Course Notes Practice Past Paper Archive

N5 Applications of Maths · SQA past paper

2022 Paper 1

Non-Calculator · 12 questions

Question 1

Measurement

2 Marks

2022 P1 Q1

Steven blew up the tyres on his bike.

In order to be safe, his tyres should be blown up to a pressure of between 35 and 45 psi.
Steven blew his tyres up to a pressure of 230 kPa.
Determine whether his tyres are at a safe pressure. Justify your answer.

Show answer

No, since 230 kPa is approximately 33 psi, which is less than the safe limit of 35 psi. (Alternatively, 35 psi is approximately 241 kPa, and 230 kPa < 241 kPa).

Question 2

Numeracy

2 Marks

2022 P1 Q2

Marie and John are both reading the same book.
Marie is using an e-book reader and John is reading a hardback book.

Marie's book 62% read, John's book 210 pages out of 350 pages read

John thinks he has read more of the book than Marie.
Is he correct? Use your working to justify your answer.

Show answer

No, since John has only read 60% of the book ( $\displaystyle \frac{210}{350} \times 100\%$ ), which is less than Marie's 62%. (Alternatively, Marie has read 217 pages, which is greater than 210).

Question 3

Statistics

(2, 2, 1, 1)6 Marks

2022 P1 Q3

The temperature, in degrees Celsius, of a restaurant fridge is recorded each day.
The temperatures over a 13 day period were:

3.2	4.2	3.3	3.6	3.7	3.2	4.2
3.3	3.4	3.6	3.2	4.1	2.9

(a) For this data, calculate:

the median
the lower quartile
the upper quartile.

(b) Construct a box plot for this set of data.

(d) The temperatures of a café fridge were also recorded for the same 13 day period.
The interquartile range of these temperatures was 0.9 degrees Celsius.
Make one valid comment comparing the temperatures of these two fridges.

Show answer

(a) Median = 3.4, Lower Quartile (Q1) = 3.2, Upper Quartile (Q3) = 3.9.
(b) Completed box plot using minimum = 2.9, Q1 = 3.2, Median = 3.4, Q3 = 3.9, maximum = 4.2.
(c) 0.7
(d) The temperatures of the café fridge were less consistent than the restaurant fridge.

Question 4

Measurement

(2, 2)4 Marks

2022 P1 Q4

Kieran and Dylan decide to redesign their garden.
There are several tasks that need to be done in order to achieve this.

Activity	Description	Preceding task	Time taken
A	lay patio	I	5 hours
B	assemble furniture	A	1 hour 30 minutes
C	remove decking	none	6 hours
D	paint fence	G	3 hours
E	lay artificial grass	I	3 hours
F	remove grass	none	2 hours
G	buy all materials	C, F	45 minutes
H	plant patio tubs	A	2 hours 15 minutes
I	roughcast wall	D	1 hour 45 minutes

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

(b) Based on the times given, calculate the minimum time to complete all of the work.
Give your answer in hours and minutes.

Show answer

(a) Completed diagram: Path follows C(6 hrs)/F(2 hrs) → G(45 mins) → D(3 hrs) → I(1 hr 45 mins) → A(5 hrs)/E(3 hrs). After A → H(2 hrs 15 mins)/B(1 hr 30 mins).
(b) 18 hours 45 minutes

Question 5

Probability and Graphical Data

3 Marks

2022 P1 Q5

Jade runs a game stall at the Christmas coffee morning.
Her game requires two spinners to be spun and allowed to come to rest.
The spinners are fair and are shown below.

Two fair spinners, one with numbers 2, 3, 4, 5, 6 and another with 0, 2, 4, 8, 9, 10, 12

The numbers on which the spinners come to rest are multiplied together.
To win a prize the answer to this multiplication must be greater than 30.
Calculate the probability of winning a prize.

Show answer

$\displaystyle \frac{11}{35}$

Question 6

Finance

2 Marks

2022 P1 Q6

Farah works in a shop.
She earns £8.40 per hour.
She gets paid overtime at time-and-a-half.
In January she worked 100 hours basic plus 30 hours overtime.
In January she paid £33.50 in income tax, £61.92 in National Insurance and £25.20 towards her pension.
Calculate Farah's net pay for January.

Show answer

£1097.38

Question 7

Geometry

3 Marks

2022 P1 Q7

Tracy decides to walk to the top of Dumyat Hill from Blairlogie car park.

The horizontal distance between these two places is 3 kilometres.
Blairlogie car park is 21 metres above sea level.
The top of Dumyat Hill is 420 metres above sea level.

Calculate the average gradient between the Blairlogie car park and the top of Dumyat Hill.
Give your answer as a fraction in its simplest form.

Show answer

$\displaystyle \frac{133}{1000}$

Question 8

Numeracy

3 Marks

2022 P1 Q8

Bryan, Jamie and Jessica bought two medium pizzas between them.

Bryan ate $\displaystyle \frac{5}{7}$ of a pizza.
Jamie ate $\displaystyle \frac{2}{3}$ of a pizza.
Jessica ate the rest.

Calculate the total amount of pizza that Jessica ate.
Give your answer as a fraction of a pizza.

Show answer

$\displaystyle \frac{13}{21}$

Question 9

Geometry

2 Marks

2022 P1 Q9

Zainab designs a new badge.
The design is based on a rectangle and a semi-circle as shown in the diagram.

Badge diagram with rectangle and semi-circle. Dimensions 10 cm height and 20 cm total width.

She decides to put gold edging around the badge.
Calculate the length of gold edging she needs.
Take $\displaystyle \pi = 3.14.$

Show answer

55.7 cm

Question 10

Finance

2 Marks

2022 P1 Q10

A youth group is planning a fundraising night to help pay for a trip.
The expenses for the night are shown.

DJ and disco	£340
Hall hire	£50
Hog roast	£770
Ticket production	£40

They will sell 200 tickets.
They need to make a profit of £2000.
Calculate the minimum ticket price to achieve this profit.

Show answer

£16

Question 11

Geometry

4 Marks

2022 P1 Q11

A flag is in the shape of an isosceles triangle with a rectangle on the top.

Flag shaped as isosceles triangle with rectangle on top. Rectangle width 10cm, height 4cm. Slant side of triangle is 13cm.

Calculate the area of the flag.

Show answer

100 cm $\displaystyle ^2$

Question 12

Probability and Graphical Data

2 Marks

2022 P1 Q12

A company delivers parcels to people's homes.
The probability of a parcel arriving damaged is 0.023.
In one month, the company delivered 700 parcels, of which 15 were damaged.
Determine if this is more or less than expected.

Show answer

Less than expected (the expected amount was 16.1 damaged parcels).