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; answers and mark schemes stay with teachers.
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 3 + 4 × 5 - 6 ÷ 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
Question 2: 1.6 The four operations
Work out 2/3 + 1/4.
Question 3: 2.1 Introduction to algebra
Pens cost 45 cents each and pencils cost 20 cents each. Write an expression for the total cost, in cents, 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
Work out (a) 4.6 × 0.3 (b) 7.2 ÷ 0.04
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
Work out (-3)² - 4 × (-2).
Question 2: 1.4 Fractions, decimals and percentages
Write 5/8 as (a) a decimal (b) a percentage.
Question 3: 1.5 Ordering
Write these numbers in order of size, starting with the smallest: 0.3, 1/4, 28%, 0.27
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 13/4 × 22/5. Give your answer as a mixed number 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 3.7² + √(19.36).
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
A calculator display shows 6.02E+05. Write this number as an ordinary number.
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
Ravi buys 3 notebooks costing $2.45 each and a pen costing $1.30. He pays with a $10 note. How much change does he get?
Question 2: 1.15 Time
Write 7.45 pm as a time 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
Write each 24-hour clock time as a 12-hour clock time using am or pm. (a) 04 20 (b) 16 05
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
A film starts at 18 40. It lasts 1 hour 55 minutes. At what time does the film finish?
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 - 7 = 18.
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 are in the teacher tools.