N5 Applications of Maths 2024 Paper 2 — Questions & Video Solutions

1

Question 1

Finance

4 Marks

2024 P2 Q1

A school currently has 1200 pupils.
The number of pupils is expected to increase by 5.3% each year for the next 4 years.
Calculate the expected number of pupils after 4 years.
Give your answer rounded to 3 significant figures.

Show answer

Expected number of pupils:
Multiplier = 1.053
$\displaystyle 1200 \times 1.053^4 = 1475.3...$
Rounded to 3 significant figures: 1480 pupils.

2

Question 2

GeometryNumeracy

(2, 1)3 Marks

2024 P2 Q2

(a) A snooker ball is a sphere with a diameter of 5.2 cm.

Calculate the volume of the snooker ball.

(b) The density of an object can be calculated using the formula below.

$\displaystyle Density = \frac{mass}{volume}$

The mass of the snooker ball is 142 grams.
Calculate the density of the snooker ball.
Give your answer in grams per cubic centimetre.

Show answer

(a) Volume = $\displaystyle \frac{4}{3} \times \pi \times 2.6^3 = 73.62...$ cm³

(b) Density = $\displaystyle \frac{142}{73.62...} = 1.92...$ g/cm³

3

Question 3

Probability and Graphical Data

2 Marks

2024 P2 Q3

A lottery consists of a draw with 49 balls numbered from 1 to 49.
In the draw six numbered balls are drawn and not replaced.
These six numbers were 3, 7, 12, 13, 28 and 42.
A further bonus ball is then drawn.

Calculate the probability of the bonus ball being a number less than 8.

Show answer

Balls remaining = 43
Numbers less than 8 remaining (1, 2, 4, 5, 6) = 5 balls
Probability = $\displaystyle \frac{5}{43}$

4

Question 4

Geometry

4 Marks

2024 P2 Q4

A section of garden is in the shape of four identical right-angled triangles.
It consists of a circular flower bed surrounded by a patio as shown.
The flower bed has a radius of 4 metres.

Garden shape with four identical right-angled triangles forming a rhombus, surrounding a circular flower bed

The patio is represented by the shaded area.
Calculate the area of the patio.

Show answer

Area of circle = $\displaystyle \pi \times 4^2 = 50.265...$ m²
Dimensions of triangles: Base = 5 + 4 = 9 m, Height = 3 + 4 = 7 m
Total area of 4 triangles = $\displaystyle 4 \times (\frac{1}{2} \times 9 \times 7) = 126$ m²
Area of patio = $\displaystyle 126 - 50.265... = 75.734...$ m²

5

Question 5

Finance

(2, 2)4 Marks

2024 P2 Q5

(a) Akira has an annual salary of £35,670.
National Insurance is calculated on a person's salary before deductions.

Annual National Insurance rates
Up to £12,584	0%
From £12,584 to £50,284	12%
Over £50,284	2%

Calculate Akira's annual National Insurance payment.

(b) Akira pays 9.4% of her annual salary into her pension.
Her annual income tax is £3994.42.
She is paid in 52 weekly payments.
Calculate Akira's weekly net pay.

Show answer

(a) Amount taxed at 12% = £35,670 - £12,584 = £23,086
National Insurance = $\displaystyle 0.12 \times 23086 = £2770.32$

(b) Pension contribution = $\displaystyle 0.094 \times 35670 = £3352.98$
Total deductions = £2770.32 + £3352.98 + £3994.42 = £10,117.72
Net annual pay = £35,670 - £10,117.72 = £25,552.28
Weekly net pay = $\displaystyle \frac{25552.28}{52} = £491.39$

6

Question 6

Geometry

4 Marks

2024 P2 Q6

A boat sails due East from a harbour.
A lighthouse is 500 metres due North of the harbour.
When the boat is at position A it is 600 metres away from the lighthouse.
It sails a further 400 metres to position B.

Diagram showing a right angled triangle with harbour, lighthouse, and positions A and B

Calculate the direct distance from position B to the lighthouse as shown by the dotted line.
Do not use a scale drawing.

