PAPER 8A
QUESTION 1 [1 mark]
Given that 28\times1356= 37968
Calculate the following: 2.8 \times 1.356
Answer type: Simple text answer
ANSWER: 3.7968
QUESTION 2 [2 marks]
In a drawer there are 6 blue pairs of socks, 9 yellow pairs of socks, 4 black pairs of socks and 5 white pairs of socks.
A pair of socks is taken from the drawer at random.
What is the probability that the pair of socks chosen is white?
Give your answer as a fraction in simplest form.
Answer type: Fraction
ANSWER: \dfrac{5}{24}
WORKING:
Total number of socks =6+9+4+5
Number of white socks =5
Probability =\dfrac{5}{24}
QUESTION 3 [1 mark]
Here are six numbers:
0.42, \,\,\,\, \dfrac{3}{6}, \,\,\,\, \dfrac{3}{9}, \,\,\,\, -1.27, \,\,\,\, 0.55, \,\,\,\, \dfrac{2}{10}
Order the numbers from least to most.
Answer type: Multiple choice type 1
A: -1.27, \dfrac{2}{10}, \,\,\,\, \dfrac{3}{9}, \,\,\,\, 0.42, \,\,\,\, \dfrac{3}{6}, \,\,\,\, 0.55
B: -1.27, \dfrac{2}{10}, \,\,\,\, \dfrac{3}{9}, \,\,\,\, \dfrac{3}{6}, \,\,\,\, 0.42, \,\,\,\, 0.55
C: \dfrac{2}{10}, \,\,\,\, \dfrac{3}{9}, \,\,\,\, 0.42, \,\,\,\, \dfrac{3}{6}, \,\,\,\, 0.55, \,\,\,\, -1.27
D: 0.55, \dfrac{3}{6}, \,\,\,\, 0.42, \,\,\,\, \dfrac{3}{9}, \,\,\,\, \dfrac{2}{10}, \,\,\,\, -1.27
QUESTION 4 [2 marks]
If 200 grams of one ingredient is used in a recipe, which calls for a ratio of 4: 7 with a second ingredient, how much of the second ingredient is needed?
Answer type: Simple text answer
ANSWER: 350 grams
WORKING:
4 parts for ingredient one, 7 parts for the second ingredient.
200\div4=50
50\times7=350 grams
QUESTION 5 [2 marks]
A student is been sponsored to cycle a distance of 50 kilometres. He travels 20 miles. How many kilometres more does he need to travel to reach his 50 kilometre target? You may use the approximation that 1 mile is 1.6 kilometres.
Answer type: Simple text answer
ANSWER: 18 km
WORKING:
20 miles \times \, 1.6=32 km
50-32=18 km
QUESTION 6 [2 marks]
Find the missing angle labelled x
Answer type: Simple text answer
ANSWER: x= 125 \degree
WORKING:
x = 360 - 90 - 145 =125\degree
QUESTION 7 [3 marks]
A tin of biscuits has 36 assorted biscuits.
The probability that a biscuit selected at random has a chocolate coating on it is 0.75
How many biscuits do not have chocolate on them?
Answer type: Simple text answer
ANSWER: 9 biscuits
WORKING:
1-0.75 =0.25 0.25 \times 36 = 9
QUESTION 8 [2 marks]
Iron has a density of 7.8 g/cm^3
Calculate the mass of a 3.2 cm^3 lump of iron.
Answer type: Simple text answer
ANSWER: 24.96 g
WORKING:
\text{Mass}=\text{Density} \times \text{Volume}= (7.8 g/cm^3) \times (3.2 cm^3) =24.96 g
PAPER 8B
QUESTION 1 [2 marks]
Calculate the following: (4+2^2)^2-2
Answer type: Simple text answer
ANSWER: 62
WORKING:
(4+2^2)^2-2=(4+4)^2-2=8^2-2=64 - 2 = 62
QUESTION 2 [4 marks]
Sarah has started reading a new book.
