Cambridge IGCSE 0580 Core starter questions: weeks 27–39
52 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Core, weeks 27–39 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.
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Week 27
Question 1: 9.1 Classifying statistical data
Is each type of data categorical, discrete or continuous? (a) eye colour (b) the number of brothers and sisters a student has
Question 2: 9.3 Averages and range
Here are seven numbers: 4, 7, 2, 7, 9, 3, 5 Find (a) the mode (b) the median (c) the range.
Question 3: 8.3 Probability of combined events
Two fair six-sided dice are rolled and their scores are added. Find the probability that the total is 7.
Question 4: 8.1 Introduction to probability
A fair six-sided dice is rolled. Find the probability of (a) a prime number (b) a number greater than 4.
Week 28
Question 1: 9.4 Statistical charts and diagrams
In a pictogram, one symbol represents 6 hours of sunshine. (a) Monday is shown by 21/2 symbols. How many hours of sunshine were there on Monday? (b) Tuesday had 9 hours of sunshine. How many symbols are needed for Tuesday?
Question 2: 9.1 Classifying statistical data
Is each type of data categorical, discrete or continuous? (a) the height of a tree (b) the number of cars in a car park
Question 3: 9.3 Averages and range
Find the mean of 12, 15, 9, 14.
Question 4: 9.4 Statistical charts and diagrams
The ordered stem-and-leaf diagram shows some data. 2 1 5 8; 3 0 2 7 7; 4 1 4 6 9; 5 3 Key: 3 | 2 represents 32 (a) How many values are there? (b) Find the range. (c) Write down the mode.
Week 29
Question 1: 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 2: 9.5 Scatter diagrams
A scatter diagram shows that as the outside temperature increases, the number of hot drinks sold at a café decreases. What type of correlation does this show?
Question 3: 9.4 Statistical charts and diagrams
A bar chart shows the favourite fruit of some students: apples 7, bananas 12, grapes 5, oranges 6. (a) How many students were asked? (b) What fraction of the students chose bananas? Give your answer in its simplest form.
Question 4: 9.2 Interpreting statistical data
The table shows the rainfall, in mm, in a town. Month Jan Feb Mar Apr May; Rainfall (mm) 42 35 58 61 47 (a) Which month was the wettest? (b) How much more rain fell in the wettest month than in the driest month?
Week 30
Question 1: 9.2 Interpreting statistical data
A pie chart shows the favourite sports of 36 students. The angle of the sector for football is 120^∘. How many students chose football?
Question 2: 9.5 Scatter diagrams
What type of correlation would you expect between the heights of adults and their shoe sizes?
Question 3: 6.1 Pythagoras' theorem
The two shorter sides of a right-angled triangle are 6 cm and 8 cm. Find the length of the hypotenuse.
Question 4: 9.2 Interpreting statistical data
Kai asks 10 people at a gym whether they exercise every day. 9 of them say yes. Kai says, "90% of the people in my town exercise every day." Give one reason why Kai's conclusion may not be correct.
Week 31
Question 1: 6.2 Right-angled triangles
In a right-angled triangle, angle A is opposite a side of 3 cm. The other two sides are 4 cm (next to A) and 5 cm (the hypotenuse). Write down, as fractions, sin A, cos A and tan A.
Question 2: 6.1 Pythagoras' theorem
A right-angled triangle has hypotenuse 13 cm and one other side 5 cm. Find the length of the third side.
Question 3: 9.2 Interpreting statistical data
Two teams play five games. The points they score are: Team X: 12, 15, 9, 20, 14 Team Y: 16, 17, 15, 18, 14 (a) Find the mean and the range for each team. (b) Compare the two teams.
Question 4: 9.5 Scatter diagrams
What type of correlation would you expect between people's house numbers and their heights?
Week 32
Question 1: 1.13 Percentages
A jacket costs $80. In a sale the price is reduced by 35%. Work out the sale price.
Question 2: 2.5 Equations
The angles of a triangle are x^∘, 2x^∘ and (x + 20)^∘. Write an equation in x and solve it.
Question 3: 4.6 Angles
Two parallel lines are crossed by a straight line. One of the angles formed is 64^∘. Find (a) the angle corresponding to it (b) the angle co-interior to it.
