GCSE Module 3 Foundation
- what you need to know

This is a list of all the topics that you need to know for Module 3 Foundation level. An idea of the grade level is given in brackets

Integers

• Understand positive and negative integers (G)
• Add and subtract negative integers (F)
• Multiply and divide negative integers (E)
• Find the factors of a number (G)
• Find the least common multiple (LCM) of two simple numbers (C)
• Find the highest common factor (HCF) of two simple numbers (C)
• Recognise prime numbers (C)
• Write a number as a product of prime factors (C)
• Find the reciprocal of a number (C)

Rounding

• Round to the nearest integer (G)
• Write an integer correct to the nearest 10 or the nearest 100 (G)
• Round numbers to given powers of 10 and to given numbers of decimal places (F)
• Round a number to one significant figure (E)
• Estimate answers to problems involving decimals (G)
• Estimate square roots (F)
• Estimate answers to calculations involving division (D)
• Estimate answers to calculations involving division by numbers less than one (C)
• Find minimum and maximum values (C)

Decimals

• Write down the place value of a digit, for example, what is the value of the 4 in 0.24? (F)
• Order decimals, for example, which is bigger, 0.24 or 0.3? (F)
• Add and subtract decimals (E)
• Multiply two decimals, such as 2.4 × 0.7 (D)
• Divide a number by a decimal, such as 1 ÷ 0.2 and 2.8 ÷ 0.07 (C)
• Convert decimals to fractions and fractions to decimals (D)

Fractions

• Find equivalent fractions (G)
• Simplify fractions (F)
• Arrange fractions in order of size (F)
• Work out fractions of quantities (E)
• Find one number as a fraction of another (E)
• Do calculations with simple fractions involving addition (E)
• Do calculations with simple fractions involving subtraction (D)
• Do calculations with mixed numbers (C)
• Do calculations with simple fractions involving multiplication (E)
• Do calculations with simple fractions involving division (C)

Indices

• Calculate squares and square roots (with and without the use of a calculator) (F)
• Calculate cubes and cube roots (with and without the use of a calculator) (E)
• Use function keys on a calculator for powers and roots (E)
• Use the terms square, positive square root, negative square root, cube and cube root (D)
• Remember the square numbers from 2 × 2 to 15 × 15 and the square roots that go with them (D)
• Recall the cubes of 2, 3, 4, 5 and 10 (D)
• Use index notation and index laws for positive and negative powers (C)

Percentages

• Understand that percentage means 'out of 100' (F)
• Change a percentage to a fraction or a decimal and vice versa (F)
• Compare percentages, fractions and decimals (E)
• Work out a percentage of a given quantity (E)
• Calculate simple interest (E)
• Increase or decrease a quantity by a given percentage (D)
• Express one quantity as a percentage of another (D)
• Work out a percentage increase or decrease (C)

Ratio & Proportion

• Solve simple ratio and proportion problems, such as finding the ratio of teachers to students in a school (D)
• Solve more complex ratio and proportion problems, such as sharing out money between two groups in the ratio of their numbers (C)
• Solve ratio and proportion problems using the unitary method (C)