CIE Maths IGCSE Topic Questions

C1 Number

C1.1 Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square and cube numbers, common factors and common multiples, rational and irrational numbers (e.g. π, 2 ), real numbers, reciprocals

C1.2 Understand notation of Venn diagrams.

C1.3 Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers.

C1.4 Use directed numbers in practical situations.

C1.5 Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts

C1.6 Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, �, � , ⩾, ⩽

C1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.

C1.8 Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets

C1.9 Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.

C1.10 Give appropriate upper and lower bounds for data given to a specified accuracy.

C1.11 Demonstrate an understanding of ratio and proportion

C1.12 Calculate a given percentage of a quantity

C1.13 Use a calculator efficiently

C1.14 Calculate times in terms of the 24-hour and 12-hour clock. Read clocks, dials and timetables

C1.15 Calculate using money and convert from one currency to another.

C1.16 Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest

C1.17 Extended curriculum only.

E1 Number

E1. Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square and cube numbers, common factors and common multiples, rational and irrational numbers (e.g. π, 2 ), real numbers, reciprocals.

E1.2 Use language, notation and Venn diagrams to describe sets and represent relationships between sets.

E1.3 Calculate with squares, square roots, cubes and cube roots and other powers and roots of number

E1.4 Use directed numbers in practical situations

E1.5 Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts.

E1.6 Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, �, � , ⩾, ⩽.

E1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.

E1.8 Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets

E1.9 Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.

E1.10 Give appropriate upper and lower bounds for data given to a specified accuracy.

E1.11 Demonstrate an understanding of ratio and proportion

E1.12 Calculate a given percentage of a quantity. Express one quantity as a percentage of another. Calculate percentage increase or decrease. Carry out calculations involving reverse percentages.

E1.13 Use a calculator efficiently. Apply appropriate checks of accuracy

E1.14 Calculate times in terms of the 24-hour and 12-hour clock. Read clocks, dials and timetables.

E1.15 Calculate using money and convert from one currency to another.

E1.16 Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest.

E1.17 Use exponential growth and decay in relation to population and finance.

C2 Algebra and graphs

C2.1 Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in formulae.

C2.2 Manipulate directed numbers. Use brackets and extract common factors.

C2.3 Extended curriculum only.

C2.4 Use and interpret positive, negative and zero indices.

C2.5 Derive and solve simple linear equations in one unknown.

C2.6 Extended curriculum only.

C2.8 Extended curriculum only.

C2.9 Extended curriculum only.

C2.10 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data

C2.11 Construct tables of values for functions of the form ax + b, ±x 2 + ax + b, x a (x ≠ 0), where a and b are integer constants. Draw and interpret these graphs. Solve linear and quadratic equations approximately, including finding and interpreting roots by graphical methods. Recognise, sketch and interpret graphs of functions

C2.12 Extended curriculum only.

C2.13 Extended curriculum only.

E2 Algebra and graphs

E2.1 Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in complicated formulae

E2.2 Manipulate directed numbers. Use brackets and extract common factors.

E2.3 Manipulate algebraic fractions.

E2.4 Use and interpret positive, negative and zero indices.

E2.5 Derive and solve linear equations in one unknown.

E2.6 Represent inequalities graphically and use this representation to solve simple linear programming problems.

E2.7 Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences.

E2.8 Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.

E2.9 Use function notation, e.g. f(x) = 3x – 5, f: x ⟼ 3x – 5, to describe simple functions. Find inverse functions f –1(x). Form composite functions as defined by gf(x) = g(f(x)).

E2.10 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.

E2.11 Construct tables of values and draw graphs for functions of the form axn (and simple sums of these) and functions of the form abx + c.

E2.12 Estimate gradients of curves by drawing tangents.

E2.13 Understand the idea of a derived function. Use the derivatives of functions of the form axn and simple sums of not more than three of these.

C3 Coordinate geometry

C3.1 Demonstrate familiarity with Cartesian coordinates in two dimensions. Notes/Examples

C3.2 Find the gradient of a straight line.

C3.3 Extended curriculum only.

C3.4 Interpret and obtain the equation of a straight line graph in the form y = mx + c.

C3.5 Determine the equation of a straight line parallel to a given line.

C3.6 Extended curriculum only.

E2 Algebra and graphs

E3.1 Demonstrate familiarity with Cartesian coordinates in two dimensions.

E3.2 Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.

E3.3 Calculate the length and the coordinates of the midpoint of a straight line from the coordinates of its end points.

E3.4 Interpret and obtain the equation of a straight line graph.

E3.5 Determine the equation of a straight line parallel to a given line

E3.6 Find the gradient of parallel and perpendicular lines.

C4 Geometry

C4.1 Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence.

