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Cambridge IGCSE · exam years 2025–2027 · official edition v3. Original bilingual Classovia targets and activities linked to topic codes and source pages.
Official exam syllabusClassify numbers and use factors, multiples and prime factorisation to justify a calculation.
Find HCF and LCM of 36 and 84; explain when each is useful.
Represent a two-set situation using membership, intersection, union and complement.
Make a two-set diagram for 20 learners: 12 study art, 9 study music, 5 study both.
Connect squares and cubes with their inverse roots and evaluate numerical powers.
Evaluate 13 squared, the square root of 196 and the cube root of 64 without a calculator.
Move accurately between fraction, decimal and percentage representations.
Express 7/20 as a decimal and percentage; represent all three on one diagram.
Compare signed quantities and use inequality notation to describe their order.
Order -0.6, -2/3, 0.05 and 3/8; justify the comparison of the negative values.
Calculate with signed integers, fractions and decimals while preserving operation order.
Evaluate 3/4 + 2(1.5 - 0.25) and explain the order of steps.
Simplify numerical powers using index rules, including zero and negative indices.
Simplify 2^(-2) times 2^5 and verify by writing both factors as ordinary numbers.
Convert between ordinary numbers and standard form and calculate with powers of ten.
Write 0.00072 in standard form, then multiply it by 300000.
Choose a useful rounding accuracy and estimate before calculating precisely.
Estimate 49.7 times 19.8, then compare the estimate with the exact result.
State the interval of possible original values for a rounded measurement.
A length is 8.4 cm to the nearest tenth: give the lower and upper bounds.
Use equivalent ratios to divide quantities and compare proportional situations.
Divide 150 in the ratio 2:3; then adjust a recipe from four people to six.
Interpret rate units and solve speed, pay and conversion problems with consistent units.
A journey covers 84 km in 1 hour 45 minutes. Calculate average speed.
Use percentage multipliers for discounts, increases and simple or compound interest.
Compare a 10% increase followed by a 10% decrease with the original value 200.
Enter multi-step calculations correctly and interpret the display in context.
Evaluate (7.6 + 2.4)/3 without intermediate rounding; explain the final accuracy.
Read timetables and calculate elapsed time across clock formats and time zones.
Find elapsed time from 22:45 to 01:20 the next day, then apply a two-hour time-zone change.
Calculate costs, change and currency conversions using the direction of the exchange rate.
At 1 unit of A = 1.25 units of B, convert 80 A to B and 50 B to A.
Translate a relationship into algebra and substitute values with correct signs.
For a = -2 and b = 5, evaluate 3a - b and explain why substitution needs brackets.
Collect terms, expand a single bracket and factor out common factors.
Expand 4(2x - 3), then factorise 12x + 18; check by reversing each operation.
Simplify algebraic powers with positive, zero and negative indices and solve simple index equations.
Simplify x^7 / x^3 and (2x^2)^3; state relevant restrictions.
Solve linear and simultaneous linear equations and rearrange straightforward formulas.
Solve 3x + 7 = 22 and the pair x + y = 9, x - y = 3; verify by substitution.
Read inequality statements and represent numerical intervals on a number line.
Draw -2 < x <= 3 on a number line and identify its integer solutions.
Continue patterns and derive nth terms for linear, simple quadratic and simple cubic sequences.
Find the nth term of 5, 8, 11, 14 and explain how to test it with n = 1.
Read and construct travel or conversion graphs and interpret their gradients.
Sketch a distance-time graph for 10 km travelled in 30 minutes, a stop, then a return.
Plot permitted linear, quadratic and reciprocal functions from tables and solve associated equations graphically.
Plot y = x^2 - 4 for integer x from -3 to 3 and estimate its roots.
Recognise and sketch linear and quadratic shapes, identifying symmetry and roots.
Sketch y = x^2 - 9 and y = 2x + 1; label roots and the quadratic symmetry line.
Locate and interpret points in all four quadrants.
