1. Number

• Identify and use: • natural numbers • integers (positive, zero and negative) • prime numbers • square numbers • cube numbers • common factors • common multiples • rational and irrational numbers • reciprocals. Example tasks include: • convert between numbers and words, e.g. six billion is 6 000 000 000 10 007 is ten thousand and seven • express 72 as a product of its prime factors • find the highest common factor (HCF) of two numbers • find the lowest common multiple (LCM) of two numbers.

• Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets. Venn diagrams are limited to two or three sets. The following set notation will be used: • n(A) Number of elements in set A • ∈ “… is an element of …” • ∉ “… is not an element of …” • A′ Complement of set A • ∅ The empty set • Universal set • A ⊆ B A is a subset of B • A ⊈ B A is not a subset of B • A ∪ B Union of A and B • A ∩ B Intersection of A and B. Example definition of sets: A = {x: x is a natural number} B = {(x, y): y = mx + c} C = {x: a ⩽ x ⩽ b} D = {a, b, c, … }.

• Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers. Includes recall of squares and their corresponding roots from

• Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.

• Recognise equivalence and convert between these forms. Candidates are expected to be able to write fractions in their simplest form. Recurring decimal notation is required, e.g. •..01 70 1777f=o •..0 123 0 1232323f=oo •..0 123 0 123123f= Includes converting between recurring decimals and fractions and vice versa, e.g. write.01 7o as a fraction.

• Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, <, ⩾ and ⩽.

• Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets. Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.

E1.7.1Understand and use indices (positive, zero, negative, and fractional).

• Understand and use indices (positive, zero, negative, and fractional).

E1.7.2Understand and use the rules of indices

• Understand and use the rules of indices. Examples include: • 662 = • 16 1644 = • find the value of 7 –2, 812, 8 3 2-. e.g. find the value of 2–3 × 24, (23)2, 23 ÷ 24.

• Use standard form A × 10ⁿ, where n is a positive or negative integer and 1 ≤ A < 10.

• Convert numbers into and out of standard form.

• Calculate with values in standard form.

• Round values to a specified degree of accuracy.

• Make estimates for calculations involving numbers, quantities and measurements.

• Round answers to a reasonable degree of accuracy in the context of a given problem. Includes decimal places and significant figures. e.g. write 5764 correct to the nearest thousand. For example, estimate a calculation by rounding each value to one significant figure.

• Give upper and lower bounds for data rounded to a specified accuracy.

• Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy. e.g. write down the upper bound of a length measured correct to the nearest metre. Example calculations include: • calculate the upper bound of the perimeter or the area of a rectangle given dimensions measured to the nearest centimetre • find the lower bound of the speed given rounded values of distance and time.

• Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context. e.g. 20: 30:

• Use common measures of rate.

• Apply other measures of rate.

• Solve problems involving average speed. e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption. e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45 km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm³ (grams per cubic centimetre).

• Calculate a given percentage of a quantity.

• Express one quantity as a percentage of another.

• Calculate percentage increase or decrease.

• Calculate with simple and compound interest.

• Calculate using reverse percentages. Problems may include repeated percentage change. Formulas are not given. e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: • deposit • discount • profit and loss (as an amount or a percentage) • earnings • percentages over 100%.

• Use a calculator efficiently, retaining unrounded values during a calculation and rounding only the final answer.

• Enter values appropriately on a calculator, including time expressed as decimal hours or in degrees, minutes and seconds.

• Interpret calculator displays appropriately in context, including money and time.

• Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.

• Calculate times in terms of the 24-hour and 12-hour clock.

• Read clocks and timetables. 1 year = 365 days. In the 24-hour clock, for example, 3.15 a.m. will be denoted by 03 15 and 3.15 p.m. by 15 15. Includes problems involving time zones, local times and time differences.

• Calculate with money.

• Convert from one currency to another.

• Use exponential growth and decay. e.g. depreciation, population change. Knowledge of e is not required.

• Understand and use surds, including simplifying expressions.

• Rationalise the denominator. Examples include: • 20 25= • 200 32 62− =. Examples include: • 10 25= • − + = +.