On Saturday she reads \dfrac{2}{15} of the book.
On Sunday she reads a further \dfrac{1}{3} of the total number of pages in the book.
On Monday she reads another \dfrac{1}{5} of the total number of pages in the book.
On Tuesday she finishes the book.
The ratio she read on Tuesday morning to Tuesday evening was 1:2
What fraction of the book did she read on Tuesday evening?
Write your answer in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{2}{9}
WORKING:
\dfrac{2}{15}+\dfrac{1}{3} + \dfrac{1}{5}= \dfrac{2}{15}+ \bigg(\dfrac{1}{3} \times \dfrac{5}{5} \bigg) + \bigg(\dfrac{1}{5}\times \dfrac{3}{3} \bigg)
\dfrac{2}{15}+\dfrac{5}{15}+\dfrac{3}{15}=\dfrac{10}{15}
1-\dfrac{10}{15}=\dfrac{1}{3}
There are 1+2=3 parts in the ratio
1 part = \dfrac{1}{3} \div 3 = \dfrac{1}{9}
She read \dfrac{1}{9} \times 2 = \dfrac{2}{9} on Tuesday evening
QUESTION 3 [3 marks]
The diagram below shows a rectangle with a section missing.
Work out the area of the shape.
Answer type: Simple text answer
ANSWER: 15275 cm^2
WORKING:
Area of big rectangle = 120 \times 195 = 23400 cm^2
Area of missing rectangle = (120-55) \times (195 - 70) = 65 \times 125 = 8125 cm^2
Area = 23400 - 8125 = 15275 cm^2
QUESTION 4 [3 marks]
The cost of printing for students is given as:
\text{Cost in pence} = 4 \times \text{number of black and white pages} + 10 \times \text{number of colour pages}
The cost of binding a booklet of less than 50 pages costs £2
The cost of binding a booklet of 50 pages or more costs £2 plus 5p per page.
Work out how much a booklet of 45 black and white pages, and 15 colour pages will cost to print and bind.
Give your answer in pounds.
Answer type: Simple text answer
ANSWER: £5.80
WORKING:
Print cost = \text{Cost in pence} = 4 \times 45 + 10 \times 15=330\text{p}=£3.30
Total number of pages = 45 + 15 = 60
Cost of binding = 200 + 10 \times 5 = 250 \text{p} = £2.50
Total cost = £3.30 + £2.50 = £5.80
QUESTION 5 [3 marks]
The diagram below shows a quarter-circle with radius 4 cm
You are given that \pi = 3.14
Calculate the perimeter of the quarter-circle.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER:
WORKING:
Curved edge = \dfrac{1}{4} \times 2 \pi \times r = \dfrac{1}{4} \times 2 \times 3.14 \times 4 = 6.28 cm
Perimeter = 6.28 + 4 + 4 = 14.28 cm
QUESTION 6 – here
A high street shop records the number of days it rains in a month and the number of umbrellas they sell.
Question 6(a) [2 marks]
A scatter graph is plotted to show the relationship between the number of rainy days in a month and the number of umbrellas sold.
Choose the correct plot.
Answer type: Multiple choice type 1
A:
B:
C:
D:
ANSWER: A
Question 6(b) [1 mark]
Use the graph to estimate the number of whole umbrellas they will sell if it rains for 10 days in a month.
Answer type: Simple text answer
ANSWER: 8
QUESTION 7 [4 marks]
A castle under siege has enough food for 300 men for 90 days.
After 40 days, 150 men have left the castle.
How long would the food last at the same rate?
Answer type: Simple text answer
ANSWER: 100 days
WORKING:
300 men \times \, 90 days of food = \, 27000 days worth of food for one person
300 men \times \, 40 days of food = \, 12000 days worth of food for one person used
15000 days of food \div \, 150 men = \, 100 days worth of food left
QUESTION 8 [4 marks]
3 years ago, Rachel deposited £2200 into a savings account that pays 1.5\% compound interest per year.
