Here you can find example questions covering the Cambridge IGCSE Mathematics Syllabus. You can also try a demo test to get a better understanding of how BOFA works. The syllabus has been taken from the Cambridge Assessment International Education syllabus document and the Cambridge Assessment International Education syllabus update document.

Topic	Core Curriculum Ref / Description	Extended Curriculum Ref / Description
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. $pi$, $sqrt2$), real numbers, reciprocals	E1.1 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. $pi$, $sqrt2$), real numbers, reciprocals.
Number	C1.2 Understand notation of Venn diagrams. Definition of sets e.g. $A={x:x "is a natural number"}$ $B={a,b,c,...}$	E1.2 Use language, notation and Venn diagrams to describe sets and represent relationships between sets. Definition of sets e.g. $A={x:x "is a natural number"}$ $B={(x,y):y=mx+c}$ $C={x:a le x le b}$ $D={a,b,c,...}$
Number	C1.3 Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers.	E1.3 Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers.
Number	C1.4 Use directed numbers in practical situations. e.g. temperature changes, flood levels.	E1.4 Use directed numbers in practical situations. e.g. temperature changes, flood levels.
Number	C1.5 Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts. Recognise equivalence and convert between these forms.	E1.5 Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts. Recognise equivalence and convert between these forms.
Number	C1.6 Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ≥, ≤.	E1.6 Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ≥, ≤.
Number	C1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices. Use the standard form $A xx 10^n$ where $n$ is a positive or negative integer, and $1 le A le 10$.	E1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices. Use the standard form $A xx 10^n$ where $n$ is a positive or negative integer, and $1 le A le 10$.
Number	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.	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.
Number	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.	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.
Number	C1.10 Give appropriate upper and lower bounds for data given to a specified accuracy. e.g. measured lengths.	E1.10 Give appropriate upper and lower bounds for data given to a specified accuracy. e.g. measured lengths. Obtain appropriate upper and lower bounds to solutions of simple problems given data to a specified accuracy. e.g. the calculation of the perimeter or the area of a rectangle.
Number	C1.11 Demonstrate an understanding of ratio and proportion. Calculate average speed. Use common measures of rate.	E1.11 Demonstrate an understanding of ratio and proportion. Increase and decrease a quantity by a given ratio. Calculate average speed. Use common measures of rate.
Number	C1.12 Calculate a given percentage of a quantity. Express one quantity as a percentage of another. Calculate percentage increase or decrease.	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. e.g. finding the cost price given the selling price and the percentage profit.
Number	C1.13 Use a calculator efficiently. Apply appropriate checks of accuracy.	E1.13 Use a calculator efficiently. Apply appropriate checks of accuracy.
Number	C1.14 Calculate times in terms of the 24-hour and 12-hour clock. Read clocks, dials and timetables.	E1.14 Calculate times in terms of the 24-hour and 12-hour clock. Read clocks, dials and timetables.
Number	C1.15 Calculate using money and convert from one currency to another	E1.15 Calculate using money and convert from one currency to another
Number	C1.16 Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest. Extract data from tables and charts.	E1.16 Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest. Extract data from tables and charts.
Number		E1.17 Use exponential growth and decay in relation to population and finance. e.g. depreciation, growth of bacteria.
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. Rearrange simple formulae. Construct simple expressions and set up simple equations.	E2.1 Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in complicated formulae. Rearrange simple formulae. Construct and rearrange complicated formulae and equations.
Algebra and graphs	C2.2 Manipulate directed numbers. Use brackets and extract common factors. Expand products of algebraic expressions.	E2.2 Manipulate directed numbers. Use brackets and extract common factors. Expand products of algebraic expressions. Factorise where possible expressions of the form: $ax+bx+kay+kby$ $a^2x^2-b^2y^2$ $a^2+2ab+b^2$ $ax^2+bx+c$
Algebra and graphs		E2.3 Manipulate algebraic fractions. Factorise and simplify rational expressions.
Algebra and graphs	C2.4 Use and interpret positive, negative and zero indices. Use the rules of indices.	E2.4 Use and interpret positive, negative and zero indices. Use and interpret fractional indices. Use the rules of indices.
Algebra and graphs	C2.5 Derive and solve simple linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns.	E2.5 Derive and solve simple linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns. Derive and solve simultaneous equations, involving one linear and one quadratic. Derive and solve quadratic quations by factorisation, completing the square and by use of the formula. Derive and solve linear inequalities.
