PAPER 1
PAPER 1A
QUESTION Write the following numbers in order of size.
3.2 \, 3.27 \, 3.72 \, 3.702 \, 3.02Start with the smallest number.
QUESTION
Work out
QUESTION
The probability of a hockey team winning a game is 0.22
The probability that they lose the game is 0.41
What is the probability that the team draws?
QUESTION
What is \dfrac{1}{20} as a percentage?
QUESTION
The distance between two towns on a map measures 8 cm.
The map has a scale of 1:25 000
What is the actual distance between the two towns in km?
QUESTION
The probability of event A happening is 0.15
Work out the probability of event A not happening.
QUESTION
Work out 6+3^2\times2
QUESTION
\dfrac{1}{2}-\dfrac{2}{5}=
Give your answer in its simplest form.
QUESTION
What is 60 as a fraction of 360? Give your answer in its simplest form.
QUESTION
Write in digits five hundred and seven thousand, seven hundred and twenty three.
QUESTION
An electric car has a range of 380 miles when fully charged.
The car has 30\% battery charge remaining.
How many more miles can the car drive before completely running out of power.
QUESTION
Plot the coordinate (4,3) on the graph below.
******************* IMAGE *******************
QUESTION
What is the value of 6ab when a=3 and b=2?
QUESTION
Calculate 6.402+3.545
QUESTION
A class of 40 students measure their shoe sizes and summarise this information in a frequency table.
******************* IMAGE *******************
What is the modal shoe size of the class?
PAPER 1B
QUESTION
Work out \dfrac{9.624+17.837}{4.5}
Give your answer as a decimal rounded to 2 decimal places.
QUESTION
What is 1 m^3 equivalent to in cm^3?
QUESTION
******************* IMAGE *******************
Which decimal describes the amount of the shape that is shaded?
QUESTION
******************* IMAGE *******************
Draw a plan view that accurately represents the 3D shape shown.
******************* IMAGE *******************
QUESTION
Peter rolls an ordinary 6 sided dice.
It has faces marked 1, 2, 3, 4, 5 and 6
Write down the probability that he rolls an even number. Give your answer as a decimal.
QUESTION
Savannah has an annual income of £19410.
She has a personal allowance of £11850. She pays 20\% tax on the rest of her income.
How much tax should she pay in a year?
QUESTION
John is paid on the first day of every month.
He aims to spend \frac{1}{3} of his pay on food and \frac{1}{4} of his pay on rent.
What fraction of his pay will John have left? Write your answer in its simplest form.
QUESTION
Wall tiles are sold either as a single tile or as a box.
******************* IMAGE *******************
Brian needs enough tiles to cover a wall of 4 \text{ m}^2.
Boxes of tiles are sold full.
Which option should he choose?
You must show all of your working.
QUESTION
******************* IMAGE *******************
Find the perimeter of the isosceles triangle.
QUESTION
Nabeel travelled to London by train, her journey was made up of two parts.
One train into York and then another train into London.
The first train departed at 07:05 and the journey lasted for 12 minutes.
The second train departed at 07:27 and the journey lasted for 122 minutes.
The total distance travelled was 197 miles.
What was Nabeela’s average speed for the entire journey in mph to 2 decimal places?
QUESTION
The diagram below shows a cylinder.
The radius of the cylinder is 3 cm and the height is 12 cm.
******************* IMAGE *******************
Find the total surface area of the cylinder. Give your answer to 2 decimal places.
QUESTION
The table gives information about the number of girls and boys in Years 9 and 10.
******************* IMAGE *******************
Complete the two-way table and hence find the probability that a student selected at random is a boy. Give your answer to 3 decimal places.
QUESTION
Lucy has £5000. She is looking for the best savings account to save her money for one year.
Bank A pays 2\% compound interest. It adds interest every 6 months.
Bank B pays 3.15\% annual interest rate.
Which bank should the Lucy choose?
Explain your decision, including calculations to support your decision.
QUESTION
A bike was reduced by 20\% in a sale.
If its sale price was £520, what was its original price?
QUESTION
Ben flips an unbiased coin 3 times.
He states he is more likely to get heads, tails, then heads than all tails for the three flips.
Is he correct? Explain your answer.
You must show use of calculations to support your explanation.
PAPER 1 ANSWERS
1A
1 – 3.02\, 3.2 \, 3.27 \, 3.702 \, 3.72
2 – 3\frac{17}{20}
3 – P (draw) = 0.37
4 – 5\%
5 – 2 km
6 – 0.85
7 – 24
8 – \frac{1}{10}
9 – \frac{1}{6}
10 – 507723
11 – 114 miles
12 – See graph below
13 – 36
14 – 9.947
15 – (size) 5
******************* IMAGE *******************
1B
1 – 6.10
2 – 1000000 cm^3
3 – 0.75
4 – \textbf{B} ******************* IMAGE *******************
5 – 0.5
6 – £1512
7 – \frac{1}{4}+\frac{1}{3}\equiv (\frac{1}{4}\times \frac{3}{3})+(\frac{1}{3}\times \frac{4}{4})=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}, 1-\frac{7}{12}=\frac{5}{12}
8 – Area single = 200 cm^3, Area box = 3200 cm^3
Area of wall = 40000 cm^3
\frac{40000}{200} = 200 tiles, \frac{40000}{3200} = 12.5 boxes = \, 13 full boxes
Single tile cost: 200 \times £0.49 = £98
Cost of the box of tiles: 13 \times £7.99 = £103.87
Single tiles are better value
9 – Perimeter = 11.5+5.6+5.6 =22.7 cm
10 – Journey = 12+10+122 = 144 minutes = \, 2.4 hours
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{197}{2.4} = 82.08 mph
11 – Area of top = \pi\times3^2=9\pi
Area of base = \pi \times 3^2=9\pi
Area of curved surface =12\times6\pi=72\pi
Surface Area = 72\pi+9\pi+9\pi =90\pi =282.74 cm^2
12 – ******************* IMAGE *******************
P(Boy) = \frac{159}{355} = 0.449
13 – Bank A — £5000 \times 1.02^2 = £5202
Bank B — £5000 \times 1.0315 = £5157.50
Lucy should choose Bank A.
14 – £520 \div 0.8 = £650
15 – P(H,T,H)= 0.5 \times 0.5 \times 0.5=0.125
P(T,T,T)= 0.5 times 0.5 \times 0.5=0.125
or some calculation of the event probabilities.
Ben is incorrect, likelihood of both events is equal.
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PAPER 2
PAPER 2A
QUESTION
Write the numbers in increasing order starting with the smallest.
QUESTION
Work out 600+1200\div300
QUESTION
What is 30 as a fraction of 360? Give your answer in its simplest form.
QUESTION
Work out 7+4^2\times3
QUESTION
******************* IMAGE *******************
Describe the nature of the correlation shown in the scatter graph.
QUESTION
******************* IMAGE *******************
Draw the plan of the 3D shape.
******************* IMAGE *******************
QUESTION
Here are the ages of 9 children at a birthday party.
9, 10, 12, 13, 10, 11, 14, 10, 12
Find the mode.
QUESTION
Calculate 5.402-3.215
QUESTION
What is 1.5 hours equivalent to in seconds?
QUESTION
What is 2.5\% of 140 g?
QUESTION
******************* IMAGE *******************
What 3D shape can be created with the net shown?
QUESTION
What is \dfrac{5}{7}-\dfrac{1}{3}?
QUESTION
The mean of 3 numbers is the same as the median.
The range of the numbers is also the same as the median.
The largest of the numbers is 9.
What are the other 2 numbers?
QUESTION
How long would it take you to travel 3 kilometres, if you walked at 6 km/h?
Give your answer in minutes.
QUESTION
Plot the coordinate (6,8) on the graph below.
******************* IMAGE *******************
PAPER 2B
QUESTION
What is the number in the tens position in 825.217?
QUESTION
What is 48000 cm equivalent to in km?
QUESTION
What is 18\% of £25000?
QUESTION
******************* IMAGE *******************
Find the missing angle labelled A
QUESTION
Calculate (3y^2 + 4y^2) - 2y \times 5y when y = 3
QUESTION
Megan is a florist.
