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Cambridge IGCSE 0580 Extended starter questions: weeks 34–44

44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 34–44 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 34

Question 1: 2.2 Algebraic manipulation
Expand and simplify (3x - 2)(x + 5).
Question 2: 2.5 Equations
Solve 7 - 2(x - 4) = 3x.
Question 3: 4.4 Similarity
In triangle ABC, D is on AB and E is on AC, and DE is parallel to BC. AD = 4 cm, AB = 10 cm and DE = 6 cm. Find BC.
Question 4: 4.8 Circle theorems II
A circle has radius 15 cm. A chord of the circle has length 24 cm. Work out the distance of the chord from the centre of the circle.

Week 35

Question 1: 2.5 Equations
Solve 2x² - 5x - 9 = 0. Give your answers correct to 2 decimal places.
$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Simplify (6x²y)/(9xy³).$

Question 2: 2.3 Algebraic fractions
Simplify (6x²y)/(9xy³).
Question 3: 2.2 Algebraic manipulation
Factorise completely 12x²y - 18xy.
Question 4: 2.5 Equations
Solve 5x - 8 = 27.

Week 36

$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Write x/4 - x/6 as a single fraction.$

Question 1: 2.3 Algebraic fractions
Write x/4 - x/6 as a single fraction.
Question 2: 2.5 Equations
Solve 3(x + 4) = 33.
Question 3: 2.6 Inequalities
x is greater than -3 and at most 5. (a) Write this as a single inequality. (b) How many integers satisfy it?
Question 4: 2.8 Proportion
y is directly proportional to x. When x = 5, y = 35. Find y when x = 8.

Week 37

Question 1: 2.8 Proportion
y is inversely proportional to x. When x = 5, y = 6. Find y when x = 10.
Question 2: 2.10 Graphs of functions
Complete the table of values for y = x² - 2x - 3. x -2 -1 0 1 2 3 4; y
$Cambridge IGCSE 0580 Extended starter question on 2.3 Algebraic fractions: Simplify (x² - 16)/(x² + 7x + 12).$

Question 3: 2.3 Algebraic fractions
Simplify (x² - 16)/(x² + 7x + 12).
Question 4: 2.5 Equations
Make the letter in brackets the subject of each formula. (a) C = 2π r [r] (b) y = 3x + 5 [x]

Week 38

Question 1: 2.10 Graphs of functions
Complete the table of values for y = 12/x. x 1 2 3 4 6 12; y
Question 2: 2.11 Sketching curves
Lina sketches the curve y = (x + 3)(x - 1). Without drawing it accurately, state (a) the two points where her curve meets the x-axis (b) the point where it meets the y-axis (c) the equation of the curve's axis of symmetry.
Question 3: 2.9 Graphs in practical situations
A travel graph shows Sam's walk. He leaves home at 10 00 and walks 3 km in 45 minutes. He stops for 30 minutes, then walks home in 1 hour. (a) Find his speed on the way out, in km/h. (b) At what time does he arrive home?
Question 4: 2.8 Proportion
y is directly proportional to x^2. When x = 5, y = 50. (a) Find y when x = 3. (b) Find the positive value of x when y = 72.

Week 39

Question 1: 2.13 Functions
f(x) = 4x - 9. Find (a) f(3) (b) f(-1).
Question 2: 2.10 Graphs of functions
(a) Complete the table of values for y = x² - 5x + 4. x 0 1 2 3 4 5; y (b) The graph of y = x² - 5x + 4 is drawn from this table. Use the table to write down the solutions of x² - 5x + 4 = 0.
Question 3: 2.11 Sketching curves
For the curve y = 8/x - 2, give the equations of the two asymptotes and find where the curve cuts the x-axis. Use these to sketch the curve.
Question 4: 2.9 Graphs in practical situations
The graph of a taxi fare against distance is a straight line from (0, 3) to (10, 21), where the distance is in km and the fare is in pounds. (a) Write down the fixed charge. (b) Work out the charge per kilometre.

Week 40

Question 1: 2.12 Differentiation
y = x³ - 6x² + 5. (a) Find the gradient of the curve at the point where x = 1. (b) Find the values of x where the gradient of the curve is zero.
Question 2: 2.13 Functions
g(x) = x² - 6. (a) Find g(-4). (b) Solve g(x) = 30.
Question 3: 2.12 Differentiation
Find dy/dx when y = 2x⁵ - 3x² + 8.
Question 4: 2.13 Functions
f(x) = 7 - 3x. Find f⁻¹(x).

Week 41

Question 1: 6.3 Exact trigonometric values
Without using a calculator, write down the exact value of (a) cos 30° (b) sin 45°.
Question 2: 6.4 Trigonometric functions
Without using a calculator, solve sin x = -0.5 for 0° ≤ x ≤ 360°.
Question 3: 6.5 Non-right-angled triangles
In triangle ABC, CA = 8 cm, CB = 11 cm and angle ACB = 40°. Work out the area of the triangle.
Question 4: 2.12 Differentiation
Find the gradient of the curve y = x⁴ + 7x at the point where x = -1.

Week 42

Question 1: 6.5 Non-right-angled triangles
In triangle ABC, angle A = 48°, angle B = 67° and BC = 9 cm. Work out the length of AC.
Question 2: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid measures 6 cm by 4 cm by 3 cm. Work out the length of a diagonal joining opposite corners of the cuboid.
Question 3: 6.3 Exact trigonometric values
Without using a calculator, write down the exact value of (a) tan 60° (b) sin 90° (c) cos 0°.
Question 4: 6.4 Trigonometric functions
For 0° ≤ x ≤ 360°, the graph of y = 3cos x is drawn. (a) Write down the maximum value of y. (b) Write down the value of x where y is a minimum.

Week 43

Question 1: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid has a base 12 cm by 5 cm and height 9 cm. Work out the length of a diagonal of the base.
Question 2: 6.2 Right-angled triangles
In a right-angled triangle, one angle is 35° and the hypotenuse is 12 cm. Find the side opposite the 35° angle. Give your answer correct to 3 significant figures.
Question 3: 6.5 Non-right-angled triangles
In triangle ABC, AB = 10 cm, AC = 7 cm and angle BAC = 115°. Work out the length of BC.
Question 4: 2.12 Differentiation
Find the coordinates of the point on the curve y = x² + 4x - 3 where the gradient is -2.

Week 44

Question 1: 4.4 Similarity
Two bottles are similar. Their heights are 18 cm and 27 cm. The diameter of the base of the smaller bottle is 6.4 cm. Find the diameter of the base of the larger bottle.
Question 2: 5.3 Circles, arcs and sectors
A sector of a circle has radius 6 cm and angle 90°. Find its area in terms of π.
Question 3: 5.5 Compound shapes and parts of shapes
A cuboid measures 10 cm by 6 cm by 4 cm. A cylindrical hole of radius 1.5 cm is drilled straight through it, from one 10 cm by 6 cm face to the opposite face. Work out the volume of the solid that is left. Give your answer correct to 3 significant figures.
Question 4: 4.3 Scale drawings
The bearing of B from A is 070°. Work out the bearing of A from B.

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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