Plot (-3, 2), (2, -4) and their reflections in the axes.
Generate coordinate pairs and draw a straight line from its equation.
Make a value table for y = -2x + 3 and draw the line with labelled intercepts.
Read the gradient of a straight line from rise and run on a coordinate grid.
Draw a line through grid points (1, 2) and (5, 10); count rise and run to find its gradient.
Connect gradient and intercept with a line equation and derive it from a graph.
Write the line with gradient 3 and y-intercept -2; find its x-intercept.
Use equal gradients to derive a parallel line equation through a specified point.
Find the line parallel to y = 2x + 1 through (3, -2).
Describe plane shapes, solids and geometric relationships using precise vocabulary.
Compare a prism and pyramid using faces, vertices and nets.
Measure lines and angles, construct a triangle from three side lengths, and interpret nets.
Construct a triangle with side lengths 5, 6 and 7 cm using ruler and compasses; show arcs.
Use a drawing scale and three-figure bearings to represent and interpret journeys.
At 1 cm : 2 km, represent an 8 km route on bearing 060 degrees.
Find corresponding lengths using a scale factor and explain why shapes are similar.
Two similar triangles have corresponding sides 4 and 10. Find the image of a side of length 6.
Identify reflection and rotational symmetry and describe each precisely.
Mark the symmetry lines of a regular hexagon and state its rotational order.
Combine angle facts for lines, triangles, quadrilaterals and polygons with written reasons.
Find each interior angle of a regular octagon and justify the calculation.
Apply the angle in a semicircle and the perpendicular radius-tangent relationship.
Draw a diameter triangle and a tangent at one endpoint; identify the right angles with reasons.
Convert length, area, volume and capacity with the correct power of the conversion factor.
Convert 2.4 m squared to cm squared and explain why the factor is not 100.
Choose and apply area and perimeter formulas for common plane shapes.
Calculate the area of a trapezium with parallel sides 8 and 14 cm and height 5 cm.
Calculate circle measures and use sector fractions to find arc length and area.
A sector has radius 6 cm and angle 120 degrees. Find its arc length and area.
Use nets and cross-sections to choose correct formulas for solids, with units.
A prism has cross-section area 18 cm squared and length 7 cm. Find its volume.
Split or subtract component shapes and justify which measurements are needed.
Find the area of a 10 by 8 rectangle with a 3 by 2 corner removed.
Identify the hypotenuse and use Pythagoras to find a missing side in a right triangle.
Find the hypotenuse for legs 8 and 15, then verify by substitution.
Choose sine, cosine or tangent to calculate a missing angle or side.
A right triangle has hypotenuse 12 and an angle of 35 degrees. Find the opposite side.
Perform and describe one reflection, rotation, translation or positive enlargement completely.
Translate a triangle by vector (3, -2) and describe which lengths and angles stay unchanged.
Build a sample space and use probability and its complement consistently.
For a fair die, find the probability of a prime result and of a non-prime result.
Estimate probability from random trial data and use it to predict frequencies.
A colour appears in 18 of 60 random trials. Predict its frequency in 250 similar trials.
Use sample spaces and simple tree diagrams for two-event situations with replacement.
A bag has 3 red and 2 blue counters. Find the probability of two reds with replacement.
Distinguish categorical, discrete and continuous data and organise observations.
Classify shoe size, height and preferred subject; explain suitable data collection choices.
Read tables and diagrams critically and compare distributions using evidence.
Compare two class score tables and explain why a taller bar alone may be misleading.
Choose mean, median or mode and calculate range for ungrouped data.
For 4, 5, 5, 8, 13, calculate all three averages and the range; discuss the outlier.
Choose and construct suitable charts, frequency tables and stem-and-leaf diagrams.
Make a stem-and-leaf diagram for 12, 15, 21, 21, 28 and include a key.
Describe correlation and use a sensible line of best fit within the observed range.
Sketch positive, negative and no correlation; explain why correlation is not causation.