She is arranging flowers for a display and has 16 roses, 8 daffodils and 13 tulips.
What is the probability of Megan randomly selecting a tulip to add to the display next?
Give your answer to three decimal places.
QUESTION
******************* IMAGE *******************
Using the diagram, find the distance of Flamborough from Aberdeen in km.
QUESTION
Three shops sell three different sized bottles of water.
Amazer shop sells water in 1 L bottles
Best-Value sells water in 50 cl bottles
Cheapest Buy sells 750 ml bottles of water
******************* IMAGE *******************
Using the three statements above, work out who got the cheapest water per millilitre.
You Must show clearly how you got your answer.
QUESTION
The diagram below shows a sphere.
The radius of the sphere is 5 cm.
******************* IMAGE *******************
Using the equation A= 4\pi r^2, calculate the surface area of the sphere.
Give your answer to 2 decimal places.
QUESTION
A water tank starts to leak so that 5\% of the water is lost every minute.
Given that the water tank was full to start with, what percentage of water is left in the tank after 11 minutes?
Give your answer to 2 decimal places
QUESTION
Sarah has a box of 20 sweets. 8 are strawberry flavour, 7 are fizzy cola flavour and the rest are blueberry flavour.
What is the probability of Sarah randomly selecting a blueberry flavour sweet from the box?
Give your answer as a fraction in its simplest form.
QUESTION
23 boys and 22 girls take a maths test.
The mean mark for the boys was 44. The mean mark for the girls was 42.
Find the mean mark for all 45 students.
Give your answer to 1 decimal place.
QUESTION
It takes 22 hours for a hosepipe with a flow of 12 litres per minute to fill a swimming pool.
How long will it take if its flow is reduced to 5 litres per minute?
QUESTION
Last year Robert had two jobs. Robert worked:
in an office for 10 months and earned £1500 per month,
at a cafe for 15 weekends and earned £50/latex] per weekend.</p> <p>What fraction of his total income last year came from his work at the cafe?</p> <p>Write the fraction in its simplest form.</p> <p>QUESTION</p> <p>The table gives information about the types of drinks sold at a local cafe over the weekend.</p> <p>******************* IMAGE *******************</p> <p>Complete the two-way table and find the probability that a customer both enters the cafe on a Saturday and orders a coffee to [latex]2 decimal places.
PAPER 2 ANSWERS
2A
1 - 10001,\,\,\,\, 10010,\,\,\,\, 11010, \,\,\,\, 11011, \,\,\,\, 11100
2 - 6
3 - \frac{1}{12}
4 - 55
5 - No correlation
6 - ******************* IMAGE *******************
7 - 10
8 - 2.187
9 - 5400 seconds
10 - 3.5 g
11 - Cube
12 - \frac{8}{21}
13 - 3 and 6
14 - time = 3 \div 6=0.5 hours = \, 30 minutes
15 - see graph below
******************* IMAGE *******************
2B
1 - 2
2 - 0.48 km
3 - £4500
4 - 92\degree
5 - -27
6 - \frac{13}{16+8+13} = 0.351
7 - \sqrt{50^2+110^2} = \sqrt{2500 + 12100} = \sqrt{14600} = 120.8 km
8 - Jack: 4A + 5B +9C = 8.96
(4 \times 1) + (5 \times 0.5) + (9 \times 0.750) = 13.25 litres
\frac{8.96}{13.25} = £0.676 per litre
Sophie: 8A + 10B = 8.92
(8 \times 1) + (10 \times 0.5) = 13 litres
\frac{8.92}{13} = £0.686 per litre
Kabiria: 9A + 9B + 5C = 11.77
(9 \times 1) + (9 \times 0.5) + (5 \times 0.750) = 17.25 litres
\frac{11.77}{17.25} = £0.682 per litre
Jack bought the cheapest water per millilitre.
9 - 4\times \pi \times 5^2=100\pi= 314.16 cm^2
10 - (1-\frac{5}{100})^{11} = 56.88\%
11 - \frac{5}{20} = \frac{1}{4}
12 - Total marks for boys = 1012
Total mark for girls = 924
Mean = (1012 + 924) \div 45 = 1936 \div 45 = 43.0
13 - 22 hrs \times \, 720 litres per hr = \, 15840 litres needed
15840 litres \div \, 300 litres per hr = \, 52.8 hrs
14 - Total income = £15750, \frac{750}{15750} = \frac{1}{21}
15 - ******************* IMAGE *******************
P(Coffee on Saturday) = \frac{104}{387}= 0.27
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PAPER 3
PAPER 3A
QUESTION
Work out 24-3^2\times2
QUESTION
Calculate the following: 0.7^2
QUESTION
Estimate 3.9 \times 11.1
QUESTION
What is \dfrac{8}{7} + \dfrac{6}{4}?
Give your answer as an improper fraction.
QUESTION
Find the median of the following set of values
QUESTION
What is Laura’s average speed if she travels 126 miles in 2 hours?
QUESTION
******************* IMAGE *******************
Describe the nature of the correlation shown in the scatter graph.
Answer type: Multiple choice type 1
A:
Strong positive correlation
B:
Strong negative correlation
C:
Weak positive correlation
D:
No correlation
QUESTION
What is \dfrac{3}{4} as a percentage?
QUESTION
What is the value of 2a^2b when a=4 and b=0.5
QUESTION
The probabilities of a spinner landing on each of its three colours are shown in the table below.
******************* IMAGE *******************
One is missing.
Complete the table below giving your answer as a fraction in its simplest form.
QUESTION
What is the decimal equivalent to 78.5\% ?
QUESTION
What is 0.1 \text{ cm}^2 equivalent to in \text{mm}^2 ?
Answer type: Multiple choice type 1
A: 0.01 \text{ mm}^2
B: 1 \text{ mm}^2
C: 10 \text{ mm}^2
D: 100 \text{ mm}^2
QUESTION
What is 1\dfrac{3}{5} + 2\dfrac{1}{4} ?
Give your answer as an improper fraction.
QUESTION
******************* IMAGE *******************
What is the name of the 3D shape can be created with the net shown?
QUESTION
What is 25\% of 24 seconds?
PAPER 3B
QUESTION
Write the number 1854 in words.
QUESTION
Which of the following, results in the largest answer:
0.1 \times 0.2, 1 \times 0.2, 2.1 \times 1.2, 1.1 \times 2.1
QUESTION
A football club sells 50 blue raffle tickets and 125 yellow raffle tickets.
Tickets are drawn randomly.
What is the probability that the first ticket drawn will be a blue ticket?
Give your answer as a decimal rounded to 3 decimal places.
QUESTION
A sofa in a 25\% off sale costs £330
How much does it normally cost?
QUESTION
Sarah is saving a portion of her pocket money each month.
In March she saves £9.39
In April she saves £12.02
In May she saves £14.88
Work out how much she has saved in total over the three months.
QUESTION
The passenger list on a cruise ship shows that:
\dfrac{1}{10} of the passengers come from Italy.
\dfrac{1}{4} of the passengers come from Sweden.
And 520 passengers come from the UK.
How many passengers are there all together?
QUESTION
The diagram shows the floor plan to a storeroom.
The owner has ordered 14 items that each need at least 200 cm^2 of room.
CD = 15 cm, CA=45 cm, AB=100 cm, FE=15 cm, EB=10 cm
******************* IMAGE *******************
Is there enough room in the storeroom for all the items?
You must show your working.
QUESTION
The height of 13 students are listed below.
141 cm, 130 cm, 135/latex] cm, [latex]144 cm, 130 cm, 152 cm, 145 cm,
140 cm, 153 cm, 160 cm, 180 cm, 120 cm, 134 cm
Find the mean of the students heights, giving your answer to 3 significant figures.
QUESTION
This is a conversion graph between litres and pints.
******************* IMAGE *******************
Using the conversion graph, what is 4 pints in litres?
QUESTION
Harry invests £4000 in a fund which earns 1.1\% compound return per year.
