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Cambridge IGCSE 0580 Extended starter questions: weeks 45–55

44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 45–55 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 45

Question 1: 7.1 Transformations
The point (2, 5) is rotated about the origin. Write down its image after a rotation of (a) 90° clockwise (b) 180°.
Question 2: 7.4 Vector geometry
OABC is a parallelogram. OA = a and OC = c. Find, in terms of a and c, (a) OB (b) AC.
Question 3: 8.3 Probability of combined events
A fair spinner numbered 1, 2 and 3 is spun and a fair coin is thrown. (a) How many possible outcomes are there? (b) Find the probability of a 3 and a head.
Question 4: 8.4 Conditional probability
Events A and B are such that P(A) = 0.6, P(B | A) = 0.3 and P(B | A') = 0.5. (a) Find P(B). (b) Find P(A | B).

Week 46

Question 1: 9.6 Cumulative frequency diagrams
The table shows the cumulative frequencies of the marks of 80 students in a test. Mark ≤ 10 ≤ 20 ≤ 30 ≤ 40 ≤ 50 ≤ 60; Cumulative frequency 4 13 29 47 62 80 How many students scored more than 50 marks?
Question 2: 9.7 Histograms
The table shows the heights, h cm, of some seedlings. Height h Frequency; 0 < h ≤ 10 15; 10 < h ≤ 15 20; 15 < h ≤ 20 28; 20 < h ≤ 40 24 Work out the frequency density for each class.
Question 3: 9.2 Interpreting statistical data
The daily sales at two shops are recorded for a month. Shop A: mean 45, range 20. Shop B: mean 52, range 35. (a) Which shop sells more on average? (b) Which shop has more consistent sales? Give a reason.
Question 4: 7.1 Transformations
A triangle has vertices (1, 1), (2, 1) and (1, 3). It is enlarged with scale factor 3, centre the origin. Write down the vertices of the image.

Week 47

Question 1: 1.4 Fractions, decimals and percentages
Write 7/40 as a percentage.
Question 2: 1.6 The four operations
Without using a calculator, work out 22/3 × 11/8. Show all your working.
Question 3: 1.7 Indices I
Find the value of n when 5^n = 1/25.
Question 4: 1.18 Surds
Expand and simplify (3 + √2)(5 - √2).

Week 48

Question 1: 2.2 Algebraic manipulation
Factorise completely 12a³b - 18a²b^2.
Question 2: 2.5 Equations
Solve the simultaneous equations. 2x + y = 11 x - y = 1
Question 3: 2.6 Inequalities
A number line has a filled circle at -4 and an open circle at 1, joined by a line. (a) Write down the inequality shown. (b) Write down the smallest and the largest integers that satisfy it.
Question 4: 2.7 Sequences
The nth term of a sequence is n² + 3. (a) Write down the first three terms. (b) Find the 10th term.

Week 49

Question 1: 2.2 Algebraic manipulation
Simplify 5a + 3b - 2a + 4b.
Question 2: 2.5 Equations
Solve (2x - 3)/4 = 5.
Question 3: 2.6 Inequalities
A ride is for children who are at least 110 cm tall and less than 150 cm tall. (a) Write this as an inequality for the height, h cm. (b) Can a child who is exactly 150 cm tall go on the ride?
Question 4: 2.7 Sequences
Here are the first four terms of a sequence: 1, 8, 27, 64, … (a) Write down the next term. (b) Write down an expression for the nth term.

Week 50

Question 1: 1.10 Limits of accuracy
The mass of a bag is 3.4 kg, correct to 1 decimal place. Write down the lower bound and the upper bound of the mass.
Question 2: 1.13 Percentages
Omar invests £5000 at 2% per year compound interest. Work out the value of his investment after 3 years.
Question 3: 1.17 Exponential growth and decay
The mass of a radioactive sample halves every 5 years. The mass is 64 g now. Find the mass after 20 years.
Question 4: 3.4 Length and midpoint
A is the point (1, k) and B is the point (7, 2k + 1). The midpoint of AB has y-coordinate 8. (a) Find the value of k. (b) Find the length of AB. Give your answer as a surd in its simplest form.

Week 51

Question 1: 6.2 Right-angled triangles
A straight ramp rises 5 m over a horizontal distance of 12 m. (a) Find the length of the ramp. (b) Write down the tangent of the angle the ramp makes with the horizontal, as a fraction.
Question 2: 6.5 Non-right-angled triangles
A triangle has sides of length 6 cm, 8 cm and 11 cm. Work out the size of its largest angle, correct to 1 decimal place.
Question 3: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid has a base 12 cm by 9 cm and height 7 cm. Work out the angle between a diagonal joining opposite corners of the cuboid and the base, correct to 1 decimal place.
Question 4: 7.1 Transformations
The points (4, 6) and (8, 2) are enlarged with scale factor 1/2, centre the origin. Write down their images.

Week 52

Question 1: 1.9 Estimation
350 people are going on a trip. Each minibus can carry 16 people. How many minibuses are needed?
Question 2: 1.14 Using a calculator
Use your calculator to work out (4.6 × 10⁵)/(1.25 × 10⁻³). Give your answer in standard form.
Question 3: 1.2 Sets
n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B).
Question 4: 2.7 Sequences
Here are the first four terms of a sequence: 3, 6, 12, 24, … (a) Write down the next two terms. (b) Find an expression for the nth term.

Week 53

Question 1: 1.9 Estimation
Work out (√(29.8))/(0.51 × 4.2). Give your answer correct to 2 decimal places.
Question 2: 1.14 Using a calculator
Use your calculator to work out 3.7² + √(19.36).
Question 3: 1.2 Sets
n(ℰ) = 40, n(A) = 18 and n(B) = 22. There are 7 elements in neither A nor B. Find n(A ∩ B).
Question 4: 2.7 Sequences
Find an expression for the nth term of the sequence 0, 3, 8, 15, 24, …

Week 54

Question 1: 1.12 Rates
A tap fills a tank at a rate of 4.5 litres per minute. How long does it take to fill 72 litres?
Question 2: 1.15 Time
A night bus leaves at 22 35. The journey takes 3 hours 40 minutes. At what time does the bus arrive? Give your answer on the 24-hour clock.
Question 3: 1.16 Money
Shop A sells a pack of 6 cans of juice for £4.32. Shop B sells a pack of 8 of the same cans for £5.60. Which shop gives the better value? Show your working.
Question 4: 4.1 Geometrical terms
A solid sphere of diameter 12 cm is cut in half through its centre. (a) Write down the mathematical name of each half. (b) Write down the radius of the flat face of each half.

Week 55

Question 1: 2.1 Introduction to algebra
The time, T minutes, to cook a joint of meat of mass w kg is T = 30 + 40w. (a) Find T when w = 2.75. (b) Find w when T = 150.
Question 2: 2.4 Indices II
Simplify 3x² × 4x^5.
Question 3: 2.9 Graphs in practical situations
A distance–time graph shows that a car travels 120 km between 09 00 and 10 30. Work out its average speed.
Question 4: 3.1 Coordinates
The points (-2, 3) and (4, 3) are plotted. (a) Write down the equation of the line through both points. (b) How far apart are the two points?

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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