Question 1:
The table shows a group of students different eye and hair colours.
Question 1(a): [2 marks]
Find the values of a, b, c, d from the table above.
Answer type: Multiple answers type 1
ANSWER:
a=5, b=7, c=17, d=30
Workings:
a = 13 - 8 = 5 b = 15 - 8 = 7 c = 7 + 10 = 17 d = 15 + 15 = 30Marks = 3
Question 1(b): [2 marks]
Using the table, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: C
Workings:
There are a total of 13 students with blue eyes and 17 with a different colour.
Of the students with blue eyes, 8 have fair hair and 5 have dark hair.
Of the students with a different eye colour, 7 have fair hair and 10 have dark hair.
Marks = 3
Question 2:
There are 150 pupils in Year 8, 85 of the pupils are boys, the rest are girls.
14 of the boys were late to school on Monday.
8 girls were late to school on Monday.
Question 2(a): [2 marks]
Using the information, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: B
WORKING:
There are 150-85=65 girls.
85-14=71 boys were on time.
65-8=57 girls were on time.
Marks = 4
Question 2(b): [2 marks]
A pupil is chosen at random.
Find the probability they are a girl, who arrived on time.
Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{57}{150}
Workings:
Find the corresponding value in the Frequency Tree from part (a).
Marks = 1
Question 3:
There are 100 members in a local diving club.
45 of the members are male, the rest are female.
13 of the female members are under 17, the rest are 17 or over.
\dfrac{3}{5} of the males are under 17, the rest are 17 or over.
Question 3(a): [3 marks]
Using the information, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
WORKING:
There are 100-45=55 females.
55-13=42 females are 17 or over.
\dfrac{3}{5} \times 45 = 27 males are under 17.
45-27=18 males are 17 or over.
Marks = 5
Question 3(b): [1 mark]
What percentage of the members are under 17?
Answer type: Simple text answer
ANSWER: 40 %
WORKING:
27+13=40 out of 100 members are under 17.
Marks = 2
Question 4: [3 marks]
There are 200 pupils in a 6th form.
In the 6th form there are two year groups: lower sixth and upper sixth.
There are 120 pupils in lower sixth.
The ratio of male to female pupils in lower sixth is 5:7.
45\% of the upper sixth pupils are female.
Using the information, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: D
WORKING:
There are 200-120=80 pupils in upper sixth.
There are 50:70 male to female students in lower sixth, by scaling up the ration in the question.
45\% = 0.45 \times 80 = 36 females in upper sixth.
80-36=44 males in upper sixth.
Marks = 6
Question 5:
Over 1 weekend, 400 people go to the cinema.
The cinema sells two different types of ticket:
Standard Tickets for £5.00, VIP Tickets for £7.00
140 people bought VIP tickets.
80 people used a 10\% off voucher for their tickets.
One fifth of the VIP ticket holders used the voucher.
Question 5(a): [3 marks]
Using the information, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: D
WORKING:
400-260=140 people bought standard tickets.
\dfrac{1}{5} \times 140 = 28 VIP ticket holders used the voucher.
140-28=112 VIP ticket holders didn’t use the voucher.
80-28=52 standard ticket holders used the voucher.
260-52=208 standard ticket holders didn’t use the voucher.
Marks = 4
Question 5(b): [3 marks]
How much money did the cinema make in ticket sales that weekend?
Answer type: Simple text answer
ANSWER: £2234.20
WORKING:
10\% off gives ticket prices of £4.50 for standard and £6.30 for VIP.
Sales without vouchers: 208 \times £5 + 112 \times £7 = £1824
Sales with vouchers: 52 \times £4.50 + 28 \times £6.30 = £410.40
Total: £1824 + £410.40 = £2234.20
Marks = 4
Question 6:
345 GCSE students are asked to pick one language out of French, Spanish or Italian.
French has 30 more students than Spanish.
Italian was picked by half as many students that chose French.
\dfrac{2}{3} of those studying French are female.
55\% of those studying Spanish are male.
The ratio of male to female that study Italian is 2:1.
Question 6(a): [3 marks]
Using the information, choose the correct completed frequency tree from below.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
WORKING:
Let x be the number of students who studied Italian.
Then we can form an equation from what we know, to find x:
345 = 2x + (2x-30) + x, which can be solved to find that x=75, i.e. 75 students studied Italian.
Therefore 2 \times 75 = 150 students chose French and 150-30=120 students chose Spanish.
\dfrac{2}{3} \times 150 = 100 male French students.
150-100 = 50 female French students.
0.55 \times 120 = 66 male Spanish students.
120-66 = 54 female Spanish students.
50:25 is the ratio of male to female students that studied Italian.
Marks = 4
Question 6(b): [1 mark]
How many of the GCSE students are male?
Answer type: Simple text answer
ANSWER: 166
WORKING:
50+66+50 = 166Marks = 1