How much would the fund be worth after 10 years, given that you removed half of the balance after 5 years?
QUESTION
Leslie is mixing paint to get a specific shade of purple.
He needs to make up 3 tins each of 1.5 L of paint.
To make the colour he mixes blue, red and white paint in the ratio 4 : 2 : 3
How much blue paint does Leslie need to complete the order?
QUESTION
Part of a circle is attached to a right angle triangle shown below.
CD = 6 cm,
CB = 12 cm,
AB = 13.4 cm.
******************* IMAGE *******************
Find the perimeter of the shape.
Give your answer to 2 decimal places.
QUESTION
******************* IMAGE *******************
Draw a line of best fit for the scatter graph.
Hence, estimate the Maths score for a student who studied for 8 hours.
QUESTION
Ben has 450 songs in his playlist.
\dfrac{2}{3} of the songs are pop songs.
\dfrac{1}{4} of these pop songs are also in the genre indie pop.
How many indie pop songs does Ben have in his playlist?
QUESTION
Find the mode and range of the following list of numbers.
280,\, 350,\, 320,\, 400,\, 350,\, 490,\, 590,\, 470,\, 280,\, 410,\, 350PAPER 3 ANSWERS
3A
1 - 6
2 - 0.49
3 - 40
4 - \frac{37}{14}
5 - 57
6 - average speed = 126 \div 2 = 63 mph
7 - 10
8 - 75\%
9 - 16
10 - \frac{1}{2}
11 - 0.785
12 - 10 mm^2
13 - \frac{77}{20}
14 - Cube
15 - 6 seconds
******************* IMAGE *******************
3B
1 - One thousand, eight hundred and fifty four.
2 - 2.1 \times 1.2
3 - \frac{50}{50+125} = 0.286
4 - £330 \div 0.75 = £440
5 - £36.29
6 - 1-\frac{4}{40}-\frac{10}{40}=\frac{26}{40} from the UK, \frac{26}{40} = \frac{520}{800}
So there is a total of 800 passengers all together
7 - 45\times 15=675[latex] cm[latex]^2
\frac{1}{2}\times 70\times 35=1225 cm^2
85\times 10=850 cm^2
Total area =1225+675+850=2750 cm^2
Total area required =14\times200=2800 cm^2
There is not enough space in the storeroom.
8 - Mean = \frac{1864}{13} = 143 cm (3 sf)
9 - 4 \text{ pints} \approx 2.3 \text{ litres}
10 - 4000\times (1 +\frac{1.1}{100})^5 =4224.893533
4224.893533 \div 2 = 2112.446767 2112.446767 \times (1+\frac{1.1}{100})^5 = £ 2231.2211 - 4.5 \div 9 = 0.5 L
0.5 \times 4 = 2 L of blue paint.
12 - Perimeter =12+13.4+6+(\frac{1}{4} \times 2\pi \times 6) =31.4+3\pi=40.82 cm
13 - 85\pm2\%
See graph on previous page
14 - \frac{2}{3} \times 450 = 300 pop songs
\frac{1}{4} \times 300 = 75 indie pop songs
15 - \text{mode} = 350;
\text{range} = 590-280=310
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PAPER 4
PAPER 4A
QUESTION
Work out 16-2^2\times3
QUESTION
Find 56\% of £8200
QUESTION
Work out 2(18\div3)^2
QUESTION
What is 3\dfrac{1}{2} - 2\dfrac{1}{4}?
Give your answer as an improper fraction.
QUESTION
******************* IMAGE *******************
What 3D shape can be created with this net?
QUESTION
What is 0.035 meters equivalent to in cm?
QUESTION
******************* IMAGE *******************
Plot the coordinate (2,10) on the graph below.
QUESTION
The probability of event A not happening is 0.35
Work out the probability of event A happening.
QUESTION
Work out the percentage decrease from 6750 to 5400
QUESTION
******************* IMAGE *******************
Find the missing angle labelled A.
QUESTION
Calculate 8-2.285
QUESTION
What is 1\dfrac{1}{3} of 360?
QUESTION
Calculate the time it took to walk 5 miles if traveling at 2.5 mph.
QUESTION
Find the median of the following set of values
-12 \,\, -4 \,\, 7 \,\, 16 \,\, 26 \,\, -18 \,\, 2QUESTION
Arrange these temperatures in order, from lowest to highest
-4\degree C,\,\,\,\, -9\degree C,\,\,\,\, 1\degree C, \,\,\,\, -2\degree C, \,\,\,\, 3\degree CPAPER 4B
QUESTION
What is the value of \dfrac{8a}{2b} when a=2 and b=4?
QUESTION
******************* IMAGE *******************
Draw the plan view that accurately represents the 3D shape shown.
******************* IMAGE *******************
QUESTION
******************* IMAGE *******************
How would you describe the correlation of the data shown in the scatter graph?
QUESTION
Write the numbers in increasing order starting with the smallest.
QUESTION
Rory has a box of pens. 8 of the pens are black, 12 are blue and 10 are green.
What is the probability of Rory randomly selecting a blue pen from the box?
Give your answer as a decimal.
QUESTION
Trihao is driving from Cambridge to London.
Assume the distance between Cambridge and London is 100 km.
Given that Trihao drives at an average speed of 80 km/h, work out his journey time.
Give your answer in minutes.
QUESTION
A gardener is planning a new garden that is in the shape of a parallelogram.
It features two ponds and a flower bed.
The rest of the space will be filled with grass.
The plan of the garden has been drawn to scale on a 1 cm grid labelled below.
Scale: 1 cm = 5 m
******************* IMAGE *******************
Calculate the area that will be covered with grass.
Give your answer to 2 decimal places.
QUESTION
Margherita pizza comes in three different sizes and at three different prices.
******************* IMAGE *******************
Work out which pizza is the best value for money.
You must show clearly how you got your answer.
QUESTION
A car has a range of 440 miles on a full tank. The tank holds 60 litres.
The fuel gauge on the car shows that there is 24 litres remaining in the tank.
How many more miles can the car drive before completely running out of fuel?
QUESTION
A steel rod is in the shape of a cylinder, shown below.
The steel rod has a density of 9.8 g per cm^3.
The rod has a volume of 60 cm^3.
******************* IMAGE *******************
Find the mass of the rod.
QUESTION
Work out 1.06 \text{ million} \div 4.2 \text{ thousand} to 2 decimal places.
QUESTION
The diagram shows a plan of some cardboard packaging.
******************* IMAGE *******************
Calculate the total area of the cardboard used.
QUESTION
A car depreciates at a rate of 12\% per year.
Now 2 years old the value off the car is £12235.52
Work out the original value of the car.
QUESTION
A school is investigating how much their students use social media.
They give their results, measured in minutes, in the table.
******************* IMAGE *******************
By calculating means, work out the difference in the average times spent on Facebook and Twitter.
QUESTION
Three friends flip the same biased coin several times.
Their results are shown in the table below.
******************* IMAGE *******************
Each of the friends calculates their own probability of heads.
State which friend is likely to have the probability closest to the true probability.
You must explain your answer.
PAPER 4 ANSWERS
4A
1 - 4
2 - £4592
3 - 72
4 - \frac{5}{4}
5 - Square-based pyramid
6 - 3.5 cm
7 - See graph below
8 - 0.65
9 - 20\%
10 - 114\degree
11 - 5.715
12 - 480
13 - \text{Time} =\frac{(5)}{(2.5)}=\frac{10}{5}=2 hours
14 - 2
15 - -9\degree C ,\,\,\,\, -4\degree C ,\,\,\,\, -2\degree C , \,\,\,\, 1\degree C , \,\,\,\, 3\degree C
******************* IMAGE *******************
4B
1 - 2
2 - ******************* IMAGE *******************
3 - There is a strong positive correlation between the number of cinema visits and the year.
