# iGCSE Mathematics (0580) Core Syllabus: iGCSE Exam Style Practice Questions- Paper 3

### Assessment

All candidates take two components.
Candidates who have studied the Core syllabus content, or who are expected to achieve a grade D or below, should be entered for Paper 1 and Paper 3. These candidates will be eligible for grades C to G.
Candidates who have studied the Extended syllabus content and who are expected to achieve a grade C or above should be entered for Paper 2 and Paper 4. These candidates will be eligible for grades A* to E.

### Core candidates take:

Core candidates – Paper 3

• Time: 120 minutes (104 marks)
• Structured questions
• No marks deducted from incorrect answers
• 65 % weight
• Externally assessed

### 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,$$\sqrt{2}$$ ), real numbers, reciprocals.
• C1.2 Understand notation of Venn diagrams.
Definition of sets
e.g. A = {x: x is a natural number}
B = {a, b, c, …}
• 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.
Recognize equivalence and convert between these forms.
• C1.6 Order quantities by magnitude and demonstrate
familiarity with the symbols
$$=,\neq ,>,<,\geqslant ,\leqslant$$
• C1.7 Understand the meaning of indices (fractional, negative and zero) and use the rules of indices.
Use the standard form A × 10n where n is a positive or negative integer, and 1 ⩽ A < 10.
• 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.
Calculate average speed.
Use common measures of rate.
• C1.12 Calculate a given percentage of a quantity.
Express one quantity as a percentage of another.
Calculate percentage increase or decrease.
• C1.13 Use a calculator efficiently.
Apply appropriate checks of accuracy.
• C1.14 Calculate times in terms of the 24-hour and 12-hour clock.
• 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.
Extract data from tables and charts.

### 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.
Rearrange simple formulae.
Construct simple expressions and set up simple equations.
• C2.2 Manipulate directed numbers.
Use brackets and extract common factors.
Expand products of algebraic expressions.
• C2.4 Use and interpret positive, negative and zero indices.
Use the rules of indices.
• C2.5 Derive and solve simple linear equations in one unknown.
Derive and solve simultaneous linear equations in two unknowns.
• C2.7 Continue a given number sequence.
Recognize patterns in sequences including the term to term rule and relationships between different sequences.
Find and use the nth term of sequences.
• 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 $$ax+b,\pm x^2+ax+b,\frac{a}{x}(x\neq 0)$$, 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.

### C3 Coordinate geometry

• C3.1 Demonstrate familiarity with Cartesian
coordinates in two dimensions.
• C3.2 Find the gradient of a straight line.
• 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.

### 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.
Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.
• 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 Recognize congruent shapes.
• C4.6 Recognize rotational and line symmetry
(including order of rotational symmetry) in two dimensions.
• 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
• angle properties of regular polygons
• angle in a semicircle
• angle between tangent and radius of a circle.

### 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.
Solve simple problems involving the arc length and sector area as fractions of the circumference and area of a circle.
• 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.
• C5.5 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.

### C7 Vectors and transformations

• C7.1 Describe a translation by using a vector represented by e.g.  $$\begin{pmatrix} x\\ y \end{pmatrix} ,\overrightarrow{AB}$$, a
Multiply a vector by a scalar.
• 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.
Recognize and describe reflections, rotations, translations and enlargements.

### 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.

### C9 Statistics

• C9.1 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.
Appreciate restrictions on drawing conclusions from given data.
• 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.
• C9.7 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.