Show answer

Distance from harbour to A:
$\displaystyle \sqrt{600^2 - 500^2} = 331.66...$ m
Distance from harbour to B = 331.66... + 400 = 731.66... m
Distance from lighthouse to B:
$\displaystyle \sqrt{500^2 + 731.66...^2} = 886.18...$ m

7(a)

Question 7(a)

Numeracy

1 Mark

2024 P2 Q7(a)

Rab bought a house at auction to modernise and then sell.
The purchase price was £85,800.
In addition, he paid:
• 1.5% of the purchase price in legal fees
• a fee of £250 to the auction house.

(a) Calculate the total amount that Rab paid for the house.

Show answer

Total paid = $\displaystyle 1.015 \times 85800 + 250 = £87,337$

7(b)

Question 7(b)

Finance

3 Marks

2024 P2 Q7(b)

(b) Rab wanted to lay tiles on the hallway floor.
He needs 36 boxes of tiles.
He looked at three different shops before buying the tiles.

Shop A	Shop B	Shop C
£26 per box	£32 per box	£22 per box
Special offer: Buy 2 boxes and get a third box half price	Special offer: 30% discount on total price when 20 or more boxes are purchased

Determine the lowest price for buying 36 boxes of tiles.
Use your working to justify your answer.

Show answer

Shop A cost: 36 boxes = 12 sets of 3. Each set = 26 + 26 + 13 = £65. Total = $\displaystyle 12 \times 65 = £780$
Shop B cost: $\displaystyle 36 \times 32 \times 0.70 = £806.40$
Shop C cost: $\displaystyle 36 \times 22 = £792$
Lowest price is £780 at Shop A.

7(c)

Question 7(c)

Measurement

(2, 2)4 Marks

2024 P2 Q7(c)

(c) (i) Rab modernised the house.
The work done is shown in the table.

Activity	Description	Preceding task	Time in days
A	clear rubbish from house and garden	none	7
B	landscape the garden	A	10
C	plaster the walls	E, G	9
D	decorate the house	C	8
E	rewire the house	F	15
F	fix the roof	A	18
G	re-plumb the house	F	11
H	lay all the flooring	C	6
I	advertise the house for sale	B, D, H	1

Complete the diagram to show the tasks and the time taken for each.

(ii) Calculate the minimum time required for the renovations to be completed.

Show answer

(i) Top path tasks: F (18), E (15) or G (11), C (9), D (8) or H (6). Bottom path: B (10).

(ii) Critical path length: A (7) + F (18) + E (15) + C (9) + D (8) + I (1) = 58 days.

7(d)

Question 7(d)

Numeracy

3 Marks

2024 P2 Q7(d)

(d) Rab employed GreenPlant Gardeners to landscape the garden.
The company told Rab that 3 workers would take 10 days to landscape the garden.
The company were able to provide 2 extra workers.
All the workers work at the same rate.
They work Monday to Friday each week.
The work started on the morning of Monday 2 October.
Determine the date the work will finish.

Show answer

Total worker-days required = $\displaystyle 3 \times 10 = 30$ days
Time for 5 workers = $\displaystyle \frac{30}{5} = 6$ days
Working Monday to Friday, 6 working days from Monday 2 October finishes on Monday 9 October.

8(a) & (b)

Question 8(a) & (b)

Statistics

(1, 3, 2)6 Marks

2024 P2 Q8(a) & (b)

A bathroom company counts the number of visitors to their shop in Stirling each Sunday.
A sample of these results is shown.

44, 55, 32, 39, 43, 26, 34

(a) For these results, calculate:
(i) the mean
(ii) the standard deviation.

The number of visitors to the company's shop in Aberdeen each Sunday was also recorded.
The mean number of visitors was 49 and the standard deviation was 3.2.

(b) Make two valid comments about the number of visitors each Sunday to the shops in Stirling and Aberdeen.

Show answer

(a) (i) Mean = $\displaystyle \frac{273}{7} = 39$

(ii) Standard deviation = $\displaystyle \sqrt{\frac{540}{7-1}} = 9.48...$

(b) On average, the number of visitors to the Aberdeen shop on a Sunday was greater.
The number of visitors to the Aberdeen shop was more consistent.

8(c)

Question 8(c)

Numeracy

2 Marks

2024 P2 Q8(c)

(c) The shop tracks the methods used to purchase a new bathroom.
The three methods available are debit card, credit card or cash.
Last year the purchase methods used were in a ratio of 3:4:2 respectively.
172 bathrooms were purchased using a credit card.
Calculate the total number of bathrooms purchased last year.