4 - 5.01, \,\,\,\, 5.11, \,\,\,\, 5.131, \,\,\,\, 5.855, \,\,\,\, 5.9
5 - 0.4
6 - \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{100}{80} = 1.25 hours = \, 75 minutes
7 - Total area = base \times height =50\times 30=1500 m^2
Flower bed area = \frac{(15+5)}{2} \times 30=300 m^2
Pond area = \frac{1}{2}\times \pi r^2=50\pi[latex] m[latex]^2[latex]</p> <p>Pond area [latex]= \frac{1}{2} \times \pi r^2=50\pi[latex] m[latex]^2[latex]</p> <p>Grass area [latex]= 1500-300-50\pi-50\pi=885.84[latex] m[latex]^2[latex]</p> <p>8 - Small area = [latex]16\pi inches^2
Medium area = 25\pi inches^2
Large area = 36\pi inches^2
Small = \dfrac{799}{16} = 49.94p
Medium = \dfrac{999}{25} = 39.96p
Large = \dfrac{1299}{36} = 36.08p ; Large is the best value
9 - \frac{24}{60} \times 440 = 176 miles
10 - \text{Mass} = \text{D} \times \text{V} = (9.8 g/cm^3) \times (60 cm^3) =588 g
11 - 252.38
12 - Rectangle ABCD : Area =5\times7=35[latex] cm[latex]^2[latex]</p> <p>Rectangle [latex]CEFG : Area =6\times9=54[latex] cm[latex]^2[latex]</p> <p>Triangle [latex]DCG : Area = \frac{1}{2} \times 5\times9=22.5[latex] cm[latex]^2[latex]</p> <p>Total Area = [latex]35+54+22.5=111.5[latex] cm[latex]^2[latex]</p> <p>13 - [latex]12235.52 = x \times 0.88^2
x = 12235.52 \div 0.88^2 = £1580014 - Facebook Mean = 463 \div 5 = 92 minutes 36 seconds
Twitter Mean = 480 \div 5 = 96 minutes
Difference = 3 minutes 24 seconds
15 - Sonya is most likely to be the closest to the true probability because she did the most trials (120)
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PAPER 5
PAPER 5A
QUESTION
Write the numbers in increasing order starting with the smallest.
QUESTION
What is the decimal equivalent to 45.5\% ?
QUESTION
Work out (16-3\times4)^2
QUESTION
What is \dfrac{11}{4} - \dfrac{3}{2}
Give your answer as an improper fraction.
QUESTION
******************* IMAGE *******************
Find the missing angle labelled x.
QUESTION
******************* IMAGE *******************
Describe the nature of the correlation shown in the following scatter graph.
QUESTION
Given that 28\times1356= 37968
Calculate the following: 37.968 \div 2.8
QUESTION
Write the number 160251 in words.
QUESTION
Work out 200\times60\div12
QUESTION
******************* IMAGE *******************
Draw the plan view that accurately represents the 3D shape shown.
******************* IMAGE *******************
QUESTION
Here are the ages of 9 children at a birthday party:
9 10 12 13 10 11 14 10 12
Find the median.
QUESTION
What is 104 mm equivalent to in meters?
Answer type: Multiple choice type 1
A: 10.4 m
B: 1.04 m
C: 0.104 m
D: 0.0104 m
QUESTION
What is the value of 11ab^2 when a=\dfrac{1}{4} and b=2?
QUESTION
Harry is 15 minutes late for a film that is two hours long.
What fraction of the film does he miss? Give your answer in its simplest form.
QUESTION
Work out the percentage decrease from 1250 to 1100
PAPER 5B
QUESTION
What is \dfrac{13}{20} as a percentage?
QUESTION
Plot the coordinate (8,2) on the graph below.
******************* IMAGE *******************
QUESTION
Wayde van Niekerk set the world record for the 400 m with a time of 43 seconds.
Determine his average speed over the course of the race.
QUESTION
What is 75\% of 8 miles?
QUESTION
What is \dfrac{3}{79} as a decimal correct to three decimal places?
QUESTION
The time taken to build a house is inversely proportional to the number of builders.
If there are 6 builders, it takes 80 days to complete the house.
How many builders must be employed to build the house in just 16 days?
QUESTION
Sugar can be purchased from four different shops.
******************* IMAGE *******************
Work out which shop provides the best value per gram of sugar.
You must show your working.
QUESTION
In 2016, there were 10000 electric cars in the United Kingdom.
In 2019, there were 150000 electric cars.
The percentage increase of electric cars, year on year is the same.
Assuming the percentage increase remains the same, how many electric cars would you expect there to be in 2021?
QUESTION
Laura earns £200 per week. She is given a pay rise equal to \dfrac{2}{5} of her weekly income.
Work out her new weekly income.
QUESTION
Work out \dfrac{9.624+\sqrt{17.837}}{45-4.5}
Write down all the digits on your calculator display.
QUESTION
******************* IMAGE *******************
Find the missing angle labelled x in the regular polygon.
QUESTION
******************* IMAGE *******************
Using the diagram, find the distance of Birmingham from Durham to the nearest km.
QUESTION
300 students are asked to choose between strawberry and chocolate ice-cream.
54\% of the students picked chocolate.
48\% of the students are girls.
26\% of the students are girls who chose chocolate.
******************* IMAGE *******************
Work out the number of boys who selected strawberry.
QUESTION
A multivitamin contains 16.2 mg of vitamin C. This is 24\% of the recommended daily intake.
What daily intake of vitamin C is recommended?
Give your answer in milligrams.
QUESTION
A shape is made from a cylinder of radius 5 cm and height 4 cm.
A cuboid measuring 6 cm wide, 1 cm long and 4 cm deep is cut out of the center as shown.
******************* IMAGE *******************
Calculate the surface area of the new shaped formed by removing the cuboid.
Give your answer as a decimal to 2 decimal places.
PAPER 5 ANSWERS
5A
1 - -15,\,\,\,\, -5,\,\,\,\, 5, \,\,\,\, 25, \,\,\,\, 35
2 - 0.455
3 - 16
4 - \frac{5}{4}[latex]</p> <p>5 - [latex]45\degree
6 - No correlation
7 - 13.56
8 - One hundred and sixty thousand, two hundred and fifty one.
9 - 1000
10 - ******************* IMAGE *******************
11 - 11
12 - 0.104 m
13 - 11
14 - \frac{1}{8} of the film
15 - 12\%
******************* IMAGE *******************
5B
1 - 65\%
2 - See graph
3 - \text{speed}=\frac{\text{distance}}{\text{time}}=\frac{400}{43}=9.3 m/s
4 - 6 miles
5 - 0.038
6 - 6 builders \times 80 days = \, 480 work days in total
480 \div 16 = 30 people
7 - Shop A = \dfrac{79}{500} = 0.158p per gram
Shop B = 0.158p per gram
Shop C = 0.099p per gram
Shop D = \dfrac{129}{1250} = 0.1032p per gram
Shop C is the cheapest
8 - Identifying 3 years,
10000 \times r^3 =150000
r^3=15 , r=2.47
10000\times 2.47^5=919358 , (Accept 912330)
9 - \frac{2}{5} of £200 = £80
£200 + £80 = £280
10 - 0.3419107967
11 - 135\degree
12 - 228 km
13 - The number of boys who selected Strawberry is 72
14 - 16.2 \div 0.24 = 67.5 mg
15 - Surface area of cylinder = 2 \pi r^2 + 2 \pi rh
2 \times \pi \times 5^2 + 2 \times \pi \times 5 \times 4 = 90 \piSurface area of cylinder – 2 cuboid faces:
90\pi -(2\times6\times1)=270.7433Inside faces: 6\times4\times2 =48, 4\times1\times2=8
Total: 270.7433+48+8=326.74 cm^2
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PAPER 6
PAPER 6A
QUESTION
Fifty students were asked how many books they each took to school on Monday.
The results are summarized in the table below.
******************* IMAGE *******************
QUESTION
Evaluate [(3^3 - 2^3 )+5]\div6
QUESTION
What is 12\% of 600 GB?
QUESTION
What is \, 5\dfrac{1}{4} - 1\dfrac{1}{5} ?
Give your answer as a mixed number fraction.
QUESTION
This is a conversion graph between litres and pints.
******************* IMAGE *******************
Using the conversion graph, what is 5 litres in pints?
