Cambridge IGCSE 0580 Extended starter questions: weeks 23–33
44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 23–33 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.
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Week 23
Question 1: 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 2: 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 3: 5.4 Surface area and volume
A prism has a cross-section of area 12 cm² and a length of 9 cm. Find its volume.
Question 4: 5.5 Compound shapes and parts of shapes
A semicircle has diameter 10 cm. Find its area in terms of π.
Week 24
Question 1: 6.3 Exact trigonometric values
Without using a calculator, write down the exact value of (a) sin 30^∘ (b) cos 60^∘ (c) tan 45^∘.
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: 4.7 Circle theorems I
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.
Week 25
Question 1: 8.1 Introduction to probability
A bag contains 3 red, 5 blue and 2 green counters. One counter is taken at random. Find (a) P(blue) (b) P(not green)
Question 2: 8.2 Relative and expected frequencies
Ella throws a coin 50 times and gets 22 heads. (a) Find the relative frequency of heads. (b) How many heads would you expect in 300 throws of a fair coin?
Question 3: 8.3 Probability of combined events
Two fair coins are thrown. (a) List all the possible outcomes. (b) Find the probability of two heads.
Question 4: 6.3 Exact trigonometric values
Without using a calculator, write down the exact value of (a) cos 30^∘ (b) sin 45^∘.
Week 26
Question 1: 8.4 Conditional probability
A bag has 5 red and 3 blue beads. Two are taken without replacement. Find the probability that both are red.
Question 2: 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 3: 9.3 Averages and measures of spread
Here are seven numbers: 4, 7, 2, 7, 9, 3, 5 Find (a) the mode (b) the median (c) the range.
Question 4: 8.1 Introduction to probability
The probability that it rains tomorrow is 0.35. (a) Find the probability that it does not rain tomorrow. (b) Is rain more likely than no rain? Give a reason.
Week 27
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: 9.2 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 3: 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 4: 8.4 Conditional probability
Of 40 students, 24 play tennis; of those, 9 also play golf. 6 students play golf only. A student is chosen at random from those who play golf. Find the probability they also play tennis.
Week 28
Question 1: 9.5 Scatter diagrams
What type of correlation would you expect between the heights of adults and their shoe sizes?
Question 2: 9.3 Averages and measures of spread
Find the mean of 12, 15, 9, 14.
Question 3: 9.6 Cumulative frequency diagrams
Find the interquartile range of: 3, 5, 6, 8, 9, 12, 14, 15, 18, 21, 25.
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: 9.7 Histograms
When drawing a frequency polygon for grouped data, at what x-value is the point for the class 20 < t ≤ 40 plotted?
Question 2: 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?
Question 3: 9.3 Averages and measures of spread
Find the mean of 3.2, 4.8, 5.1, 2.9, 4.0.
Question 4: 9.5 Scatter diagrams
What type of correlation would you expect between people's house numbers and their heights?
Week 30
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: 9.7 Histograms
A class 10 < h ≤ 25 has frequency 36. Work out the frequency density.
Question 3: 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 4: 9.3 Averages and measures of spread
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.
Week 31
Question 1: 7.2 Vectors in two dimensions
Find the magnitude of -5; 12.
Question 2: 7.3 Magnitude of a vector
a = 3; -2, b = -1; 4. Find 2a - 3b.
Question 3: 7.4 Vector geometry
OA = a, OB = b. M is the midpoint of AB. Find OM in terms of a and b.
Question 4: 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.
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: 3.5 Equations of linear graphs
Write down the equation of (a) the vertical line through (3, -1) (b) the horizontal line through (3, -1).
Question 4: 4.6 Angles
A regular polygon has 10 sides. Find (a) the size of each exterior angle (b) the size of each interior angle.
Week 33
Question 1: 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.
Question 2: 4.8 Circle theorems II
PA and PB are tangents to a circle, centre O. Angle APB = 48°. Find angle AOB.
Question 3: 4.7 Circle theorems I
AB is a diameter of a circle, and C is a point on the circle. AB = 13 cm and AC = 5 cm. Find BC.
Question 4: 1.13 Percentages
Sara invests $2400 at 3.5% per year simple interest. Work out the total interest after 4 years.
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.