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Cambridge IGCSE 0580 Extended starter questions: weeks 1–11

44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 1–11 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 1

Question 1: 1.1 Types of number
Here is a list of numbers: 4, 9, 11, 15, 27, 31, 36 From the list, write down (a) the prime numbers (b) the square numbers (c) a cube number.
Question 2: 1.6 The four operations
Work out 18 - 6 ÷ 3 × 2.
Question 3: 2.1 Introduction to algebra
Find the value of 3a + 2b when a = 4 and b = -5.
Question 4: 1.1 Types of number
Find the highest common factor (HCF) of 28 and 42.

Week 2

Question 1: 1.1 Types of number
Write down the reciprocal of (a) 5 (b) 2/3
$Cambridge IGCSE 0580 Extended starter question on 1.6 The four operations: A jug is 3/5 full of juice. Ben pours out an amount equal to 1/4 of the jug's capacity. What fraction of the jug is full now?$

Question 2: 1.6 The four operations
A jug is 3/5 full of juice. Ben pours out an amount equal to 1/4 of the jug's capacity. What fraction of the jug is full now?
Question 3: 2.1 Introduction to algebra
Pens cost 45 pence each and pencils cost 20 pence each. Write an expression for the total cost, in pence, of x pens and y pencils.
Question 4: 1.1 Types of number
Find the lowest common multiple (LCM) of 18 and 30.

Week 3

Question 1: 1.3 Powers and roots
Work out (a) 7² (b) √81 (c) 4³
Question 2: 1.6 The four operations
Without using a calculator, work out (a) 0.36 × 2.5 (b) 0.84 ÷ 0.12
Question 3: 1.1 Types of number
Here are five numbers: √16, √7, 0.333… (recurring), π, 5/9 Which of them are irrational?
Question 4: 2.1 Introduction to algebra
v = u + at. Find v when u = 4.5, a = 9.8 and t = 3.

Week 4

Question 1: 1.4 Fractions, decimals and percentages
Write 5/8 as (a) a decimal (b) a percentage.
Question 2: 1.5 Ordering
In a quiz, Priya scored 0.6 of the marks, Sam scored 5/8 of the marks, Tom scored 61% and Uma scored 0.65 of the marks. List the four students in order of their scores, lowest first.
Question 3: 1.7 Indices I
Work out (a) 5⁰ (b) 2⁻³
Question 4: 1.3 Powers and roots
Work out 3√(125) + √36.

Week 5

Question 1: 1.7 Indices I
Write each answer as a single power. (a) 3⁴ × 3⁵ (b) 7⁸ ÷ 7³
Question 2: 1.8 Standard form
Write these numbers in standard form. (a) 45 000 (b) 0.0062
Question 3: 1.9 Estimation
Write 0.047362 correct to (a) 2 decimal places (b) 3 significant figures.
$Cambridge IGCSE 0580 Extended starter question on 1.4 Fractions, decimals and percentages: Write 0.45 as a fraction in its simplest form.$

Question 4: 1.4 Fractions, decimals and percentages
Write 0.45 as a fraction in its simplest form.

Week 6

Question 1: 1.9 Estimation
Write 38 452 correct to (a) the nearest hundred (b) 2 significant figures.
Question 2: 1.14 Using a calculator
Use your calculator to work out √(14.44) + 2.3^3. Write down all the figures on your calculator display.
Question 3: 1.10 Limits of accuracy
The length of a pencil is 12 cm, correct to the nearest centimetre. Write down the lower bound and the upper bound of the length.
Question 4: 1.7 Indices I
(a) Write (2³)² as a single power of 2. (b) Work out its value.

Week 7

Question 1: 1.11 Ratio and proportion
Write each ratio in its simplest form. (a) 24: 36 (b) 1.5 kg: 600 g
Question 2: 1.12 Rates
A car travels 150 km in 2.5 hours. Work out its average speed.
Question 3: 1.9 Estimation
By rounding each number to 1 significant figure, estimate the value of (49.7 × 3.12)/0.198. Show your working.
Question 4: 1.14 Using a calculator
Kim types (5.7 + 2.16)/(0.8²) into her calculator. (a) Write down every figure the display should show. (b) Write the value on the display correct to 3 significant figures.

Week 8

Question 1: 1.13 Percentages
Find 15% of £60.
Question 2: 1.11 Ratio and proportion
Share £45 in the ratio 4: 5.
Question 3: 1.12 Rates
A metal block has a mass of 240 g and a volume of 30 cm^3. Work out its density.
Question 4: 1.13 Percentages
Write 18 as a percentage of 72.

Week 9

Question 1: 1.17 Exponential growth and decay
A car is worth £18 500. Its value decreases by 12% each year. Work out its value after 4 years. Give your answer correct to the nearest pound.
Question 2: 1.16 Money
Leo buys 5 bottles of water at £1.35 each and 2 sandwiches at £2.40 each. He pays with a £20 note. How much change does he get?
Question 3: 1.15 Time
A lesson starts at 13 50 and lasts 75 minutes. At what time does the lesson end? Give your answer on the 24-hour clock.
Question 4: 1.13 Percentages
Increase 250 by 12%.

Week 10

Question 1: 1.18 Surds
Simplify √75.
Question 2: 1.2 Sets
ℰ = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, A = multiples of 2 and B = multiples of 3. List the members of (a) A ∩ B (b) A ∪ B
Question 3: 1.17 Exponential growth and decay
A population of bacteria doubles every hour. At first there are 300 bacteria. How many bacteria are there after 4 hours?
Question 4: 1.16 Money
The exchange rate is £1 = 0.92 euros. Change 375 euros into pounds. Give your answer correct to the nearest penny.

Week 11

Question 1: 2.1 Introduction to algebra
Find the value of 2x² - 3x when x = -2.
Question 2: 2.2 Algebraic manipulation
Simplify 5a + 3b - 2a + 4b.
Question 3: 1.18 Surds
Simplify √8 + √50.
Question 4: 1.2 Sets
ℰ = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and A = even numbers. (a) Find n(A). (b) List the members of A'.

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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