QUESTION
What is 60\times400\div30 ?
QUESTION
Write the numbers in increasing order starting with the smallest.
1.101, \,\,\,\, 0.11, \,\,\,\, 1.10, \,\,\,\, 0.01QUESTION
Express 0.125 as a fraction in its simplest form.
QUESTION
******************* IMAGE *******************
What 3D shape can be created with the 2D net as shown above?
QUESTION
Write the number 58051 in words.
QUESTION
Calculate 106.284-38.691
QUESTION
If 60 g of sweets cost £1.10, find the cost of 300 g of sweets.
QUESTION
Rory has a box of pens. 8 of the pens are black, 12 are blue and 10 are green.
What is the probability of Rory randomly selecting a black pen from the box?
Give your answer as a fraction in its simplest form.
QUESTION
What is 3.5 m^2 equivalent to in cm^2 ?
QUESTION
What is the value of 12a-5ab when a=3 and b=4?
PAPER 6B
QUESTION
Write the numbers in increasing order starting with the smallest.
QUESTION
Work out 2.5^2-2.1^2
QUESTION
******************* IMAGE *******************
Which of the following plan views accurately represents the 3D shapes shown?
Answer type: Multiple choice type 1
A: ******************* IMAGE *******************
B: ******************* IMAGE *******************
C: ******************* IMAGE *******************
QUESTION
Work out the percentage increase from 1250 to 1750
QUESTION
What is \, \dfrac{11}{3} - \dfrac{7}{6} ?
Give your answer as an improper fraction.
QUESTION
Dani recorded the heights of members of her extended family, to the nearest cm :
163, 185, 164, 170, 188, 154, 168, 179Find the median of their heights.
QUESTION
The following grouped frequency table shows the time taken (in minutes) by a class of students to complete a 1500 m race.
******************* IMAGE *******************
Estimate the mean time it took students to complete the distance.
Give your answer to 2 decimal places.
QUESTION
A conservation group try to estimate the population of different types of trees that are found in a nearby forest:
\dfrac{1}{18} of the trees are oak
\dfrac{2}{9} of the trees are beech
and \dfrac{1}{4} of the trees are pine.
What fraction of the trees in the forest are not oak, beech or pine?
QUESTION
Work out \sqrt{\dfrac{148.221-28.837}{81}}
Give your answer as a decimal rounded to 3 decimal places.
QUESTION
Anna needs to be at the museum for the open evening at 18.00 h.
She will walk to the museum from the bus depot at a speed of 3 mph.
To arrive at the bus depot she will catch the bus at the stop from near her house. The bus travels at an average speed of 25 mph.
On the walk from her house to the bus stop, she will average a speed of 6 mph.
The bus depot is 0.7 miles from the museum.
The bus journey from the bus stop to bus depot is 2.2 miles.
The walk from her house to the bus stop is 0.3 miles.
Buses leave the bus stop at 15 minute intervals starting from 07:00 h.
What is the latest bus Anna can catch and still arrive at the museum on time?
QUESTION
In the diagram the combined area of triangles ACB and FDE are equal to the area of the parallelogram BCDF.
CD = x, DE = x, FE = 2 cm
******************* IMAGE *******************
Find the value of x.
QUESTION
Katie completes two events at her school sports day, hurdles and javelin.
******************* IMAGE *******************
Complete the probability tree and calculate the probability that Katie wins one event and loses the other.
QUESTION
A grain of rice weighs approximately 0.015 g
Work out how many grains of rice are in a 600 g bag of rice.
QUESTION
A plane flies between two airports that are 7130 km apart.
Given that the plane travels at a constant speed of 920 km/h, determine the time the journey took in hours and minutes.
QUESTION
32\% of people voted for the green party in a local election.
What fraction of people voted for the green party?
Write the fraction in its simplest form.
PAPER 6 ANSWERS
6A
1 - 2 books
2 - 4
3 - 72 GB
4 - 4\frac{1}{20}
5 - 5 \text{ litres} \approx 8.7 \text{ pints}
6 - 800
7 - 0.01, \,\,\,\, 0.11, \,\,\,\, 1.10, \,\,\,\, 1.101
8 - \frac{1}{8}
9 - Triangular Prism
10 - Fifty eight thousand and fifty one.
11 - 67.593
12 - \frac{1.10}{60} \times 300 = £5.50
13 - \frac{4}{15}
14 - 35000 cm^2
15 - -24
******************* IMAGE *******************
6B
1 - 947,\,\,\,\, 968,\,\,\,\, 989, \,\,\,\, 993, \,\,\,\, 998
2 - 1.84
3 - \textbf{C}
4 - 40\% (accept 140\%)
5 - \frac{5}{2}
6 - \frac{8 + 1}{2}=4.5;
The 4th value is 168 and the 5th value is 170, so the median is 169
7 - Estimated mean = \frac{373}{45}= 8.29 minutes
(See table)
8 - \frac{2}{36} + \frac{8}{36} + \frac{9}{36} = \frac{19}{36}, 1-\frac{19}{36}=\frac{17}{36}
9 - 1.214
10 - Walk from the depot to the museum:
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{0.7}{3} = 0.23 hours = \, 14 minutes
Bus journey:
\text{Time} = \frac{2.2}{25} = 0.088 hours = \, 5 minutes
Walk from her house to the bus stop: \text{Time} = \frac{0.3}{6} = 0.05 hours = \, 3 minutes
22 minutes journey time. Subtracting this from 18:00 gives 17:38 but, because the buses go every 15 minutes, the last bus she can get is 17:30
11 - Area of Triangles ACB and DFE
Putting the triangles together makes a rectangle with sides 2 and x
Area of triangles together =2\times x=2x
Area of Parallelogram =x\times x=x^2
x^2=2x x^2-2x=0 x(x-2)=0x=0 or x=2
x=212 - 0.6 \times 0.5 = 0.3
0.4 \times 0.4 = 0.16 0.16 + 0.3 = 0.4613 - 600 \div 0.015 = 40000 grains
14 - \text{time }=\frac{\text{distance}}{\text{speed}}=\frac{7130}{920}=7.75 hours
So, we have 7 hours and 0.75 hours ( 7 hours and 45 minutes)
15 - \frac{8}{25}
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PAPER 7
PAPER 7A
QUESTION
What is \dfrac{1}{3} as a percentage?
Give your answer rounded to two decimal places.
QUESTION
Estimate 2001 \times 31.01
QUESTION
What is 48000 cm equivalent to in km?
QUESTION
It takes 4 people 2 hours to tidy a house.
How long would it take if 8 people volunteered to tidy the same house?
QUESTION
Calculate the distance travelled by a family of 5 who have driven for 5 hours at a speed of 34 mph.
QUESTION
What is \dfrac{4}{5}[latex] of [latex]240?
Answer type: Multiple choice type 1
A:
180
B:
192
C:
204
D:
208
QUESTION
******************* IMAGE *******************
Draw the side elevation of the 3D shape shown.
******************* IMAGE *******************
QUESTION
Write the numbers in increasing order starting with the smallest.
1.045, \,\,\,\, 1.445, \,\,\,\, 4.115, \,\,\,\, 5.411, \,\,\,\, 0.1445QUESTION
Find the median of the following set of values
52 \,\, 71 \,\, 102 \,\, 194 \,\, 197 \,\, 22 \,\, 55QUESTION
Calculate the following:
(7+5)^2\div6^2-1QUESTION
Plot the coordinate (6,7) on the graph below.
******************* IMAGE *******************
QUESTION
A car hire firm charges a fixed £50 fee then charges per mile driven.
******************* IMAGE *******************
Using the conversion graph, how much would it cost to drive 125 miles?
QUESTION
What is 5\dfrac{3}{4} + 2\dfrac{1}{2} ?
Give your answer as a mixed number fraction.
QUESTION
Work out 400+1800\div30
QUESTION
The 2D shape in the diagram is a regular polygon.
******************* IMAGE *******************
Find the two missing angles labelled x and y.
PAPER 7B
QUESTION
Megan is a florist. She is arranging flowers for a display and has 16 roses, 8 daffodils and 13 tulips.
