Math for IGCSE
MATHEMATICS A
Answer ALL TWENTY FOUR questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. (a) Simplify h7 ×h2
....................................................... (1)
G = c2 – 4c
(b) Find the value of G when c = –5
G = .......................................................(2)
(c) Solve
= 2x + 3
Show clear algebraic working.
x = .......................................................(3)
2. Harold bought an antique clock for £1200 The clock increased in value by 8% per
year. Find the value of the clock exactly 3 years after Harold bought the clock. Give
your answer correct to the nearest £.
£.......................................................(3)
3. The frequency table gives information about the ages of the 80 people in a train
carriage.
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(a) Complete the cumulative frequency table.
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the median age of the people in the train
carriage.
....................................................... years (2)
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4. The table gives information about the length of time, in minutes, that each of 60
students took to travel to school on Monday.
(a) Write down the modal class interval.
.......................................................(1)
(b) Work out an estimate for the mean length of time taken by these 60 students to
travel to school on Monday. Give your answer correct to one decimal place.
....................................................... minutes (4)
5.
Correctly complete the following four statements by writing a word from the box on
each of the dotted lines.
(i)
10 is a .......................................................................... of 40
(ii)
49 is a .......................................................................... number.
(iii)
17 is a .......................................................................... number.
(iv)
48 is a .......................................................................... of 8
(Total for Question 5 is 4 marks)
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6.
ABC, BDF and ADE are straight lines.
(a) Write down the size of angle x.
.......................................................° (1)
(b) Work out the size of angle y.
.......................................................° (1)
(c) (i) Work out the size of angle z.
.......................................................° (1)
(ii) Give a reason for your answer.
...................................................................................................................................
.............................................................................................................. (2)
7. (a) Simplify 9x + 7y – 2x – 10y
....................................................... (2)
(b) Simplify 8t × 3t
....................................................... (1)
(d) Factorise 7h + h2
....................................................... (1)
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8. Show that 5
...................................................... (3)
9. Calvin asked some teachers how many children they have. The table shows
information about his results.
..................................................... (1)
(b) Complete the pictogram for the information in the table.
..................................................... (2)
(c) Find the total number of teachers Calvin asked
..................................................... (1)
(d) Find the ratio of the number of teachers with 1 child to the number of teachers
with 2 children. Give your ratio in its simplest form.
..................................................... (2)
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10. (a) Write these decimals in order of size. Start with the smallest decimal.
0.607
0.66
0.0632
0.615
0.006 79
..................................................... (1)
(b) Write 24 as a fraction of 80.
Give your fraction in its simplest form.
..................................................... (2)
(c) Write 9% as a decimal.
..................................................... (1)
43% of a class had a school lunch.
(d) What percentage of the class did not have a school lunch?
..................................................... (1)
(e) Work out of 18.54 kg.
..................................................... (2)
(f) Increase 4600 by 27%
..................................................... (3)
11. (a) Write down the cube root of 64
..................................................... (1)
(b) Calculate the value of 23 × 45
..................................................... (2)
(c) Express 600 as a product of powers of its prime factors. Show your working
clearly.
..................................................... (3)
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12. (a) On the grid, draw the graph of y = -2x + 4 for values of x from -1 to 5.
(4)
(b) Show by shading on the grid, the region defined by all three of the inequalities
y
y
x
1
Label your region R.
(3)
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Math for IGCSE
13.
14. On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3.
(3)
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15. (a) Solve 5(4 – x) = 7 – 3x.
Show clear algebraic working.
..................................................... (3)
(b) Factorise fully 16m3 g3 + 24m2g5
..................................................... (2)
(c) (i) Factorise y2 – 2y – 48
..................................................... (2)
(ii) Hence, solve y2 – 2y – 48 = 0
..................................................... (1)
16. A = 2 × 343
B = 16 × 337
(a) Find the highest common factor (HCF) of A and B.
..................................................... (1)
(b) Express the number A × B as a product of powers of its prime factors.
Give your answer in its simplest form.
..................................................... (2)
17. Here is a list of six numbers written in order of size.
4 7
x
10
y
y
The numbers have
a median of 9
a mean of 11
Find the value of x and the value of y.
..................................................... (4)
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18. Here is a 10-sided polygon.
Work out the value of x.
..................................................... (4)
19. Solve the simultaneous equations
7x – 2y = 34
3x + 5y = −3
Show clear algebraic working.
..................................................... (4)
20.
L, M, N and P are points on a circle, centre O
Angle MNP = 58°
(a) (i) Find the size of angle MLP
.......................................................°(1)
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(ii) Give a reason for your answer.
.......................................................(1)
(b) Find the size of the reflex angle MOP
.......................................................°(2)
21. Express
as a single fraction in its simplest form.
.......................................................(5)
22. Freya keeps hens.
The table shows information about the number of boxes of eggs she sold in each of 52
weeks.
(a) Write down the modal class.
.......................................................(1)
(b) Work out an estimate for the mean number of boxes of eggs that Freya sold each
week.
Give your answer correct to 3 significant figures.
.......................................................(4)
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Dan picks at random one of the 52 weeks.
(c) Find the probability that in this week Freya sold at least 15 boxes of eggs.
.......................................................(2)
23. The table gives some information about the average price of a litre of petrol in
England.
........................................
% (3)
The average price of a litre of petrol in England increased by 20% from January 2010
to January 2012.
(b) Work out the average price of a litre of petrol in England in January 2010.
Give your answer in pence, correct to 1 decimal place.
........................................
(3)
24. Solve the simultaneous equations
3x + 4y = 6
5x + 6y = 11
Show clear algebraic working.
x = .........................................
y = .........................................(4)
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