iGCSE Mathematics (0580) :C8.3 Understand that the probability of an event occurring = 1 – the probability of the event not occurring.. iGCSE Style Questions Paper 3

Question

(a) One day a survey is taken of the ages of 120 children at a fairground.
The results are shown in the frequency table.

(i) On the grid, draw a bar chart for this data.
Complete the scale on the frequency axis.

Answer/Explanation

Ans: Correct diagram with scale 

(ii) What is the modal age group?

Answer/Explanation

Ans: 10 to 12 cao

(iii) One of the 120 children is chosen at random.
Write down the probability that the child is aged 4 to 6.

Answer/Explanation

Ans: \(\frac{19}{120}\) or 0.158[3….] or 15.8[3……]%

(b) Lalia says the probability of taking a yellow bead from a bag containing yellow beads and black beads is \(\frac{7}{5}.\)

Explain why \(\frac{7}{5}\) cannot be a correct probability

Answer/Explanation

Ans: Probability must be between 0 and 1 oe 

(c) Another bag contains 9 green marbles and 11 red marbles.
A marble is taken at random.
Write down the probability that the marble is
(i) green,

Answer/Explanation

Ans: \(\frac{9}{20}\)   or 0.45 or 45% 

(ii) blue.

Answer/Explanation

Ans: 0 oe

Question

Mrs Singh and Mr Patel are teachers.
They take their two classes to the theatre to see a play.
(a) (i) Mrs Singh has 20 girls in her class.
The ratio of girls : boys = 5 : 3.
Show that Mrs Singh has 32 students in her class.
(ii) Mr Patel has 40 students in his class.
The ratio of girls : boys = 3 : 2.
For the 72 students in the two classes, work out the ratio of
total number of girls : total number of boys.
Give your answer in its simplest form.
(b)

Four teachers go to the theatre with the 72 students.
Calculate the total cost of the tickets.
$……………….
(c) The play is in three parts.
Each part lasts for 45 minutes.
There is a 20 minute interval between each part.
The first part starts at 1330.
Work out the time that the play ends.
(d) Mr Patel pays $3.60 for a programme.
Last year, the price of a programme was $3.20 .
Calculate the percentage increase in the price of a programme.
……………… %
(e) The probability that a student loses their theatre ticket is \(\frac{1}{18}\).
(i) Write down the probability that a student does not lose their ticket.
(ii) Work out how many of the 72 students you would expect to lose their ticket.

Answer/Explanation

Answer:

(a) (i) \(\frac{20}{5} \times (5+3)\) or \(\frac{20}{5} \times 8\)
(ii) 11 : 7

(b) 430.5[0]

(c) 16.25 or 4.25 pm

(d) 12.5

(e) (i) \(\frac{17}{18}\) oe
(ii) 4

Question

(a) The scale drawing shows the positions of two buoys, A and B, in the sea.
       The scale is 1 centimeter represents 20 kilometers.

(i) Work out the actual distance between buoy A and buoy B.

km [2]

(ii) Measure the bearing of buoy B from buoy A.[1]

(iii) Buoy C is 120 km from buoy B on a bearing of 300°.
         On the scale drawing, mark the position of buoy C. [2]

(iv) Marco sails his boat so that he is always equidistant from buoy A and buoy B.

         On the scale drawing, use a straight edge and compasses only to construct the path of the boat. Show all your construction arcs. [2]

(b) The amount of fuel, t liters, in the boat’s fuel tank is 135 liters, correct to the nearest liter.
       Complete the statement about the value of t.

____ \(\leqslant t< \) ____ [2]

(c) Marco has ropes of four different colours.
       He takes a rope at random.

       Complete the table. [2]

(d) When Marco arrives at a port the temperature is 5°C.
        At midnight the temperature has fallen by 7°C.

        Find the temperature at midnight.

°C [1]

(e) Last year the cost to keep a boat at the port was \($\)14 per night.
        This year the cost has increased by 12%.

        Calculate the cost this year.

\($\)[2]

(f) Marco watched 25 boats enter the port, of which 9 had a mast.
      There are a total of 200 boats in the port.

      Calculate an estimate of the number of boats in the port that have a mast.[2]

Answer/Explanation

Ans:

8(a)(i) 220

8(a)(ii) [0]80°

8(a)(iii) C in correct position

8(a)(iv) Correct line drawn with 2 pairs of correct arcs

8(b) 134.5, 135.5

8(c) 0.41

8(d) –2

8(e) 15.68 cao

8(f) 72

Question

 (a) Jian has a fair spinner in the shape of a regular hexagon.
The spinner is numbered 2, 2, 3, 4, 4, 5.


