2018 Paper 2

2018 P2 Q1

Jack bought a car 3 years ago costing £1400.
The car has decreased in value by 13% each year.

(a) Calculate the current value of the car.
Give your answer to 2 significant figures.

Jack sells his car for £950.

(b) Calculate his loss as a percentage of the original price.

2018 P2 Q2

The number of podcasts Omar downloaded each month for a year is shown in the table below.

12	34	19	9	22	13
21	19	5	26	10	28

(a) For this data, calculate:
• the median
• the lower quartile
• the upper quartile.

(b) Construct a boxplot for this data.

2018 P2 Q3

Ross is changing his internet package.
The table below shows the internet packages he is considering.

Package	Speed (Mbps)	Usage	Monthly line rental	Monthly broadband cost	Initial fee	Length of contract
A	52	25 GB	£8.95	£19.99	£59.99	12 months
B	52	Unlimited	£8.95	£20.99	£59.99	12 months
C	38	50 GB	£7.99	£16.99	£59.99	12 or 18 months
D	52	Unlimited	£7.99	£18.99	£109.99	12 or 18 months
E	52	50 GB	£6.99	£15.99 for 1st 12 months then £19.99	Free	24 months

Ross requires:
• a minimum speed of 52 Mbps
• at least 50 GB of usage
• a 12 month contract.

Ross will choose the package with the lowest overall annual price.
Which package will he choose?
Use your working to justify your answer.

2018 P2 Q4(a)

Nicola has joined a gym.
The pie chart shows the proportion of time that Nicola will spend on each type of workout exercise.

Nicola spent 1 hour and 45 minutes exercising in the gym.

(a) Calculate how long, in minutes, Nicola spent on resistance training.

2018 P2 Q4(b)

Nicola spent 21 minutes exercising on a treadmill.
Her average speed was $\displaystyle 6\mathord{\cdot}6\text{ km/h}.$

(b) Calculate the distance she ran on the treadmill.

2018 P2 Q5(a)

Three tonnes of sheep food will feed 350 sheep for 18 days.
The number of sheep increases by 100.

(a) How long will the same weight of food now last?

2018 P2 Q5(b)

The storage container for the sheep food is in the shape of a cylinder, with dimensions as shown below.

(b) Calculate the volume of the storage container.

2018 P2 Q6

Ali, Kate and Jim are paid to deliver leaflets advertising a new restaurant.
They shared the money they were paid in a ratio of 3:5:7.
Jim received £154.

Calculate how much the restaurant paid, in total, to deliver the leaflets.

2018 P2 Q7

Sam drives from Paris in France to Zurich in Switzerland.
He knows:
• his car will cover an average of 47 miles per gallon of fuel
• the fuel tank holds 50 litres of fuel when it is full
• it is 650 km from Paris to Zurich.

Conversions
1 mile	$\displaystyle 1\mathord{\cdot}609\text{ km}$
1 gallon	$\displaystyle 4\mathord{\cdot}545\text{ litres}$

Will Sam be able to complete his journey with one full tank of fuel?
Use your working to justify your answer.

2018 P2 Q8(a)(b)

Scott decides to build a new track bike.
Scott needs to buy a frame, a handlebar, a pair of pedals, a saddle, 2 wheels and 2 tyres.
Different retailers offer these parts.
The prices, in pounds, are shown in the table.

Retailer	Handlebar	Pedals (pair)	Wheels (each)	Saddle	Tyres (each)
Bikes 2 Go	63.33	33.33	51.25	41.66	54.98
Bikevelo	55.49	42.50	46.66	62.37	58.33
Velo cycles	68.83	36.66	61.20	53.99	61.66
Cycle trax	59.50	43.33	52.25	63.33	69.99
EP bikes	71.58	41.66	44.49	47.85	49.99

Scott can buy the parts from different retailers.
The bike frame costs £2640.95.

(a) Calculate the minimum total cost of the frame and parts.

Scott cannot afford to pay for the bike all at once.
The cash price of the complete bike from EP bikes is £2991.00.
He chooses to buy the complete bike from EP bikes, as they are the only retailer offering a finance package.
The finance package consists of:
• a deposit of 15% of the cash price
• 36 payments of £76.50.

(b) Calculate how much more this finance package will cost compared to the minimum total cost.