Question 4: 9.3 Averages and range
Find the mean of 3.2, 4.8, 5.1, 2.9, 4.0.
Week 33
Question 1: 7.1 Transformations
Write down the image of each point after the translation. (a) (3, 2) translated by 4; -5 (b) (-1, 6) translated by -2; 3
Question 2: 1.13 Percentages
Sara invests $2400 at 3.5% per year simple interest. Work out the total interest after 4 years.
Question 3: 2.5 Equations
Solve 5x - 7 = 18.
Question 4: 4.6 Angles
Five of the interior angles of a hexagon are 110^∘, 125^∘, 130^∘, 118^∘ and 102^∘. Find the sixth angle.
Week 34
Question 1: 7.1 Transformations
The point (4, 1) is reflected. Write down its image after a reflection in (a) the y-axis (b) the x-axis.
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: 2.5 Equations
Solve 3(x + 4) = 33.
Question 4: 4.6 Angles
The angles of a quadrilateral are x^∘, 2x^∘, 3x^∘ and 4x^∘. Find the largest angle.
Week 35
Question 1: 2.10 Graphs of functions
Complete the table of values for y = x² - 2x - 3. x -2 -1 0 1 2 3 4; y
Question 2: 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 3: 2.10 Graphs of functions
Complete the table of values for y = 12/x. x 1 2 3 4 6 12; y
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 36
Question 1: 2.11 Sketching curves
The graph of y = x² - 9 is sketched. Write down (a) the coordinates of the points where it crosses the x-axis (b) the coordinates of the point where it crosses the y-axis (c) the equation of its line of symmetry.
![Cambridge IGCSE 0580 Core starter question on 2.5 Equations: Make the letter in brackets the subject of each formula. (a) C = 2π r [r] (b) y = 3x + 5 [x]](/igcse-frontend/img/questions/igcse-maths-0580-core-2-5-equations-starter-question-cie0580c-w36-q2.webp)
Question 2: 2.5 Equations
Make the letter in brackets the subject of each formula. (a) C = 2π r [r] (b) y = 3x + 5 [x]
Question 3: 2.7 Sequences
The nth term of a sequence is n² + 3. (a) Write down the first three terms. (b) Find the 10th term.
Question 4: 2.10 Graphs of functions
(a) Complete the table of values for y = x² - 5x + 4. x 0 1 2 3 4 5; y (b) The graph of y = x² - 5x + 4 is drawn from this table. Use the table to write down the solutions of x² - 5x + 4 = 0.
Week 37
Question 1: 2.6 Inequalities
Describe how you would show x ≥ 1.5 on a number line.
Question 2: 3.5 Equations of linear graphs
Write down the equation of the straight line with (a) gradient 2 and y-intercept 5 (b) gradient -1/2 and y-intercept 3.
Question 3: 3.6 Parallel lines
Is the line y = 2x + 5 parallel to the line 2y = 4x - 3? Give a reason.
Question 4: 2.11 Sketching curves
Sketch the graph of y = (x - 1)(x - 5). On your sketch, show the coordinates of the points where the graph meets the axes. Write down the equation of the line of symmetry.
Week 38
Question 1: 1.13 Percentages
Find 15% of $60.
Question 2: 1.11 Ratio and proportion
The ratio of boys to girls in a club is 3: 5. There are 35 girls. How many students are in the club altogether?
Question 3: 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 4: 1.8 Standard form
Write these as ordinary numbers. (a) 3.07 × 10⁵ (b) 8 × 10⁻⁴
Week 39
Question 1: 4.4 Similarity
Triangles ABC and DEF are similar, with A corresponding to D, B to E and C to F. AB = 5 cm, DE = 15 cm and BC = 7 cm. Find EF.
Question 2: 4.7 Circle theorems
PT is a tangent to a circle with centre O, touching it at T. (a) Write down the size of angle OTP. (b) Angle TOP = 58^∘. Find angle OPT.
Question 3: 4.3 Scale drawings
A scale drawing uses a scale of 1 cm to 5 m. A wall is 23 m long. How long is the wall on the drawing?
Question 4: 4.5 Symmetry
Write down the number of lines of symmetry and the order of rotational symmetry of (a) an equilateral triangle (b) a rhombus that is not a square.
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.