Algebra and graphs		E2.6 Represent inequalities graphically and use this representation to solve simple linear programming problems.
Algebra and graphs	C2.7 Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences. Find and use the $n^"th"$ term of sequences.	E2.7 Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences. Find and use the $n^"th"$ term of sequences.
Algebra and graphs		E2.8 Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.
Algebra and graphs		E2.9 Use function notation, e.g. $f(x)=3x-5$, $f:x mapsto 3x-5$, to describe simple functions. Find inverse functions $f^-1(x)$. Form composite functions as defined by $gf(x)=g(f(x))$.
Algebra and graphs	C2.10 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.	E2.10 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data. Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration. Calculate distance travelled as area under a speed–time graph.
Algebra and graphs	C2.11 Construct tables of values for functions of the form $ax+b$, $+-x^2+ax+b$,$a/x$ ($xne0$), 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	E2.11 Construct tables of values and draw graphs for functions of the form $ax^n$ (and simple sums of these) and functions of the form $ab^x+c$. Solve associated equations approximately, including finding and interpreting roots by graphical methods. Draw and interpret graphs representing exponential growth and decay problems. Recognise, sketch and interpret graphs of functions
Algebra and graphs		E2.12 Estimate gradients of curves by drawing tangents.
Algebra and graphs		E2.13 Understand the idea of a derived function. Use the derivatives of functions of the form $n^"th"$ , and simple sums of not more than three of these. Apply differentiation to gradients and turning points (stationary points). Discriminate between maxima and minima by any method.
Co-ordinate geometry	C3.1 Demonstrate familiarity with Cartesian coordinates in two dimensions.	E3.1 Demonstrate familiarity with Cartesian coordinates in two dimensions
Co-ordinate geometry	C3.2 Find the gradient of a straight line.	E3.2 Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.
Co-ordinate geometry		E3.3 Calculate the length and the coordinates of the midpoint of a straight line from the coordinates of its end points.
Co-ordinate geometry	C3.4 Interpret and obtain the equation of a straight line graph in the form $y=mx+c$	E3.4 Interpret and obtain the equation of a straight line graph.
Co-ordinate geometry	C3.5 Determine the equation of a straight line parallel to a given line.	E3.5 Determine the equation of a straight line parallel to a given line.
Co-ordinate geometry		E3.6 Find the gradient of parallel and perpendicular lines.
Geometry	C4.1 Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence. Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.	E4.1 Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence. Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.
Geometry	C4.2 Measure and draw lines and angles. Construct a triangle given the three sides using a ruler and a pair of compasses only.	E4.2 Measure and draw lines and angles. Construct a triangle given the three sides using a ruler and a pair of compasses only.
Geometry	C4.3 Read and make scale drawings.	E4.3 Read and make scale drawings.
Geometry	C4.4 Calculate lengths of similar figures.	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.
Geometry	C4.5 Recognise congruent shapes.	E4.5 Use the basic congruence criteria for triangles (SSS, ASA, SAS, RHS).
Geometry	C4.6 Recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions.	E4.6 Recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions. Recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone). Use the following symmetry properties of circles: equal chords are equidistant from the centre the perpendicular bisector of a chord passes through the centre tangents from an external point are equal in length.
Geometry	C4.7 Calculate unknown angles using the following geometrical properties: angles at a point angles at a point on a straight line and intersecting straight lines angles formed within parallel lines angle properties of triangles and quadrilaterals angle properties of regular polygons angle in a semicircle angle between tangent and radius of a circle.	E4.7 Calculate unknown angles using the following geometrical properties: angles at a point angles at a point on a straight line and intersecting straight lines angles formed within parallel lines angle properties of triangles and quadrilaterals angle properties of regular polygons angle in a semicircle angle between tangent and radius of a circle. angle properties of irregular polygons angle at the centre of a circle is twice the angle at the circumference angles in the same segment are equal angles in opposite segments are supplementary; cyclic quadrilaterals alternate segment theorem.
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.	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.
Mensuration	C5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.	E5.2 Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.
Mensuration	C5.3 Carry out calculations involving the circumference and area of a circle. Solve simple problems involving the arc length and sector area as fractions of the circumference and area of a circle.	E5.3 Carry out calculations involving the circumference and area of a circle. Solve problems involving the arc length and sector area as ractions of the circumference and area of a circle.
Mensuration	C5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. Carry out calculations involving the surface area and volume of a sphere, pyramid and cone.	E5.4 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. Carry out calculations involving the surface area and volume of a sphere, pyramid and cone.