Show answer

Credit card shares = 4
1 share = $\displaystyle \frac{172}{4} = 43$
Total shares = 3 + 4 + 2 = 9
Total bathrooms = $\displaystyle 9 \times 43 = 387$

8(d)

Question 8(d)

Finance

3 Marks

2024 P2 Q8(d)

(d) The advertised price for a deluxe bathroom is £6700.
It can be bought using a payment plan.
The payment plan is £325 more expensive than the advertised price.
The payment plan consists of:
• a deposit of 12.5% of the advertised price
• 50 equal monthly instalments.

Calculate the monthly instalment.

Show answer

Deposit = $\displaystyle 0.125 \times 6700 = £837.50$
Total cost of payment plan = $\displaystyle 6700 + 325 = £7025$
Amount left to pay = $\displaystyle 7025 - 837.50 = £6187.50$
Monthly instalment = $\displaystyle \frac{6187.50}{50} = £123.75$

9(a)

Question 9(a)

Finance

2 Marks

2024 P2 Q9(a)

Emma is planning a holiday to Spain.
Her sister, who lives in the USA, sent her $100 for her birthday.
Emma exchanged it for euros to use as spending money.

Exchange Rates:
£1 = 1.11 euros
£1 = $1.30

(a) Calculate how many euros Emma received.

Show answer

Dollars to pounds = $\displaystyle \frac{100}{1.30} = £76.92...$
Pounds to euros = $\displaystyle 76.92... \times 1.11 = 85.38$ euros

9(b)

Question 9(b)

Finance

3 Marks

2024 P2 Q9(b)

Emma worked overtime to earn some extra spending money.
Her basic rate of pay is £12.80 an hour.
She is contracted to work 37.5 hours per week. She is paid time-and-a-half for any overtime she works.
Last week Emma worked 5 days from 07:30 until 12:30.
After a lunch break she then worked from 13:00 until 17:30 on each of those 5 days.

(b) Calculate how much Emma earned last week.

Show answer

Hours worked per day = 5 hours (morning) + 4.5 hours (afternoon) = 9.5 hours
Total hours worked in 5 days = $\displaystyle 5 \times 9.5 = 47.5$ hours
Overtime hours = 47.5 - 37.5 = 10 hours
Normal pay = $\displaystyle 37.5 \times 12.80 = £480$
Overtime pay = $\displaystyle 10 \times 12.80 \times 1.5 = £192$
Total pay = £480 + £192 = £672

9(c)

Question 9(c)

Finance

4 Marks

2024 P2 Q9(c)

Emma intends to fly to Alicante airport.
She considers two options:
• a bus to Edinburgh Airport for a flight to Alicante, or
• drive to Manchester Airport for a flight to Alicante.

The costs associated with each option are shown below.

Edinburgh	Manchester
Return flights: £256	Return flights: £152
Return bus fare: £14.50	Parking: £49
	Fuel costs: ?

The return journey from Emma's house to the car park at Manchester Airport is 492 miles.
Emma's car will cover an average of 48 miles per gallon of fuel.
1 gallon = 4.545 litres.
1 litre of fuel costs £1.42.

(c) Determine which option is cheaper for Emma.

Show answer

Edinburgh total cost = £256 + £14.50 = £270.50
Manchester fuel cost:
Number of gallons = $\displaystyle \frac{492}{48} = 10.25$ gallons
Number of litres = $\displaystyle 10.25 \times 4.545 = 46.58...$ litres
Fuel cost = $\displaystyle 46.58... \times 1.42 = £66.15...$
Manchester total cost = £152 + £49 + £66.15 = £267.15
Manchester is cheaper (£267.15 < £270.50).

9(d)

Question 9(d)

Measurement

3 Marks

2024 P2 Q9(d)

Emma chose to fly from Edinburgh.
Her plane took off at 11:30 local time.
The time in Alicante is 1 hour ahead of the time in Edinburgh.
The plane flew 1552.5 miles at an average speed of 575 miles per hour.

(d) Calculate the local time that the plane landed in Alicante.

Show answer

Time of flight = $\displaystyle \frac{1552.5}{575} = 2.7$ hours = 2 hours 42 minutes
Local time in Alicante when flight left = 12:30
Landing time = 12:30 + 2 hours 42 minutes = 15:12 (or 3:12 pm)