Jian spins the spinner.
Find the probability that the spinner lands on
(i) an even number,
………………………………………….
(ii) a number less than 6,
………………………………………….
(iii) the number 1
(b) Mei has two fair square spinners, A and B.
Spinner A is numbered 1, 2, 2, 4 and spinner B is numbered 3, 3, 4, 5.


She spins both spinners and adds the two numbers.
(i) Complete the table to show all the possible outcomes.


(ii) Use the table to write down the probability that the total is
(a) 5,
………………………………………….
(b) more than 5.
………………………………………….
(c) Ning has a spinner numbered 1 to 6.
She spins it 50 times and her results are shown in the table.


(i) Write down the mode.
………………………………………….
(ii) Find the median.
………………………………………….
(iii) Work out the mean.
………………………………………….

Answer/Explanation

(a)(i)\(\frac{2}{3}\)
(ii) 1
(iii) 0
(b)(i) 5 6
8 9
in the correct places
(ii)(a)\( \frac{5}{16}\)
(b) \(\frac{9}{16}\)
(c)(i) 1
(ii) 2
(iii) 2.76

Question

 20 students choose their favourite science subject.
The results are shown in the bar chart.


(a) Work out how many more students choose biology than physics.
………………………………………….
(b) Write down the fraction of students whose favourite science subject is chemistry.
………………………………………….
(c) One of the 20 students is picked at random.
Write down the probability that this student did not choose biology.
………………………………………….
(d) Only one of the averages, median, mode and mean can be found for these results.
(i) Write down the average that can be found.
………………………………………….
(ii) Find this average for these results.
………………………………………….
(iii) Explain why the range cannot be found.
……………………………………………………………………………………………………………………………
(e) The results are to be shown in a pie chart.
(i) Complete the table,


(ii) Complete the pie chart.

Answer/Explanation

(a) 5
(b)\(\frac{3}{20}\)
(c)\(\frac{9}{20}\)
(d)(i) Mode
(ii) Biology
(iii) Correct reason
(e)(i) 11 198
3 54
6 108
(ii) Correct pie chart drawn

Question

(a)

The diagram shows a fair 9-sided spinner.
The numbers on the spinner are 2, 3, 5, 5, 5, 6, 6, 7 and 8.
(i) The spinner is spun once.
Write down the probability that the spinner lands on
(a) the number 8,

Answer/Explanation

Ans: \(\frac{1}{9}oe\)

(b) a number less than 7.

Answer/Explanation

Ans: \(\frac{7}{9}oe\)

(ii) The spinner is spun 135 times.
Work out the expected number of times the spinner lands on the number 6.

Answer/Explanation

Ans: 30

(b) Hitesh throws a dice 80 times.
The results are shown in the table.

(i) Write down the mode.

Answer/Explanation

Ans: 2

(ii) Work out the range.

Answer/Explanation

Ans: 5

(iii) Work out the median.

Answer/Explanation

Ans: 3

(iv) Calculate the mean.

Answer/Explanation

Ans: 3.35

Question

(a) One day, Mahika records the number of teachers and students who cycle to school.

(i) Complete the frequency column in the table.

Answer/Explanation

Ans: 5   23 

(ii) Work out the percentage of people who cycle that are students.

Answer/Explanation

Ans: 82.1 or 82.14… 

(b) Mahika records how 120 students from Year 1 and Year 2 travel to school.
Each student walks, cycles or travels by bus.
• 48 students are in Year 1.
• 77 students walk.
• 5 students in Year 2 cycle.
• 36 students travel by bus.
• \(\frac{4}{9}\) of the students who travel by bus are in Year 1.
(i) Complete the table.

Answer/Explanation

Ans: 30     2      16       48
        47      5       20      72
        77      7       36      [120] 

(ii) One of the 120 students is chosen at random.

Work out the probability that this student does not travel by bus to school.

Answer/Explanation

Ans: \(\frac{7}{10}oe\)

(c) There have been 24 complaints about one of the buses.
The complaints are:
• The bus is late.
• The price is too high.
• The bus is crowded.
(i) Complete the table.

Answer/Explanation

Ans: 150,     90,     120 

(ii) Complete the pie chart.

Answer/Explanation

Ans: Correct pie chart drawn 

Question

 20 students choose their favourite science subject.
The results are shown in the bar chart.


(a) Work out how many more students choose biology than physics.
………………………………………….
(b) Write down the fraction of students whose favourite science subject is chemistry.
………………………………………….
(c) One of the 20 students is picked at random.
Write down the probability that this student did not choose biology.
………………………………………….
(d) Only one of the averages, median, mode and mean can be found for these results.
(i) Write down the average that can be found.
………………………………………….
(ii) Find this average for these results.
………………………………………….
(iii) Explain why the range cannot be found.
……………………………………………………………………………………………………………………………
(e) The results are to be shown in a pie chart.
(i) Complete the table,


(ii) Complete the pie chart.

