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Cambridge IGCSE 0580 Extended starter questions: weeks 12–22

44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 12–22 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 12

Question 1: 2.2 Algebraic manipulation
Expand (a) 4(2x - 3) (b) x(x + 5)
Question 2: 2.4 Indices II
Simplify (a) x⁴ × x³ (b) y⁹ ÷ y²
Question 3: 2.1 Introduction to algebra
The area of a trapezium is A = 1/2(a + b)h. Find A when a = 6.4, b = 9.2 and h = 3.5.
Question 4: 2.2 Algebraic manipulation
Factorise (a) 6x + 15 (b) x² - 7x

Week 13

Question 1: 2.5 Equations
Solve 5x - 8 = 27.
Question 2: 2.2 Algebraic manipulation
Expand and simplify (x + 4)(x - 3).
Question 3: 2.4 Indices II
Simplify (a) (m³)⁴ (b) a⁰
Question 4: 2.5 Equations
Solve 3(x + 4) = 33.

Week 14

Question 1: 2.5 Equations
Make the letter in brackets the subject of each formula. (a) C = 2π r [r] (b) y = 3x + 5 [x]
Question 2: 2.6 Inequalities
Write down the inequality shown on each number line. (a) An open circle at -2 with the line going to the right. (b) A filled (solid) circle at 3 with the line going to the left.
Question 3: 2.5 Equations
Solve the simultaneous equations. 2x + y = 11 x - y = 1
Question 4: 2.6 Inequalities
List the integers x such that -1 < x ≤ 4.

Week 15

Question 1: 2.7 Sequences
Here are the first five terms of a sequence: 1, 4, 9, 16, 25, … (a) Write down the next two terms. (b) Write down an expression for the nth term.
Question 2: 2.9 Graphs in practical situations
A straight-line conversion graph passes through (0, 0) and shows that £50 is worth 45 euros. (a) Change £20 into euros. (b) Change 90 euros into pounds.
Question 3: 2.5 Equations
Solve (2x - 3)/4 = 5.
Question 4: 2.6 Inequalities
Describe how you would show x ≥ 1.5 on a number line.

Week 16

Question 1: 3.1 Coordinates
Write down the coordinates of (a) the point 4 units to the right of the origin and 2 units down (b) the point on the y-axis 3 units above the origin.
Question 2: 3.2 Drawing linear graphs
Complete the table of values for y = 2x + 1. x -1 0 1 2 3; y
Question 3: 3.3 Gradient of linear graphs
The graph of a straight line is drawn on a grid. The line passes through the grid points (0, 1) and (2, 7). Use these points to find the gradient of the line.
Question 4: 3.5 Equations of linear graphs
The line y = 5 - 2x is drawn on a grid. (a) What is its gradient? (b) At what value does it cross the y-axis?

Week 17

Question 1: 3.4 Length and midpoint
M is halfway along the line segment from (-4, 9) to (6, -3). What are the coordinates of M?
Question 2: 3.6 Parallel lines
(a) Which two of these lines are parallel? y = 3x + 1, y = 2x + 3, y = 3x - 4, y = -3x + 1 (b) Write down the gradient of any line parallel to y = 5 - 2x.
Question 3: 3.7 Perpendicular lines
Line A has equation y = -2/5x + 1. Line B crosses line A at right angles. What is the gradient of line B?
Question 4: 3.1 Coordinates
(a) Write down the coordinates of the origin. (b) What is the x-coordinate of every point on the y-axis?

Week 18

Question 1: 4.1 Geometrical terms
Write down the mathematical name for (a) a straight line that touches a circle at exactly one point (b) a straight line from the centre of a circle to its circumference.
Question 2: 4.2 Geometrical constructions
A net is made from one regular hexagon and six identical triangles. Write down the name of the solid it folds to make.
Question 3: 4.3 Scale drawings
The scale of a map is 1: 50 000. Two villages are 4 cm apart on the map. Work out the real distance between them in kilometres.
Question 4: 3.4 Length and midpoint
On a map with a grid in kilometres, a lighthouse is at (1, 6) and a buoy is at (4, -1). Calculate the straight-line distance from the lighthouse to the buoy. Give your answer correct to 3 significant figures.

Week 19

Question 1: 4.6 Angles
(a) Two angles on a straight line are 47° and x°. Find x. (b) Three angles at a point are 110°, 95° and y°. Find y.
Question 2: 4.5 Symmetry
Write down the number of lines of symmetry and the order of rotational symmetry of (a) a rectangle that is not a square (b) a kite that is not a rhombus.
Question 3: 4.1 Geometrical terms
A pyramid has a base that is a pentagon. Write down the number of (a) faces (b) edges (c) vertices.
Question 4: 4.2 Geometrical constructions
A cube has edges of length 7 cm. Work out the total area of its net.

Week 20

Question 1: 4.4 Similarity
Two rectangles are similar. The smaller one is 4 cm wide and 6 cm long. The larger one is 10 cm wide. Find the length of the larger rectangle.
Question 2: 4.7 Circle theorems I
AB is a diameter of a circle and C is a point on the circle. Angle CAB = 35°. Find angle ABC.
Question 3: 4.6 Angles
In an isosceles triangle, the angle between the two equal sides is 40°. Find the other two angles.
Question 4: 4.5 Symmetry
(a) Write down the name of the type of triangle that has exactly one line of symmetry. (b) Write down the order of rotational symmetry of this triangle.

Week 21

Question 1: 5.1 Units of measure
Convert (a) 3.5 km to metres (b) 750 g to kilograms.
Question 2: 5.2 Area and perimeter
A rectangle is 7 cm long and 4.5 cm wide. Find (a) its perimeter (b) its area.
Question 3: 5.3 Circles, arcs and sectors
A circle has radius 5 cm. Find, in terms of π, (a) its circumference (b) its area.
Question 4: 4.4 Similarity
Triangles ABC and DEF are similar, with A corresponding to D, B to E and C to F. AB = 5 cm, DE = 15 cm and BC = 7 cm. Find EF.

Week 22

Question 1: 5.4 Surface area and volume
A cuboid measures 6 cm by 2 cm by 5 cm. Find (a) its volume (b) its total surface area.
Question 2: 5.5 Compound shapes and parts of shapes
A shape is made from a rectangle 9 cm long and 5 cm wide, with a right-angled triangle on one of its 5 cm sides. The triangle has base 5 cm and height 4 cm. Work out the area of the shape.
Question 3: 5.1 Units of measure
Convert (a) 2.4 litres to millilitres (b) 85 mm to centimetres.
Question 4: 5.2 Area and perimeter
A triangle has base 9 cm and perpendicular height 6 cm. Find its area.

More starter questions

Other weeks: Weeks 1–11 · Weeks 12–22 · Weeks 23–33 · Weeks 34–44 · Weeks 45–55. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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