Cambridge IGCSE 0580 Core starter questions: weeks 40–51
48 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Core, weeks 40–51 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 40
Question 1: 5.3 Circles, arcs and sectors
A sector has radius 12 cm and angle 60^∘. Find its arc length in terms of π.
Question 2: 5.5 Compound shapes and parts of shapes
A shape is made from a rectangle 12 cm by 6 cm with a semicircle on one of its 6 cm sides. Find the area of the shape. Give your answer correct to 3 significant figures.
Question 3: 6.2 Right-angled triangles
Which ratio, sin, cos or tan, would you use to find a side in a right-angled triangle when you know (a) an angle and the hypotenuse, and you want the side opposite the angle (b) an angle and the side next to it (not the hypotenuse), and you want the side opposite?
Question 4: 4.4 Similarity
A photo is 12 cm wide and 8 cm high. It is enlarged so that its width is 30 cm. Find its new height.
Week 41
Question 1: 8.3 Probability of combined events
The probability that Tom is late on Monday is 0.4. The probability that he is late on Tuesday is 0.3. The two events are independent. Use a tree diagram to find the probability that he is (a) late on both days (b) late on neither day.
Question 2: 9.4 Statistical charts and diagrams
60 people were asked what they drink at breakfast. 15 of them said tea. In a pie chart, what is the angle of the sector for tea?
Question 3: 9.5 Scatter diagrams
The table shows the hours of sunshine and the numbers of ice creams sold at a shop on six days. Sunshine (hours) 2 4 5 7 8 10; Ice creams sold 15 22 27 33 38 45 Describe the correlation shown by these data.
Question 4: 9.2 Interpreting statistical data
The number of minutes two buses were late on seven days are: Bus P: 3, 8, 5, 7, 5, 9, 4 Bus Q: 6, 6, 7, 5, 6, 8, 6 Use the median and the range to compare how late the two buses were.
Week 42
Question 1: 1.4 Fractions, decimals and percentages
Write 7/40 as a percentage.
Question 2: 1.6 The four operations
Put brackets into each calculation to make it correct. (a) 5 + 3 × 4 - 2 = 30 (b) 5 + 3 × 4 - 2 = 16
Question 3: 1.11 Ratio and proportion
Blue paint and white paint are mixed in the ratio 2: 7. Ali uses 1.8 litres of blue paint. How many litres of paint does he make altogether?
Question 4: 1.13 Percentages
Write 18 as a percentage of 72.
Week 43
Question 1: 1.15 Time
How many seconds are there in one week?
Question 2: 1.16 Money
The exchange rate is 1 euro = $1.10. Change 60 euros into dollars.
Question 3: 1.2 Sets
n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B).
Question 4: 1.12 Rates
A force of 360 newtons acts on an area of 0.25 m^2. Work out the pressure, using pressure = force ÷ area.
Week 44
Question 1: 1.15 Time
A train leaves at 09 48 and arrives at 13 17 on the same day. How long does the journey take? Give your answer in hours and minutes.
Question 2: 1.16 Money
Mei earns $11.85 per hour. One week she works 36 hours. How much does she earn that week?
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: 1.12 Rates
A town has a population of 84 500 and an area of 26 km^2. Work out the population density.
Week 45
Question 1: 1.1 Types of number
A bus leaves stop A every 12 minutes and a bus leaves stop B every 20 minutes. Buses leave both stops at 08 00. At what time do buses next leave both stops at the same time?
Question 2: 1.7 Indices I
(a) Write (2³)² as a single power of 2. (b) Work out its value.
Question 3: 1.8 Standard form
Work out (3.2 × 10⁴) × (2.5 × 10³). Give your answer in standard form.
Question 4: 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.
Week 46
Question 1: 5.2 Area and perimeter
A rectangle has an area of 52.5 cm² and a length of 7.5 cm. Find its perimeter.
Question 2: 5.3 Circles, arcs and sectors
The circumference of a circle is 50 cm. Find its radius. Give your answer correct to 3 significant figures.
Question 3: 5.4 Surface area and volume
A cylinder has radius 4 cm and height 10 cm. Find its volume. Give your answer correct to 3 significant figures.
Question 4: 6.1 Pythagoras' theorem
The two shorter sides of a right-angled triangle are 4.5 cm and 7 cm. Find the length of the hypotenuse. Give your answer correct to 3 significant figures.
Week 47
Question 1: 9.1 Classifying statistical data
Give one example of categorical data that could be collected about a car.
Question 2: 9.3 Averages and range
The table shows the number of goals scored by a team in 20 matches. Goals 0 1 2 3; Frequency 4 6 7 3 Find (a) the mode (b) the median.
Question 3: 9.4 Statistical charts and diagrams
A dual bar chart shows the numbers of ice creams sold at a kiosk on five days in two weeks. Week 1: Mon 12, Tue 15, Wed 9, Thu 20, Fri 18 Week 2: Mon 14, Tue 11, Wed 16, Thu 22, Fri 17 On which day was the difference between the two weeks the greatest? Write down the difference.
Question 4: 1.9 Estimation
By rounding each number to 1 significant figure, estimate the value of (49.7 × 3.12)/0.198. Show your working.
Week 48
Question 1: 9.1 Classifying statistical data
Here is a list of types of data: temperature, blood group, country of birth, time taken to run 400 m. Which two of these are categorical data?
Question 2: 9.3 Averages and range
The table shows the number of pets owned by 25 students. Pets 0 1 2 3 4; Frequency 7 9 5 3 1 Calculate the mean number of pets.
Question 3: 9.4 Statistical charts and diagrams
The marks of 11 students in a test are: 45, 52, 38, 47, 61, 55, 49, 38, 52, 60, 43 (a) Draw an ordered stem-and-leaf diagram for these marks. Include a key. (b) Find the median mark.
Question 4: 1.9 Estimation
350 people are going on a trip. Each minibus can carry 16 people. How many minibuses are needed?
Week 49
Question 1: 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.
Question 2: 2.10 Graphs of functions
(a) Complete the table of values for y = 4 - x^2. x -3 -2 -1 0 1 2 3; y (b) Use your table to solve 4 - x² = 0.
Question 3: 4.6 Angles
(a) Two angles on a straight line are 47^∘ and x^∘. Find x. (b) Three angles at a point are 110^∘, 95^∘ and y^∘. Find y.
Question 4: 4.7 Circle theorems
AB is a diameter of a circle, and C is a point on the circle. AB = 13 cm and AC = 5 cm. Find BC.
Week 50
Question 1: 1.3 Powers and roots
Use your calculator to work out (a) 2.5⁴ (b) 3√(50) Give each answer correct to 3 significant figures.
Question 2: 1.10 Limits of accuracy
The number of people at a match is 24 000, correct to the nearest thousand. (a) Write down the least possible number of people. (b) Write down the greatest possible number of people.
Question 3: 1.12 Rates
A car travels 150 km in 2.5 hours. Work out its average speed.
Question 4: 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.
Week 51
Question 1: 1.15 Time
On a certain date, the time in Tokyo is 9 hours ahead of the time in London. A plane leaves London at 19 30 London time. The flight takes 11 hours 50 minutes. At what time, Tokyo time, does the plane land?
Question 2: 1.16 Money
A phone contract costs $15 per month plus 8 cents for each minute of calls. In March, Lena makes 120 minutes of calls. How much does she pay for March?
Question 3: 1.2 Sets
Use set notation to describe (a) the elements that are in A but not in B (b) the elements that are in neither A nor B.
Question 4: 3.1 Coordinates
(a) Write down the coordinates of the origin. (b) What is the x-coordinate of every point on the y-axis?
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.