2018 P2 Q8(c)(d)

Scott trains at the velodrome on his new bike.
He records his top speed, in kilometres per hour, for each lap.
Six of these speeds are shown below.

$\displaystyle 61\mathord{\cdot}2 \quad 58\mathord{\cdot}3 \quad 59\mathord{\cdot}1 \quad 58\mathord{\cdot}8 \quad 60\mathord{\cdot}4 \quad 59\mathord{\cdot}8$

(c) For these speeds, calculate:
(i) the mean;
(ii) the standard deviation.

Scott had a mean top speed on his old bike of $\displaystyle 57\mathord{\cdot}3\text{ km/h}$ and a standard deviation of $\displaystyle 1\mathord{\cdot}21\text{ km/h}.$

(d) Make two valid comments comparing his top speed on the two different bikes.

2018 P2 Q9(a)(b)

A factory produces cans of tinned beans.
The table shows the list of tasks and the time taken to complete them.

Task	Detail	Preceding task	Time (seconds)
A	Boil beans to cook them	C	500
B	Put on lid	H, E	3
C	Blanch dried beans in water	None	300
D	Attach label	I	5
E	Put sauce in tin	F	2
F	Make the sauce	None	900
G	Put in box	D	5
H	Put beans in tin	A	2
I	Cook beans in sauce in tin	B	300

(a) Complete the diagram below to show the tasks and times in the boxes.

The factory manager thinks that the whole process can be completed in less than 25 minutes.

(b) Based on the times given, is the factory manager correct?
Use your working to justify your answer.

2018 P2 Q9(c)

The tins are packed in boxes.
Each box has dimensions $\displaystyle 60\text{ cm} \times 40\text{ cm} \times 15\text{ cm}$ as shown below.

The boxes must be packed into containers for shipping to Canada.
The container has the internal dimensions shown below.

All the boxes must be aligned in the same direction.

(c) Calculate the maximum number of boxes that will fit in the container.

2018 P2 Q9(d)

It takes 277 hours to sail from the UK to Canada.
The local time in Canada is 5 hours behind the local time in the UK.
The ship leaves the UK at 2200 on 3rd June.

(d) Calculate the date and local time that the ship will arrive in Canada.

2018 P2 Q10(a)(b)

Fiona is a vet.
She has started a new job.
Her new salary is £42,000.
National Insurance is calculated on a person's salary before deductions such as pension contributions.

National Insurance rates
Up to £8164	0%
From £8164 to £45 032	12%
Over £45 032	2%

(a) (i) Calculate Fiona's annual National Insurance payment.

Fiona's annual income tax payment is £5427.96.
She pays an annual contribution of £3360 into her pension.
Fiona is paid in 12 equal monthly payments.

(ii) Calculate Fiona's monthly net pay.

Fiona plans to rent accommodation.
She needs to work out how much she can afford to spend on rent, electricity and council tax.
The table shows her monthly outgoings.

Outgoings (£)
Car payment	395
Car insurance	28
Road tax	12
Food	380
Clothes	130
Mobile phone	64
Internet	55
Socialising	250
Loan	200
Savings	200

(b) Calculate how much she will have available per month for rent, electricity and council tax.

2018 P2 Q10(c)

Fiona is considering these 3 properties.

Annual Council Tax (to be paid in 12 equal monthly instalments)

Band A	£1000.92
Band B	£1167.72
Band C	£1334.52
Band D	£1501.32
Band E	£1834.92
Band F	£2168.64
Band G	£2502.24
Band H	£3002.64

(c) Which property is the cheapest option?
Use your working to justify your answer.

2018 P2 Q11(a)(b)

A new hotel is being planned in Benidorm.
The pool will have a walkway around three sides.
The walkway will be $\displaystyle 1\mathord{\cdot}5\text{ m}$ wide.
This is shown in the diagram.

(a) Calculate the total area of the walkway.

The walkway will be covered in tiles.
16 tiles are needed to cover 1 square metre.
The tiles are sold in boxes of 50.
Each box costs 71.95 euro.

(b) Calculate the cost of the tiles needed for the walkway.

2018 P2 Q11(c)

The swimming pool is a prism, with dimensions as shown in the diagram below.

(c) Calculate the volume of the swimming pool.
Give your answer in litres.