What is the probability of Megan randomly selecting a rose?
Give your answer to three decimal places.
QUESTION
******************* IMAGE *******************
What 3D shape can be created with the net shown above?
QUESTION
A protein bar weighs 110 g
Its ingredients list the bar being 25\% protein
How many grams of protein are there in a bar?
QUESTION
Write the numbers in increasing order starting with the smallest.
341,\,\,\,\, 311,\,\,\,\, 376, \,\,\,\, 351, \,\,\,\, 308QUESTION
Write in digits ninety four thousand, one hundred and nineteen.
QUESTION
A rectangular field is measured to be \dfrac{9}{4} km by \dfrac{11}{8} km.
What is the perimeter of the field?
Give your answer as a mixed number fraction.
QUESTION
A group of students were asked how many brothers and sisters they had. Their answers are recorded in the table below.
******************* IMAGE *******************
If a student is chosen at random, find the probability that there are 3 children in that student's family.
Give your answer as a fraction in its simplest form.
QUESTION
The number of bacteria in a petri dish grew exponentially. There were 500 in the original bacterial population. After 5 hours, the number increased to 121 500
Calculate how many bacteria there were after 8 hours.
QUESTION
******************* IMAGE *******************
Circle two of the four shapes, which have the same area.
You must show your working.
QUESTION
Mrs Smith travels on Plane M, which flies at an average speed of 825 km/h for 7 hours and 24 minutes from Location A to Location B.
She then waits at Location B for 2 hours and 11 minutes, before flying to Location C on Plane N, which flies at an average speed of 722 km/h for 4 hours and 48 minutes.
Both planes fly in a straight line to their respective destinations.
What is the total distance of her journey in km to 1 decimal place?
QUESTION
108 identical textbooks have a mass of 30 kg
Find the mass of 270 books.
QUESTION
Grayson Academy can choose from two suppliers when buying scissors.
******************* IMAGE *******************
The academy intends to purchase 250 scissors.
Which supplier is the better value for money?
You must show clearly how you got your answer.
QUESTION
Thomas is 54 years old. His eldest son is \dfrac{1}{2} is age. His youngest son is \dfrac{1}{3} of his age.
Work out the age difference between his oldest and youngest son.
QUESTION
The price of a local football club season tickets increased by 4\%.
The new price of a season ticket is £98.80
What was the price before this increase?
QUESTION
100 students in grade 11 either study French or German or Italian.
47 of the students are girls while the rest are boys.
12 girls study French. 15 girls and 17 boys study German.
A total of 30 students study Italian.
******************* IMAGE *******************
Work out how many boys study Italian.
PAPER 7 ANSWERS
7A
1 - 33.33\%
2 - 2000 \times 30 = 60000
3 - 0.48 km
4 - 4 people \times \, 2 hours = \, 8 hours of work total
1 hour each for 8 people
5 - 34\times 5=170 miles.
6 - 192
7 - See side elevation
8 - 0.1445, \,\,\,\, 1.045, \,\,\,\, 1.445, \,\,\,\, 4.115, \,\,\,\, 5.411
9 - 71
10 - 3
11 - See graph
12 - 125 \text{ miles} \approx £100
13 - 8\frac{1}{4}
14 - 460
15 - x=72\degree, y=108\degree
******************* IMAGE *******************
******************* IMAGE *******************
******************* IMAGE *******************
7B
1 - \frac{16}{16+8+13} = 0.432
2 - Cube
3 - 27.5 g
4 - 308,\,\,\,\, 311,\,\,\,\, 341, \,\,\,\, 351, \,\,\,\, 376
5 - 94119
6 - \frac{9}{4} + \frac{9}{4} + \frac{11}{8}+ \frac{11}{8} = \frac{58}{8} , Perimeter = 7\frac{1}{4} km
7 - No. of siblings = 2 , No. of students = 8/latex]</p>
<p>Probability = [latex]\frac{8}{30}
= \frac{4}{15}
8 - 121500 \div 500 = 243 , \sqrt[5]{243}=3
500 \times 3^8 = 32805009 - Shape A = \pi r^2=9\pi=28.27[latex] cm[latex]^2
Shape B = \text{base} \times \text{height}=27[latex] cm[latex]^2
Shape C = \frac{(\text{top} + \text{bottom})}{2} \times \text{height}=27[latex] cm[latex]^2
Shape D = 23[latex] cm[latex]^2
B and C are have the same area
10 - A to B: \text{Distance} = \text{S} \times \text{T} = 825 \times 7.4 = 6105 km
B to C: \text{Distance} = 722 \times 4.8 = 3465.6 km
Total distance: 6105 + 3465.6 = 9570.6 km
11 - \frac{30}{108} \times 270 = 75 kg
12 - Desk = \dfrac{250}{4} = 62.5 packs = \, 63 packs
63 \times £9.95 + £4.95 = £626.85 + £4.95 = £631.80Delaware = \dfrac{250}{2} = 125 packs
125 \times £4.99 + £2.99 = £623.75 + £2.99 = £626.74Delware Resources is the best buy.
13 - 27-18=9 years difference
14 - £98.80 \div 1.04 = £95
15 - The number of boys who study Italian is 10
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PAPER 8
PAPER 8A
QUESTION
Write the value of the 2 in the number 0.162 in words.
QUESTION
What is the decimal equivalent to 1.5\% ?
QUESTION
What is \dfrac{1}{4} as a percentage?
QUESTION
Work out (60000-4000)\div80
QUESTION
Given that 28\times1356= 37968
Calculate the following: 2.8 \times 1.356
QUESTION
Iron has a density of 7.8 g/cm^3
Calculate the mass of a 3 cm^3 lump of iron.
QUESTION
What is 0.5 km equivalent to in mm?
QUESTION
******************* IMAGE *******************
What 3D shape can be created with the net?
QUESTION
What is 70\% of 1250 ml?
QUESTION
******************* IMAGE *******************
Find the missing angle labelled A
QUESTION
Calculate the following:
QUESTION
Evaluate,
25.8-17.85QUESTION
******************* IMAGE *******************
Describe the nature of the correlation shown in the scatter graph.
QUESTION
What is the value of
when a=5, b=8, c=-1 and d=2 ?
QUESTION
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.
PAPER 8B
QUESTION
Fifty students were asked how many books they each took to school on Monday.
The results are summarized in the table below.
******************* IMAGE *******************
What is the mode?
QUESTION
An extra large lemonade contains 10\% more than a normal bottle.
The extra large bottle contains 660 ml.
How much does the normal bottle contain?
QUESTION
What is \dfrac{1}{7} of 4 weeks?
Give your answer in days.
QUESTION
Plot the coordinate (1,9) on the graph below.
******************* IMAGE *******************
QUESTION
Write the numbers in increasing order starting with the smallest.
QUESTION
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.
What fraction of the book did she read on Tuesday?
Write your answer in its simplest form.
QUESTION
The diagram below shows a rectangle with a section missing.
******************* IMAGE *******************
Work out the perimeter of the shape.
QUESTION
Jordan finishes college at 16:30 h.
He walks to his mum’s work 0.24 km away, at a speed of 2 km/h.
He waits there 7 minutes for his mum to finish work before she drives them both 7 km back home at an average speed of 26 km/h.
What time does Jordan arrive home?
Give your answer to the nearest minute. You must show your working.
QUESTION
Rachel deposits £2200 into a savings account that pays 1.5\% compound interest per year.
How much is in the saving account after 2 years?
QUESTION
A high street shop records the number of days it rains in a month and the number of umbrellas they sell.
******************* IMAGE *******************
Draw a scatter graph to show the relationship between the number of rainy days in a month and the number of umbrellas sold.
******************* IMAGE *******************
Use the graph to estimate the number of umbrellas they will sell if it rains for 10 days in a month.
QUESTION
Some numbered raffle tickets are placed in a hat.
The tickets are numbered 1 to 50 inclusive.
A ticket is selected at random.
Calculate the probability that the ticket is a factor of 48
QUESTION
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?