Answer/Explanation

(a) 5
(b)\(\frac{3}{20}\)
(c)\(\frac{9}{20}\)
(d)(i) Mode
(ii) Biology
(iii) Correct reason
(e)(i) 11 198
3 54
6 108
(ii) Correct pie chart drawn

Question

(a) Jon spins this 6-sided spinner.

The probability that the spinner lands on any of the six sides is equally likely.
Write down the probability that the spinner lands on
(i) the number 6,

Answer/Explanation

Ans: \(\frac{1}{6}oe\)

(ii) a prime number,

Answer/Explanation

Ans: \(\frac{2}{6}oe\)

(iii) a number less than 11.

Answer/Explanation

Ans: 1

(b) Felix has a 12-sided spinner with the numbers 2, 4, 5, 7 and 9 written on it.
It is equally likely to land on any side.
The table shows the probability of the spinner landing on each number.

The diagram of the spinner has been completed for the number 2.
Complete the diagram for the numbers 4, 5, 7 and 9.

Answer/Explanation

Ans: (2,2,2), 4,4,4,4,5,5,7,7,9 seen on spinner 

(c) Felix says that his spinner is more likely to land on a 2 than Jon’s spinner.
Explain why he is wrong.

Answer/Explanation

Ans: Felix’s probability is \(\frac{3}{12}\) which is
less than Jon’s probability \(\left (of\frac{2}{6} \right )\) which is \(\frac{4}{12}oe\)

(d) Felix spins his 12-sided spinner 60 times and records the results.

(i) Complete the table by working out the sector angles for the numbers 7 and 9 .

Answer/Explanation

Ans: (90°, 120°, 30°), 72°, 48° 

(ii) Complete the pie chart.

Answer/Explanation

Ans: 30° angle correct 72°, 48° 

(iii) Write down the mode.

Answer/Explanation

Ans: 4

(iv) Calculate the mean.

Answer/Explanation

Ans: 4.85 

Question

(a) Amir asked 15 friends how many hours they spent playing sport last weekend. His results are shown in the table below.

(i) Write down the mode.

Answer/Explanation

Ans: 0

(ii) Find the median.

Answer/Explanation

Ans: 1

(iii) Calculate the mean.

Answer/Explanation

Ans: 1.6

(iv) On the grid, draw a bar chart to show the information given in the table.

Answer/Explanation

Ans: Bar chart with
– horizontal axis correctly labelled
– and vertical axis correctly scaled
– and bars of correct height and equal width,
– and with equal gaps or no gaps 

(b) Amir also asked these 15 friends which was their favourite sport. His results are shown in the table below.

Amir picks one of these friends at random. Write down the probability that his friend’s favourite sport is
(i) cricket,

Answer/Explanation

Ans: \(\frac{5}{15}or\frac{1}{3}\)

(ii) not football,

Answer/Explanation

Ans: \(\frac{11}{15}\)

(iii) basketball or badminton.

Answer/Explanation

Ans: \(\frac{6}{15}or\frac{2}{5}\)

Question

30 students took a vocabulary test.
The marks they scored are shown below

7     8     5      8      3      2
6     6     3      3      6     2
7      1     5      10    2     6
6      5    8       1      2     7
3      1    5       3      10   3

(a) Complete the frequency table below.
The first five frequencies have been completed for you.
You may use the tally column to help you.

(b) (i) Find the range.

(ii) Write down the mode.

(iii) Find the median.

(iv) Calculate the mean.

(c) A student is chosen at random.
Find the probability that the student scored
(i) 1 mark,

(ii) 4 marks,

(iii) fewer than 6 marks.

Answer/Explanation

(a)

(b)(i)  Range= Max marks-Min marks

 = 10-1

  = 9

(ii) Mode= Max frequency element = 3

(iii) Median

Arrange data in ascending order :

1 1 1 2 2 2 2 3 3 3 3 3 3 5 5 5 5 6 6 6 6 6 6 7 7 7 8 8 8 10

No. of students=30

Therefore, Median =\(\frac{15th+16th element}{2}\)

 =\(\frac{5+5}{2}\)

 =5

(iv) Mean= \(\frac{3.1+4.2+6.3+0.4+4.5+5.6+3.7+3.8+0.9+2.10}{30}\)

  = 4.8

(c)(i) Probability of 1 mark scorer=\(\frac{no. of times 1 mark scored}{total  no. of students}\)

 = \(\frac{3}{30}\)

  =\(\frac{1}{10}\)

(ii) P=\(\frac{0}{30}\)

(iii) Sum of probabilities :

\(\frac{4}{30}+\frac{0}{30}+\frac{6}{30}+\frac{4}{30}+\frac{3}{30}\)=\(\frac{17}{30}\)

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