, c, …}
1.3 Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers.
1.4 Use directed numbers in practical situations.
1.5 Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts. Recognise equivalence and convert between these forms.
1.6 Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾, ⩽.
1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.
Use the standard form A × 10n where n is a positive or negative integer, and 1 ⩽ A <10
1.8 Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.
Extended curriculum continued
1.9 Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.
1.10 Give appropriate upper and lower bounds for data given to a specified accuracy.
Obtain appropriate upper and lower bounds to solutions of simple problems given data to a specified accuracy.
1.11 Demonstrate an understanding of ratio and proportion.
Increase and decrease a quantity by a given ratio.
Calculate average speed. Use common measures of rate.
1.12 Calculate a given percentage of a quantity. Express one quantity as a percentage of another.
Calculate percentage increase or decrease.
Carry out calculations involving reverse percentages.
1.13 Use a calculator efficiently.
Apply appropriate checks of accuracy.
1.14 Calculate times in terms of the 24-hour and 12-hour clock.
Read clocks, dials and timetables.
1.15 Calculate using money and convert from one currency to another.
1.16 Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest.
Extract data from tables and charts.
1.17 Use exponential growth and decay in relation to population and finance.
Notes/Examples
Includes expressing numbers as a product of prime factors. Finding the lowest common multiple (LCM) and highest common factor (HCF) of two or more numbers.
Notation Number of elements in set A n(A) “… is an element of …” ∈ “ …is not an element of …” ∉ Complement of set A A′ The empty set ∅ Universal set A is a subset of B A ⊆B A is a proper subset of B A ⊂B A is not a subset of B A ⊈ B A is not a proper subset of B A ⊄B Union of A and B A ∪ B Intersection of A and B A ∩ B
Work out 3² ∜16
e.g. temperature changes, flood levels.
Includes the conversion of recurring decimals to fractions, e.g. change 0.7 to a fraction
5½ = √5
Find the value of 5–², 100½ , 8-2/3
Work out 2-3 × 24 , (2³ )² , (2-3 ÷ 24 )
Convert numbers into and out of standard form. Calculate with values in standard form.
Applies to positive and negative numbers.
e.g. measured lengths.
e.g. the calculation of the perimeter or the area of a rectangle.
To include numerical problems involving direct and inverse proportion.
Use ratio and scales in practical situations.
Formulae for other rates will be given in the question e.g. pressure and density.
e.g. finding the cost price given the selling price and the percentage profit.
Includes discount, profit and loss.
Knowledge of compound interest formula is required.
e.g. depreciation, growth of bacteria.