C4.2 Measure and draw lines and angles. Construct a triangle given the three sides using a ruler and a pair of compasses only.

C4.3 Read and make scale drawings.

C4.4 Calculate lengths of similar figures.

C4.5 Recognise congruent shapes.

C4.7 Core curriculum continued Calculate unknown angles using the following geometrical properties:

E4 Geometry

E4.1 Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence

E4.2 Measure and draw lines and angles. Construct a triangle given the three sides using a ruler and a pair of compasses only.

E4.3 Read and make scale drawings.

E4.4 Calculate lengths of similar figures. Use the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes and surface areas of similar solids

E4.5 Use the basic congruence criteria for triangles (SSS, ASA, SAS, RHS)

E4.6 Recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions

E4.7 Calculate unknown angles using the following geometrical properties:

C5 Mensuration

C5.1 Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.

C5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.

C5.3 Carry out calculations involving the circumference and area of a circle.

C5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder

C5.5 Carry out calculations involving the areas and volumes of compound shapes.

E5 Mensuration

E5.1 Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.

E5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these

E5.3 Carry out calculations involving the circumference and area of a circle.

E5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder.

E5.5 Carry out calculations involving the areas and volumes of compound shapes.

C5 Mensuration

C5.1 Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.

C5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.

C5.3 Carry out calculations involving the circumference and area of a circle.

C5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder

C5.5 Carry out calculations involving the areas and volumes of compound shapes.

C6 Trigonometry

E5.1 Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.

E5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these

E5.3 Carry out calculations involving the circumference and area of a circle.

E5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder.

E5.5 Carry out calculations involving the areas and volumes of compound shapes.

C6 Trigonometry

C6.1 Interpret and use three-figure bearings.

C6.2 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a rightangled triangle.

C6.3 Extended curriculum only.

C6.4 Extended curriculum only.

C6.5 Extended curriculum only.

E6 Trigonometry

E6.1 Interpret and use three-figure bearings.

E6.2 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a rightangled triangle

E6.3 Recognise, sketch and interpret graphs of simple trigonometric functions.

E6.4 Solve problems using the sine and cosine rules for any triangle and the formula area of triangle = 2 1 ab sin C.

E6.5 Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.

C7 Vectors and transformations

C7.1 Describe a translation by using a vector represented by e.g. x y e o, AB or a.

C7.2 Reflect simple plane figures in horizontal or vertical lines.

C7.3 Extended curriculum only

E7 Vectors and transformations

E7.1 Describe a translation by using a vector represented by e.g. x y e o, AB or a

E7.2 Reflect simple plane figures.

E7.3 Calculate the magnitude of a vector x y e o as

C8 Probability

C8.1 Calculate the probability of a single event as either a fraction, decimal or percentage.

C8.2 Understand and use the probability scale from 0 to 1.

C8.3 Understand that the probability of an event occurring = 1 – the probability of the event not occurring.

C8.4 Understand relative frequency as an estimate of probability. Expected frequency of occurrences

C8.5 Calculate the probability of simple combined events, using possibility diagrams, tree diagrams and Venn diagrams.

C8.6 Extended curriculum only.

E8 Probability

E8.1 Calculate the probability of a single event as either a fraction, decimal or percentage.

E8.2 Understand and use the probability scale from 0 to 1.

E8.3 Understand that the probability of an event occurring = 1 – the probability of the event not occurring.

E8.4 Understand relative frequency as an estimate of probability. Expected frequency of occurrences.

E8.5 Calculate the probability of simple combined events, using possibility diagrams, tree diagrams and Venn diagrams

E8.6 Calculate conditional probability using Venn diagrams, tree diagrams and tables.

C9 Statistics

C9.1 Core curriculum Collect, classify and tabulate statistical data

C9.2 Read, interpret and draw simple inferences from tables and statistical diagrams. Compare sets of data using tables, graphs and statistical measures

C9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal intervals and scatter diagrams.

C9.4 Calculate the mean, median, mode and range for individual and discrete data and distinguish between the purposes for which they are used.

C9.5 Extended curriculum only.

C9.6 Extended curriculum only.

C9.7 Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram.

C9.8 Draw, interpret and use lines of best fit by eye.

E9 Statistics

E9.8 Draw, interpret and use lines of best fit by eye.

E9.2 Read, interpret and draw inferences from tables and statistical diagrams

E9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal and unequal intervals and scatter diagrams.

E9.4 Calculate the mean, median, mode and range for individual and discrete data and distinguish between the purposes for which they are used.

E9.5 Calculate an estimate of the mean for grouped and continuous data. Identify the modal class from a grouped frequency distribution.

E9.6 Construct and use cumulative frequency diagrams.

E9.7 Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram.

C9.8 Draw, interpret and use lines of best fit by eye.