Mensuration	C5.5 Carry out calculations involving the areas and volumes of compound shapes.	E5.5 Carry out calculations involving the areas and volumes of compound shapes.
Trigonometry	C6.1 Interpret and use three-figure bearings.	E6.1 Interpret and use three-figure bearings.
Trigonometry	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 right-angled triangle.	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 right-angled triangle. Solve trigonometric problems in two dimensions involving angles of elevation and depression. Know that the perpendicular distance from a point to a line is the shortest distance to the line.
Trigonometry		E6.3 Recognise, sketch and interpret graphs of simple trigonometric functions. Graph and know the properties of trigonometric functions. Solve simple trigonometric equations for values between 0° and 360°.
Trigonometry		E6.4 Solve problems using the sine and cosine rules for any triangle and the formula area of triangle = $1/2 ab sinC$.
Trigonometry		E6.5 Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.
Vectors and transformations	C7.1 Describe a translation by using a vector represented by e.g. $((x),(y))$, $vec(AB)$ or a Add and subtract vectors Multiply a vector by a scalar	E7.1 Describe a translation by using a vector represented by e.g. $((x),(y))$, $vec(AB)$ or a Add and subtract vectors Multiply a vector by a scalar
Vectors and transformations	C7.2 Reflect simple plane figures in horizontal or vertical lines. Rotate simple plane figures about the origin, vertices or midpoints of edges of the figures, through multiples of 90°. Construct given translations and enlargements of simple plane figures. Recognise and describe reflections, rotations, translations and enlargements.	E7.2 Reflect simple plane figures in horizontal or vertical lines. Rotate simple plane figures about the origin, vertices or midpoints of edges of the figures, through multiples of 90°. Construct given translations and enlargements of simple plane figures. Recognise and describe reflections, rotations, translations and enlargements.
Vectors and transformations		E7.3 Calculate the magnitude of a vector $((x),(y))$ as $sqrt(x^2+y^2)$. Represent vectors by directed line segments. Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors. Use position vectors.
Probability	C8.1 Calculate the probability of a single event as either a fraction, decimal or percentage.	E8.1 Calculate the probability of a single event as either a fraction, decimal or percentage.
Probability	C8.2 Understand and use the probability scale from 0 to 1.	E8.2 Understand and use the probability scale from 0 to 1.
Probability	C8.3 Understand that the probability of an event occurring = 1 – the probability of the event not occurring.	E8.3 Understand that the probability of an event occurring = 1 – the probability of the event not occurring.
Probability	C8.4 Understand relative frequency as an estimate of probability. Expected frequency of occurrences.	E8.4 Understand relative frequency as an estimate of probability. Expected frequency of occurrences.
Probability	C8.5 Calculate the probability of simple combined events, using possibility diagrams, tree diagrams and Venn diagrams.	E8.5 Calculate the probability of simple combined events, using possibility diagrams, tree diagrams and Venn diagrams.
Probability		E8.6 Calculate conditional probability using Venn diagrams, tree diagrams and tables.
Statistics	C9.1 Collect, classify and tabulate statistical data.	E9.1 Collect, classify and tabulate statistical data.
Statistics	C9.2 Read, interpret and draw simple inferences from tables and statistical diagrams. Compare sets of data using tables, graphs and statistical measures. Appreciate restrictions on drawing conclusions from given data.	E9.2 Read, interpret and draw simple inferences from tables and statistical diagrams. Compare sets of data using tables, graphs and statistical measures. Appreciate restrictions on drawing conclusions from given data.
Statistics	C9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal and unequal intervals and scatter diagrams.	E9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal and unequal intervals and scatter diagrams.
Statistics	C9.4 Calculate the mean, median, mode and range for individual and discrete data and distinguish between the purposes for which they are used.	E9.4 Calculate the mean, median, mode and range for individual and discrete data and distinguish between the purposes for which they are used.
Statistics		E9.5 Calculate an estimate of the mean for grouped and continuous data. Identify the modal class from a grouped frequency distribution.
Statistics		E9.6 Construct and use cumulative frequency diagrams. Estimate and interpret the median, percentiles, quartiles and interquartile range. Construct and interpret box-and-whisker plots.
Statistics	C9.7 Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram.	E9.7 Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram.
Statistics	C9.8 Draw, interpret and use lines of best fit by eye.	E9.8 Draw, interpret and use lines of best fit by eye.