QUESTION
A business wants to increase its number of employees by 65\% to 20460
How many employees does the company currently have?
QUESTION
******************* IMAGE *******************
Using the diagram, find the distance of Crewe from Easingwold.
QUESTION
A bag of garden stones weighs 20 kg
Given that each individual stone weighs 0.01 kg, work out how many stones are in a bag.
PAPER 8 ANSWERS
8A
1 - Two thousandths
2 - 0.015
3 - 25\%
4 - 700
5 - 3.7968
6 - \text{Mass}=\text{Density} \times \text{Volume}= (7.8 g/cm^3) \times (3 cm^3) =23.4 g
7 - 500000 mm
8 - cone
9 - 875 ml
10 - 51\degree
11 - 62
12 - 7.95
13 - Strong positive correlation
14 - 6
15 - -1.27, \frac{2}{10}, \,\,\,\, \frac{3}{9}, \,\,\,\, 0.42, \,\,\,\, \frac{3}{6}, \,\,\,\, 0.55
8B
1 - 1 book
2 - 660 \text{ ml} \div 1.10 = 600 \text{ ml}
3 - 4 days
4 - see graph
5 - -11,\,\,\,\, -8,\,\,\,\, -5, \,\,\,\, 0, \,\,\,\, 3
6 - \frac{2}{15}+\frac{1}{3} + \frac{1}{5}= \frac{2}{15}+(\frac{1}{3} \times \frac{5}{5}) + (\frac{1}{5}\times \frac{3}{3}), \frac{2}{15}+\frac{5}{15}+\frac{3}{15}=\frac{10}{15}
1-\frac{10}{15}=\frac{1}{3}7 - 120-55=65 cm
195-70=125 cm
Perimeter =120+70+65+125+55+195=630 cm
8 - Walk: \text{T} = \frac{\text{D}}{\text{S}} = \frac{0.24}{2} = 0.12 hours = \, 7 minutes
Driving: \frac{7}{26} = 0.2692 hours = \, 16 minutes
7 + 7 + 16 = 30 minutes
Adding to 16:30 gives an arrival time of 17:00
9 - 2200 \times 1.015^2 = £2266.50
10 - \approx 8 umbrellas
see graph
11 - The factors of 48 are:
1 and 48, 2 and 24, 3 and 16, 4 and 12, 6 and 8
This means that 10 numbers out of the 50 in the hat are factors of 48. \frac{10}{50} which can be simplified to \frac{1}{5}
12 - 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
13 - 20460 \div 1.65 = 12400
14 - \sqrt{5^2 + 3^2} = 5.83 cm = 58.3 km
15 - 20 \div 0.01 = 2000 stones
******************* IMAGE *******************
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PAPER 9
PAPER 9A
QUESTION
What is 1.2 km equivalent to in cm?
QUESTION
Write these fractions in order of size, starting with the smallest.
\dfrac{3}{8},\,\,\,\, \dfrac{2}{3},\,\,\,\, \dfrac{5}{6},\,\,\,\, \dfrac{3}{12}QUESTION
Estimate 49.53 \times 102.12
QUESTION
Work out (2 \times 7) + 1 \times 3
QUESTION
What is \dfrac{2}{3} as a percentage?
Give your answer rounded to two decimal places.
QUESTION
Phoebe saves all the spare change she gets in a jar until it is full.
Once sorted she finds she has £16 in 5p coins.
How many 5p coins does she have?
QUESTION
******************* IMAGE *******************
Which of the following plan views accurately represents the 3D shape shown?
Answer type: Multiple choice type 1
A: ******************* IMAGE *******************
B: ******************* IMAGE *******************
C: ******************* IMAGE *******************
QUESTION
Circle the greatest decimal from the options below.
QUESTION
What is the value of xy+2y^2 when x=5 and y=3 ?
QUESTION
What is 80\% of 150 people?
QUESTION
******************* IMAGE *******************
Find the missing angle labelled x in the regular polygon.
QUESTION
Six people sit around a table at a restaurant. Each of their ages are as follows:
23 19 20 21 24 26
Find the median age of those sat at the table.
QUESTION
Write down the value of the 6 in the number 11629 in words.
QUESTION
What is \dfrac{2}{5} of £55 ?
QUESTION
Work out the percentage increase from 1500 to 2250
PAPER 9B
QUESTION
Write the numbers in decreasing order starting with the largest.
8526,\,\,\,\, 1001,\,\,\,\, 989, \,\,\,\, 9092, \,\,\,\, 8450QUESTION
The density of copper is 8.96 g/cm^3.
Calculate the volume of 26.88 g of copper in cm^3.
QUESTION
Work out \dfrac{3.5^2\times2.3^2}{1.5^3}
Give your answer as a decimal rounded to 2 decimal places.
QUESTION
What is the number in the thousandths position in 283.157 ?
QUESTION
What is \dfrac{25}{6}+\dfrac{13}{4} ?
Give your answer as an mixed number fraction.
QUESTION
£4000 is invested in a fund which earns 11\% compound return per year.
After 5 years, you remove half the balance, leaving the remainder in the fund.
How much would the fund be worth after 10 years?
QUESTION
The diagram below shows two cuboids, A and B.
******************* IMAGE *******************
Find the combined total surface area of cuboids A and B shown.
QUESTION
Sarah earns £8.43 an hour. She thinks that most of her friends are paid more.
Here is a list of how much her friends earn per hour.
******************* IMAGE *******************
Calculate the mean, median and mode of this data.
Explain whether these averages support Sarah's assumption.
QUESTION
3 friends want to go for a hike. They pack enough water to last for 6 hours. 3 more people join the hike.
How long will their water last now?
Give your answer in hours.
QUESTION
In a rowing team, the weight of 8 women, in kilograms, is:
63, \, 60, \,57, \,66, \,62, \,65, \,69, \,58In order to be a more competitive team, the coach has said that each team member should try to increase their overall muscle mass which will result in a 2\% gain in overall body weight.
What will be the mean weight of the team if all 8 are successful in precisely meeting this 2\% weight gain?
QUESTION
Mr Smith pays £4.48 for 400 g of Edam cheese and buys 250 g of Gorgonzola. Gorgonzola costs £11.60 per kilogram.
Which type of cheese is better value for money per gram?
QUESTION
ABCDEF is a regular hexagon. Its perimeter is 21 cm.
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Calculate the length of one side.
QUESTION
A spinning wheel is made up of 3 different sections, section A, section B and section C.
\text{P(A)}=55\% , \text{P(B)}=\dfrac{2}{5}
Work out the probability of the wheel stopping on section C.
QUESTION
140 students from Year 12 and Year 13 are studying in an academy. All of the students study either Biology, Chemistry or Physics.
There are 87 students from Year 13, of which 22 take Chemistry. 21/latex] of the latex]53 students taking Biology are from Year 12.
10 of the 43 students taking Physics are from Year 12.
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Work out how many students study Chemistry in total.
QUESTION
Jenny is a race car driver, driving around a track.
She does 30 laps in 20 minutes, with an average speed of 144 km/h.
Determine the distance travelled in one lap.
PAPER 9 ANSWERS
9A
1 - 120000 cm
2 - \frac{3}{12},\,\,\,\, \frac{3}{8},\,\,\,\, \frac{2}{3}, \,\,\,\, \frac{5}{6}
3 - 5000
4 - 17
5 - 66.67\%
6 - 320 5p coins
7 - \textbf{A}
8 - 8.065
9 - 33
10 - 120 people
11 - 108\degree
12 - 22 years old
13 - Six hundred
14 - £22
15 - 50\% (accept 150\%)
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9A
1 - 9092, \,\,\,\, 8526,\,\,\,\, 8450, \,\,\,\, 1001, \,\,\,\, 989
2 - \text{Volume} = \text{mass} \div \text{density} = 26.88 \div 8.96 = 3 cm^3
3 - 19.20
4 - 7
5 - 7\frac{5}{12}
6 - 4000\times (1 +\frac{11}{100})^5=6740.23262
6740.23262 \div 2 =3370.11631 3370.11631 \times (1+\frac{11}{100})^5 =£ 5678.847 - SA of A = (5\times3)\times2 + (5\times3)\times2 + (3\times3)\times2 = 78 cm^2
SA of B = (4\times3)\times2 + (4\times2)\times2 + (3\times2)\times2 = 52 cm^2
Total surface Area = 78 + 52 = 130 cm^2
8 - Mean pay = 50.64 \div 6 = £8.44
Median = £8.46 , Mode = £8.48[latex]</p> <p>Yes, the mean, median and mode all suggest that Sarah is correct.</p> <p>9 - [latex]18 hours of water in total, per 3 walkers = 6 hrs of water, so 6 walkers have 3 hrs worth of water
10 - The combined weight of all 8 members is:
63 + 60+57+66+62+65+69+58 = 500 kg
1.02\times500 = 510 kg, 510 kg \div \, 8 =63.75 kg
11 - Edam: £4.48 \div 400 = £0.0112 per gram
Gorgonzola: £11.60 \div 1000= £0.0116 per gram
Edam is better value.
