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Cambridge IGCSE 0580 Core starter questions: weeks 1–13

52 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Core, weeks 1–13 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
$Cambridge IGCSE 0580 Core starter question on 1.6 The four operations: A jug is 3/5 full of juice. Ben pours out an amount equal to 1/4 of the jug's capacity. What fraction of the jug is full now?$

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: 1.6 The four operations
Without using a calculator, work out 22/3 × 11/8. Show all your working.
Question 2: 1.4 Fractions, decimals and percentages
Write 5/8 as (a) a decimal (b) a percentage.
Question 3: 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 4: 1.3 Powers and roots
Work out 3√(125) + √36.

Week 5

Question 1: 1.7 Indices I
Work out (a) 5⁰ (b) 2⁻³
Question 2: 1.8 Standard form
Write these numbers in standard form. (a) 45 000 (b) 0.0062
Question 3: 1.6 The four operations
Work out (7.2 - 3.45) × 1.6.
$Cambridge IGCSE 0580 Core starter question on 1.4 Fractions, decimals and percentages: Write 0.45 as a fraction in its simplest form.$

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 0.047362 correct to (a) 2 decimal places (b) 3 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
Write each answer as a single power. (a) 3⁴ × 3⁵ (b) 7⁸ ÷ 7³

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
Write 38 452 correct to (a) the nearest hundred (b) 2 significant figures.
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: 1.12 Rates
A metal block has a mass of 240 g and a volume of 30 cm^3. Work out its density.
Question 2: 1.13 Percentages
Find 15% of £60.
Question 3: 1.11 Ratio and proportion
Share £45 in the ratio 4: 5.
Question 4: 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?

Week 9

Question 1: 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 2: 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 3: 1.12 Rates
A cyclist rides at an average speed of 18 km/h for 40 minutes. How far does she ride?
Question 4: 1.13 Percentages
Write 18 as a percentage of 72.

Week 10

Question 1: 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 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: 1.11 Ratio and proportion
A recipe for 6 people uses 450 g of rice. How much rice is needed for 10 people?
Question 4: 1.13 Percentages
Increase 250 by 12%.

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: 1.15 Time
The time in Dubai is 4 hours ahead of the time in London. A plane leaves Dubai at 08 15 Dubai time and lands in London at 12 40 London time on the same day. How long is the flight? Give your answer in hours and minutes.
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'.

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.

More starter questions

Other weeks: Weeks 1–13 · Weeks 14–26 · Weeks 27–39 · Weeks 40–51. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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