Cambridge IGCSE 0580 Extended starter questions: weeks 45–55
44 short questions to open a lesson for Cambridge IGCSE Mathematics 0580, Extended, weeks 45–55 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 45
Question 1: 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 2: 7.4 Vector geometry
Show that 6; -9 is parallel to -2; 3.
Question 3: 8.3 Probability of combined events
A fair spinner numbered 1, 2 and 3 is spun and a fair coin is thrown. (a) How many possible outcomes are there? (b) Find the probability of a 3 and a head.
Question 4: 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.
Week 46
Question 1: 9.6 Cumulative frequency diagrams
Frequencies for consecutive classes are 6, 14, 22, 11, 7. Write down the cumulative frequencies.
Question 2: 9.7 Histograms
On a histogram, the bar for 40 < m ≤ 45 has frequency density 6.8. Work out the frequency.
Question 3: 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.
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 47
Question 1: 1.4 Fractions, decimals and percentages
Write 7/40 as a percentage.
Question 2: 1.6 The four operations
Work out (-3)² - 4 × (-2).
Question 3: 1.7 Indices I
Find the value of n when 5^n = 1/25.
Question 4: 1.18 Surds
Expand and simplify (3 + √2)(3 - √2).
Week 48
Question 1: 2.2 Algebraic manipulation
Simplify 5a + 3b - 2a + 4b.
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: 2.6 Inequalities
A number line has a filled circle at -4 and an open circle at 1, joined by a line. (a) Write down the inequality shown. (b) Write down the smallest and the largest integers that satisfy it.
Question 4: 2.7 Sequences
The nth term of a sequence is n² + 3. (a) Write down the first three terms. (b) Find the 10th term.
Week 49
Question 1: 2.2 Algebraic manipulation
Expand (a) 4(2x - 3) (b) x(x + 5)
Question 2: 2.5 Equations
Solve 5x - 7 = 18.
Question 3: 2.6 Inequalities
A ride is for children who are at least 110 cm tall and less than 150 cm tall. (a) Write this as an inequality for the height, h cm. (b) Can a child who is exactly 150 cm tall go on the ride?
Question 4: 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.
Week 50
Question 1: 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 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: 1.17 Exponential growth and decay
The population of a village is 8500. It increases by 2% each year. Find the population after 3 years.
Question 4: 3.4 Length and midpoint
Find the coordinates of the midpoint of the line joining (-5, -1) and (4, 6).
Week 51
Question 1: 6.2 Right-angled triangles
A straight ramp rises 5 m over a horizontal distance of 12 m. (a) Find the length of the ramp. (b) Write down the tangent of the angle the ramp makes with the horizontal, as a fraction.
Question 2: 6.5 Non-right-angled triangles
A triangle has sides 5 cm, 7 cm and 8 cm. Find the largest angle.
Question 3: 6.6 Pythagoras' theorem and trigonometry in 3D
A cuboid has base 6 cm by 8 cm and height 5 cm. Find the angle between the space diagonal and the base, to 1 d.p.
Question 4: 7.1 Transformations
The points (4, 6) and (8, 2) are enlarged with scale factor 1/2, centre the origin. Write down their images.
Week 52
Question 1: 1.9 Estimation
350 people are going on a trip. Each minibus can carry 16 people. How many minibuses are needed?
Question 2: 1.14 Using a calculator
Use your calculator to work out (8.6 + 3.9)/(4.2 - 1.7).
Question 3: 1.2 Sets
n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B).
Question 4: 2.7 Sequences
Here are the first four terms of a sequence: 3, 6, 12, 24, … (a) Write down the next two terms. (b) Find an expression for the nth term.
Week 53
Question 1: 1.9 Estimation
Work out (√(29.8))/(0.51 × 4.2). Give your answer correct to 2 decimal places.
Question 2: 1.14 Using a calculator
(a) Work out 17.4 ÷ 0.08. (b) Write your answer to part (a) correct to 3 significant figures.
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: 2.7 Sequences
Find an expression for the nth term of the sequence 0, 3, 8, 15, 24, …
Week 54
Question 1: 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?
Question 2: 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 3: 1.16 Money
Mei earns $11.85 per hour. One week she works 36 hours. How much does she earn that week?
Question 4: 4.1 Geometrical terms
Write down the name of a triangle that has (a) three equal sides (b) one angle greater than 90^∘ (c) exactly two equal sides.
Week 55
Question 1: 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.
Question 2: 2.4 Indices II
Simplify 3x² × 4x^5.
Question 3: 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.
Question 4: 3.1 Coordinates
The points (-2, 3) and (4, 3) are plotted. (a) Write down the equation of the line through both points. (b) How far apart are the two points?
More starter questions
Other weeks: Weeks 1–11 · Weeks 12–22 · Weeks 23–33 · Weeks 34–44 · Weeks 45–55. Answers and mark schemes are in the teacher tools.