12 - \text{Length of one side}=21 \div 6=3.5 cm
13 - \frac{1}{5} = 20\% so \frac{2}{5} = 40\%, \text{P(A)}+\text{P(B)}= 55\% + 40\% = 95\%
100\% - 95\% = 5\% (Accept 0.05 and \frac{1}{20})
14 - The number of students studying Chemistry is 44
See table
15 - \text{Time in Hours }=\frac{20}{60}=\frac{1}{3}
\text{Distance} =144\times\frac{1}{3}=48 km
48\div30=1.6 km
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PAPER 10
PAPER 10A
QUESTION
Estimate \dfrac{22.38\times3.1}{3.19\times2.1}
QUESTION
What is \dfrac{14}{5} - \dfrac{8}{3} ?
Give your answer as a fraction in its simplest form.
QUESTION
What is 15\% of 300 kg?
QUESTION
Find the median of the following set of values
20.21, 44.82, 27.64, 41.29, 10.74QUESTION
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Describe the nature of the correlation shown in the scatter graph.
QUESTION
A car hire firm charges a fixed £50 fee then charges per mile driven.
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Using the conversion graph, how much would it cost to drive 300 miles?
QUESTION
What is the decimal equivalent to 5\% ?
QUESTION
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What 3D shape can be created with the net shown above?
QUESTION
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Find the perimeter of the rectangle.
QUESTION
What is \dfrac{32}{50} as a percentage?
QUESTION
What is the value of \dfrac{8a}{2b}-5ab when a=3 and b=-4 ?
QUESTION
Plot the coordinate (10,3) on the graph below.
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QUESTION
Lily has 296 guests, and each requires one glass of juice each.
Estimate how many cartons of juice she will need if each carton has enough to fill 9.5 glasses.
QUESTION
What is \dfrac{1}{3} of 27?
QUESTION
Evaluate (3\times5^2)\div5-20\times4+75
PAPER 10B
QUESTION
The price of a chocolate box has increased by 25\%. The box of chocolate now costs £17.25
How much did it cost originally?
QUESTION
Work out 13.5^2-11.5^2
QUESTION
What is 10.4[latex] m[latex]^2 equivalent to in cm^2 ?
QUESTION
The probability of a badminton player winning a match is \dfrac{1}{4}.
The player is competing in two matches over the weekend.
What is the probability of the player winning neither of those games?
Give your answer as a decimal.
QUESTION
Calculate the value of [(x+11-9)^2+8.5\times2]\div 7 when x = 3
QUESTION
A conservation group try to estimate the population of different types of tress that are found in a nearby forest:
\dfrac{1}{18} of the trees are oak
\dfrac{2}{9} of the trees are beech
and \dfrac{1}{4} of the trees are pine.
The group estimates there are 720 trees in the forest. How many of these trees are not oak or pine?
QUESTION
At the store, cola is sold in a multipack of cans or in a single bottle.
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Which option is the better value for money?
You must show all your working.
QUESTION
Christopher has seven rabbits in his garden. Their weights in kilograms are listed below.
1.1, 1.9, 1.5, 1.3, 2.0, 1.3, 1.7What is the mean, mode, and median, for the weight of the rabbits?
QUESTION
A carpenter plans to carve a doorstop out of a block of wood that has a density of 5 g/cm^3.
Calculate the mass of the doorstop, in g, if this is the design:
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QUESTION
The diagram below shows a representation of a small USB drive consisting of two cuboids, ABCDEFGH and IJKLMNOP attached together.
AC=12 mm, BH=3 mm, GF=9 mm, IL=3 mm, KO=1 mm, IJ=e
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If the total surface area of the drive is 360 mm^2.
Calculate the value of e.
QUESTION
Harvey flips an unbiased coin 2 times.
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Complete the probability tree, to show the results of the two flips and calculate the probability that both flips land on heads.
QUESTION
Edith starts on a salary of £23500 and gets a raise of 6\% every year.
What will her salary be in 7 years time?
Give your answer to the nearest pound.
QUESTION
12 students need to drink [/latex]3[/latex] litres of water over the course of the day.
How much water would be needed for 20 students?
Give your answer in litres.
QUESTION
Data set A has a median value of 18.6
Data set B is comprised of 7 data points:
12, 17, 29, 16, 33, 8, 22
Calculate the median of set B.
Write a statement comparing the median values of the two data sets.
QUESTION
Holly is deciding what colour trousers and what colour jumper to wear. Her choices are given below.
Trouser colours: black, navy, purple
Jumper colours: orange, yellow, white
If she chooses to wear black trousers and a yellow jumper, that would be denoted as BY.
List all other possible outcomes for Macy’s choice of outfit.
PAPER 10 ANSWERS
10A
1 - \frac{20\times3}{3\times2} = 10
2 - \frac{2}{15}
3 - 45 kg
4 - 27.64
5 - Weak negative correlation
6 - 300 \text{ miles} \approx £170
7 - 0.05
8 - Cube
9 - Perimeter =14.3+14.3+5.6+5.6 =39.8 cm
10 - 64\%
11 - 57
12 - see graph
13 - \frac{300}{10} = 30 cartons
14 - 9
15 - 10
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10B
1 - £17.25 \div 1.25 = £13.80
2 - 50
3 - 104000 cm^2
4 - 0.75\times 0.75 = 0.5625
5 - 6
6 - \frac{1}{18} are oak hence \frac{40}{720} of the trees are oak.
\frac{9}{36} are pine hence \frac{180}{720} of the trees are pine.
There are a total of 220 oak and pine trees. So 500 trees in the forest that are not oak or pine.
7 - Single = 1500 ml
\dfrac{150}{1500} = 1 ml = \, 0.1p
Multipack = 6 \times 330 = 1980 ml
\dfrac{170}{1980} = 1 ml = \, 0.086p
Multi pack is cheaper
8 - Median = 1.5 kg
Mean = 10.8 \div 7 = 1.54 kg
Mode = 1.3 kg
9 - \text{Volume} = \frac{1}{2} \times 3 \times 5 \times 2 = 15 cm^3
\text{Mass} = 5 \times 15 = 75 g
10 - Big cuboid:
(12\times3)\times2=72
, (9\times12 )\times2=216,
(3\times9 )\times2=54
Total =342[latex] mm[latex]^2
Small cuboid:
(3\times e)\times2=6e,
(1\times e)\times2=2e,
(3\times1)\times2=6
Total =(6+8e)[latex] mm[latex]^2
Overlapping surface area =(3\times1)\times2=6[latex] mm[latex]^2
Total Area of USB = 342+(8e+6)-6=342+8e
e=2.25 mm
11 - P(H,H)=\frac{1}{2}\times \frac{1}{2} = \frac{1}{4}
12 - 23500 \times 1.06^7 = £35335
13 - 3 litres \div \, 12 students = \, 0.25 litres per student
for 20 students they would need 5 litres
14 - The median of Data set B is 17[,latex]. This shows that Data set A has a higher median than Data set B.
15 - Full list of other possible outcomes is:
BO, BW, NO, NY, NW, PO, PY, PW
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