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

• Understand and use set language, notation and Venn diagrams to describe sets. Venn diagrams are limited to two sets. The following set notation will be used: • n(A) Number of elements in set A • A′ Complement of set A • Universal set • 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 = {a, b, c, … } C = {x: a ⩽ x ⩽ b}.

• 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 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, For example, evaluate square and cube roots of familiar perfect powers.

• 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. Candidates are not expected to use recurring decimal notation. Candidates are not expected to demonstrate the conversion of a recurring decimal to a fraction and vice versa.

• 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.

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

• Understand and use the rules of indices. e.g. find the value of 7 –2. e.g. find the value of 2–3 × 24, (23)2, 23 ÷ 24.

• Use the 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. Core candidates are expected to calculate with standard form only on Paper 3.

• 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.

C1.10.1

• Give upper and lower bounds for data rounded to a specified accuracy. e.g. write down the upper bound of a length measured correct to the nearest metre. Candidates are not expected to find the bounds of the results of calculations which have used data rounded to a specified accuracy.

• 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: 40 in its simplest form is 2: 3: 4. e.g. adapt recipes; use map scales; determine best value.

• 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; formulas are not given. Percentage contexts may include deposits, discounts, profit and loss, earnings and percentages greater than 100%.

• Use a calculator efficiently.

• Enter values appropriately on a calculator.

• Interpret the calculator display appropriately. e.g. know not to round values within a calculation and to only round the final answer. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.

• 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.