GCSE Module 3 Higher
- what you need to know

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

'Mm' after a topic indicates a direct link to that topic on the Mymaths.co.uk website. You will need to login to use the Mymaths lessons. UCC students can get login details from their teacher.

You can download this list as a Pdf file by right clicking on the link and selecting save.

Integers

• Find lowest common multiple (C/B) Mm Mm
• Find highest common factor (C/B) Mm Mm
• Recognise prime numbers (C) Mm
• Write a number as the product of prime factors (C) Mm
• Find the reciprocal of a number (C)

Rounding

• Estimate answers to division calculations (D) Mm Mm
• Estimate answers to division calculations with numbers less than 1 (C) Mm Mm
• Round to significant figures (B) Mm
• Find minimum & maximum values (C) Mm Mm

Decimals

• Multiply two decimals such as 2.4 × 0.7 (D) Mm
• Divide a number by a decimal such as 1 ÷ 0.2 and 2.8 divided by 0.07 (C)
• Convert decimals to fractions and fractions to decimals (D) Mm Mm Mm
• Convert recurring decimals to fractions and fractions to recurring decimals (B) Mm Mm
• Identify recurring and terminating decimals (B)

Fractions

• Do subtraction calculations with simple fractions (D) Mm
• Do calculations with mixed numbers (C) Mm
• Do division calculations with simple fractions (C) Mm

Surds

• Simplify surds (A*) Mm
• Rationalise the denominator of a surd (A) Mm

Indices & Standard Form

• Understand and use the terms square, positive & negative, square root, cube & cube root (D)
• Know the square numbers up to 15² (D) Mm Mm
• Know the square roots up to sqrt 225 (D) Mm
• Know the cubes of 2,3,4,5 and 10 (D) Mm
• Use index notation and index laws for positive and negative powers (C) Mm
• Use index notation and index laws for fractional powers such as 16 ^¼ (A) Mm
• Use index notation and index laws for fractional powers such as 16^¾ (A*) Mm
• Use standard index form with and without a calculator (C) Mm
• Convert between ordinary numbers and standard form (B) Mm Mm

Percentages

• Increase or decrease a quantity by a given percentage (D) Mm
• Understand how to use successive percentages (B) Mm
• Work out compound interest (B) Mm
• Write one quantity as a percentage of another (D)
• Work out a percentage increase or decrease (C) Mm
• Work out reverse percentage problems (B) Mm

Ratio & Proportion

• Solve simple ratio and proportion problems, such as finding the ratio of teachers to students in a school (D) Mm
• Solve more complex ratio and proportion problems, such as sharing out money between two groups in the ratio of their numbers (C) Mm
• Solve ratio and proportion problems using the unitary method (C) Mm
• Calculate proportional changes using a multiplier (B) Mm
• Solve direct and inverse proportion problems (A) Mm
• Interpret the graphs of direct and inverse proportion relationships (A) Mm

Use of symbols

• Multiply out expressions with brackets (D) Mm
• Expand (and simplify) harder expressions  (C) Mm
• Expand (and simplify) quadratic expressions  (B) Mm
• Factorise expressions  (D) Mm
• Factorise quadratic expressions (B) Mm
• Simplify rational expressions (B)
• Factorise harder quadratic expressions (A) Mm
• Simplify harder rational expressions (A*)

Quadratic graphs

• Draw graphs of simple quadratic functions (D) Mm
• Draw graphs of harder quadratic functions (C) Mm
• Find the points of intersection of quadratic graphs with lines (C) Mm
• Use graphs to find the approximate solutions of quadratic equations (C) Mm
• Use the points of intersection of a quadratic graphs with lines to solve equations and simplify the answer (A) Mm