Now, 3 years later, she wants to use the money in her savings account to buy a moped worth £2300
Can she afford to purchase the moped?
Answer type: Multiple choice type 1
A: Yes
B: No
ANSWER: A
WORKING:
Year 1: £2200 \times 1.105 = £2233
Year 2: £2233 \times 1.015 = £2266.495
Year 3: £2266.495 \times 1.015 = £2300.492425
Yes, she does have enough money, since she has £2300.49 (nearest penny), and she needs £2300
Question 9 [3 marks]
James wants to buy 3 pairs of shorts.
Four shops sell the shorts he wants.
Which shop provides the best value for money for 3 pairs of shorts?
Answer type: Multiple choice type 1
A: Shop A
B: Shop B
C: Shop C
D: Shop D
ANSWER: B
WORKING:
Shop A:
3 \times £15 = £45
£45 \times 0.8 = £36
Shop B:
2 \times £17.50 = £35
Shop C:
3 \times £14 = £42
£42 - £5 = £37
Shop D:
3 \times £12 = £36
Shop B provides the best value for money.
QUESTION 10 [3 marks]
Ester buys a new pair of shoes. The shoe box measures 342 mm \times \, 253 mm \times \, 121 mm.
What is the volume of the shoe box in cm^3 ?
Give your answer to the nearest whole number.
Answer type: Simple text answer
ANSWER: 10470 cm^3
WORKING:
Volume = 34.2 \times 25.3 \times 12.1 = 10470 cm^3 (nearest whole number)
QUESTION 11 [4 marks]
The following grouped frequency table shows the number of hours of vigorous exercise done by members of the general public in a week.
Estimate the mean number of hours of vigorous exercise done by members of the general public in a week.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 3.59 hours
WORKING:
Find the midpoint of each group, and write them in a new column.
Then calculate \text{frequency} \times \text{midpoint} for each group, and write them in a new column.
Then, add up the frequency column, and add up the \text{frequency} \times \text{midpoint} column.
See the table below.
Estimated mean = \dfrac{298}{82} = 3.59 hours (2 dp)
QUESTION 12 [1 mark]
The diagram shows the locations of several Towns.
Using the diagram, find the distance of Town B from Town I.
Answer type: Simple text answer
ANSWER: 30 km
QUESTION 13 [5 marks]
A runner participated in 5 runs using his old pair of trainers.
The table below shows their average speed in each run.
In the runner’s first run after using a new pair of trainers, he runs 5 km in 35 minutes and 24 seconds
1 mile =1.6 km
Calculate the percentage increase from the median speed of the 5 runs using the old trainers to the first run using the new trainers.
Give your answer to 2 decimal places.
Answer type: Simple text answer
ANSWER: 4.26 \%
WORKING:
5 km =5 \div 1.6 = 3.125 miles
35 minutes and 24 seconds = 35.4 minutes = 0.59 hours
Average speed using new trainers = 3.125 \div 0.59 = 5.29661... mph
Order the 5 runs in order of speed, from slowest to fastest
4.94, 5.03, 5.08, 5.16, 5.32
The median is the middle value, which is 5.08 mph
Percentage increase = \dfrac{5.29661... - 5.08}{5.08} \times 100 = 4.26 \%
QUESTION 14 [1 mark]
What 3D shape can be created with the net?
Answer type: Multiple choice type 1
A: Cone
B: Cylinder
C: Sphere
D: Tetrahedron
ANSWER: A
QUESTION 15 [2 marks]
Bethany hires a car for 3 days whilst on holiday.
The hire company costs €35.50 for the first day then €28.50 for each following day.
£1 = €1.25
How much does she pay in total, in pounds (£)?
Answer type: Simple text answer
ANSWER: £74
WORKING:
€35.50 + (€28.50\times2)=€92.50
92.50 \div 1.25 = £74