GCSE Maths Foundations Course

Number work is the foundation of every GCSE maths paper. You need to move confidently between fractions, decimals, percentages, ratio and standard form, because the same value can be written in several ways and exam questions often ask you to compare or convert them.

• Fractions: add and subtract by finding a common denominator, multiply across the numerators and denominators, and divide by multiplying by the reciprocal.
• Conversions: divide the numerator by the denominator to turn a fraction into a decimal, then multiply by 100 to get a percentage.
• Ratio: divide the total by the sum of the parts to find one part, then multiply by the number of parts needed.
• Standard form: write large and small numbers as A x 10^n where 1 is less than or equal to A which is less than 10, and use index laws when multiplying or dividing.

Common pitfalls include adding fractions without a common denominator, forgetting to simplify final answers, and confusing the order of parts in a ratio. Before answering, decide which representation is easiest, then check whether your answer is sensible.

Algebra uses letters to represent unknown or changing numbers, letting you solve problems that plain arithmetic cannot describe efficiently. The key skills are simplifying expressions, solving equations and inequalities, factorising, and understanding straight-line graphs.

• Simplify: collect like terms by adding or subtracting coefficients, and expand brackets by multiplying every term inside by the term outside.
• Solve: do the same operation to both sides to keep the equation balanced; for inequalities, remember that multiplying or dividing by a negative number reverses the sign.
• Factorise: take out the highest common factor first; for x^2 + bx + c, find two numbers that multiply to c and add to b.
• Graphs: y = mx + c gives a straight line where m is the gradient and c is the y-intercept.

Common mistakes include treating 3x + 2 as 5x, dropping negative signs when expanding, and forgetting to substitute back to check answers. Always write each step clearly so you can spot errors and earn method marks.

Geometry and measures questions reward accurate formula use and careful checking. You should know the common angle facts, area and perimeter formulas, volume formulas, and when to apply Pythagoras or trigonometry.

• Angles: angles in a triangle sum to 180 degrees, angles on a straight line sum to 180 degrees, and angles in a quadrilateral sum to 360 degrees.
• Area: rectangle length x width, triangle 1/2 x base x height, circle pi x r^2; perimeter is the distance around the outside.
• Volume: volume of a prism is cross-sectional area x length; volume of a cylinder is pi x r^2 x height.
• Pythagoras: in a right-angled triangle, a^2 + b^2 = c^2 where c is the hypotenuse; label the triangle before substituting.

Common errors include using the diameter instead of the radius, mixing area with perimeter, and forgetting squared or cubed units. Write the formula first, substitute values, then check that the final units match the quantity asked for.

Statistics help you summarise data, while probability measures how likely an event is to happen. These topics often appear together, so learn the averages, how to read charts, and how to combine probabilities correctly.

• Averages: mean is the total divided by the count, median is the middle value after ordering, mode is the most common value, and range is the largest minus the smallest.
• Charts: read scales carefully, compare totals rather than single bars, and use two-way tables to organise categories.
• Probability: probability = favourable outcomes / total outcomes, and probabilities of all outcomes sum to 1.
• Complement: P(not A) = 1 - P(A); use sample spaces or tables to list equally likely outcomes.

Common errors include finding the mode from the highest frequency instead of the value, adding 1 when the median has two middle values, and writing probabilities greater than 1. Give probability answers as fractions, decimals or percentages and always check they are between 0 and 1.

Exam strategy is about converting your maths knowledge into marks under time pressure. The aim is not just to know a method, but to show it clearly enough that an examiner can award method marks even when the final answer is wrong.

• Read twice: underline key numbers and the question word such as find, solve or estimate, then check which units and format the answer needs.
• Show working: write the formula, substitute values, and label each step; method marks are awarded for correct reasoning.
• Manage time: do the questions you are confident about first, leave space to return, and do not spend too long on one mark.
• Review: after finishing, check calculations, units and whether answers are sensible; use the last minutes to correct small errors.

Before the exam, redo questions you previously got wrong and practise with a timer. After each practice paper, classify every mistake as careless, conceptual or timing-based, then fix the pattern rather than only the question.