IGCSE Mathematics tutor: live classes, unit by unit

What the exam asks for

• Classifying numbers and using set notation or Venn diagrams to show relationships.
• Choosing accurate methods for fractions, decimals, percentages, ratios, rates and money contexts.
• Applying index rules, standard form, estimation and bounds to calculations.
• Using proportional reasoning and exponential change in contextual problems; simplifying and rationalising surds.

Common slips to watch for

• Confusing common factors with common multiples, or misplacing set elements in overlapping regions.
• Changing a fraction, decimal or percentage without preserving its value; mishandling recurring decimals.
• Applying percentage change to the wrong starting amount or reversing a ratio division.
• Using index laws incorrectly with negative powers, or leaving surds unsimplified and denominators irrational.

What the exam asks for

• Manipulating expressions, algebraic fractions and indices, then forming and solving equations and inequalities.
• Connecting sequence patterns to rules and nth-term expressions; modelling direct and inverse proportion.
• Reading practical graphs and relating gradients, areas and changes to motion or conversion contexts.
• Constructing and interpreting function graphs, solving graphically, and using differentiation for gradients and stationary points.

Common slips to watch for

• Losing signs when expanding brackets, rearranging equations or working with negative indices.
• Reversing inequality signs incorrectly or omitting endpoint conventions when representing solutions.
• Reading axes or scales inaccurately, confusing gradient with height, or treating speed–time area as a gradient.
• Using an incorrect graph scale or curve shape; differentiating powers incorrectly or reporting stationary points without coordinates.

What the exam asks for

• Plotting and reading Cartesian coordinates and straight-line graphs from equations.
• Finding gradients and using them to identify or construct line equations in y = mx + c and x = k forms.
• Applying distance and midpoint methods to coordinate pairs.
• Using gradient relationships to construct parallel and perpendicular lines.

Common slips to watch for

• Swapping coordinate order or plotting a point in the wrong quadrant.
• Calculating gradient with inconsistent subtraction order or counting grid intervals inaccurately.
• Confusing the midpoint formula with the distance calculation.
• Using the same gradient for perpendicular lines or failing to preserve a parallel line's gradient.

What the exam asks for

• Using precise geometrical vocabulary for constructions, bearings, bisectors, similarity and congruence.
• Applying scale factors consistently to lengths and relating them to areas and volumes of similar figures.
• Finding unknown angles from polygon, triangle, parallel-line and intersecting-line relationships, with reasons.
• Applying circle theorems to determine angles and selecting the theorem that fits the diagram.

Common slips to watch for

• Confusing a perpendicular bisector with a line that merely crosses a segment, or measuring bearings from the wrong direction.
• Applying a length scale factor directly to area or volume without changing its power.
• Assuming lines are parallel or shapes are similar without sufficient information; giving an angle without a valid reason.
• Mixing up circle theorems or treating a tangent as perpendicular to a chord rather than the radius at contact.

What the exam asks for

• Convert metric units appropriately before calculating, especially for area, volume and capacity.
• Choose and apply perimeter and area formulae for standard and compound shapes.
• Use circle formulae and scale circumference or area by the correct fraction for arcs and sectors.
• Select suitable surface-area and volume formulae for solids, and interpret dimensions in context.

Common slips to watch for

• Mixing linear conversion factors with squared or cubed units when converting area or volume.
• Using a diameter where a radius is needed, or confusing arc length with sector area.
• Omitting a face or using an incorrect cross-section when finding the surface area or volume of a solid.

What the exam asks for

• Select sine, cosine, tangent or Pythagoras according to the sides and angle known in a right-angled triangle.
• Interpret bearings and identify the perpendicular distance when resolving two-dimensional situations.
• Recall exact values, interpret trigonometric graphs and find solutions across the stated angle range.
• Choose between the sine rule, cosine rule and the included-angle area formula for non-right-angled triangles.
• Represent three-dimensional situations with a clear triangle before applying trigonometry.

Common slips to watch for

• Misidentifying the opposite, adjacent or hypotenuse side, or using the wrong ratio.
• Giving only one solution to a trigonometric equation when another angle lies in the required range.
• Applying a triangle rule to the wrong sides and angles, or using a non-included angle in the area formula.
• Using an unlabelled or incorrectly oriented diagram for bearings or three-dimensional problems.

What the exam asks for

• Describe and draw reflections using the correct mirror line and the corresponding image positions.
• Specify rotations with their centre, direction and angle, and track vertices consistently.
• Use a centre and scale factor to construct enlargements and identify how image positions change.
• Represent translations with vectors, then combine or scale vectors to describe geometric relationships.

Common slips to watch for

• Giving a rotation angle without its direction or centre, or reflecting in the wrong line.
• Applying an enlargement scale factor to coordinates without accounting for its centre.
• Reversing a translation vector or making a sign error when adding, subtracting or scaling vectors.

What the exam asks for

• Place event probabilities on the zero-to-one scale and use complements to find probabilities of non-occurrence.
• Represent combined events with sample-space, Venn or tree diagrams, choosing a representation that fits the situation.
• Label tree branches with probabilities and record outcomes at their endpoints, respecting whether events involve replacement.
• Use tables or diagrams to determine conditional probabilities by restricting attention to the stated condition.

Common slips to watch for

• Adding probabilities for events that are not mutually exclusive, or failing to use a complement when appropriate.
• Using the wrong branch probabilities after an outcome is removed or replaced.
• Calculating a conditional probability with the unrestricted total instead of the outcomes satisfying the condition.

What the exam asks for

• Classifying and tabulating data, then reading tables and diagrams to compare sets and draw appropriately limited conclusions.
• Calculating and choosing suitable averages and measures of spread, including quartiles and estimates from grouped data.
• Constructing and interpreting statistical charts, scatter diagrams, cumulative frequency diagrams and histograms.
• Using graphical features to estimate values and interpreting correlation and a line of best fit.

Common slips to watch for

• Choosing an average without considering the data or the purpose of the comparison.
• Confusing quartiles, percentiles or interquartile range when reading cumulative frequency diagrams.
• Omitting or mislabelling chart features, or plotting points inaccurately on statistical diagrams.
• Treating correlation as proof of causation, or extending a line of best fit beyond what the data supports.