N5 Applications of Maths 2026 Paper 1 — Questions & Video Solutions

1

Question 1

Measurement

2 Marks

2026 P1 Q1

A tyre pressure gauge is shown.

Tyre pressure gauge with an outer scale marked in psi from 0 to 160 and an inner scale marked in bar from 0 to 11

Safety regulations require a lorry's tyre pressure must be greater than or equal to 8.2 bar.
Trevor's lorry has a tyre pressure of 112 psi.
Mark both pressures on the gauge and determine if the tyre is safe.

Show answer

112 psi lines up with approximately 7.7 bar on the inner scale.

7.7 < 8.2, so the tyre is not safe.

2

Question 2

Numeracy

3 Marks

2026 P1 Q2

Craig is a farmer.
Each of Craig's sheep receives one dose of vitamins.

On Monday he gave $\displaystyle \frac{1}{7}$ of his sheep a dose of vitamins.
On Tuesday he gave a different $\displaystyle \frac{2}{3}$ of his sheep a dose of vitamins.

Calculate the fraction of Craig's sheep that have not yet had a dose of vitamins.

Show answer

$\displaystyle \frac{1}{7}+\frac{2}{3}=\frac{3}{21}+\frac{14}{21}=\frac{17}{21}$ have had a dose.

$\displaystyle 1-\frac{17}{21}=\frac{4}{21}$

3

Question 3

Finance

2 Marks

2026 P1 Q3

Helen is saving to buy a puppy.

Her monthly net pay is £1770.
Her monthly expenses are £1420.
She plans to save 20% of her remaining money each month.

The puppy will cost £1250.
Calculate the minimum number of months it will take to save this amount.

Show answer

Remaining each month = £1770 − £1420 = £350, so she saves 20% of £350 = £70.

$\displaystyle 1250\div70=17.85\ldots$ , and 17 months gives only £1190, so she needs 18 months.

4

Question 4

Measurement

(2, 1)3 Marks

2026 P1 Q4

A company renovates houses before they are rented out.
The table shows the tasks that must be completed before the house can be rented out.

Task	Description	Preceding task	Time (hours)
A	Inspect property	none	4
B	Repair electrics	F	6
C	Service boiler	A	3
D	Empty property	A	8
E	Order materials	A	2
F	Repair plumbing	D, E	7
G	Clean property	I	12
H	Repair flooring	B	10
I	Paint property	C, H, J	24
J	Repair walls, doors and ceilings	B	5

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

Incomplete activity network diagram: the starting box is labelled A with a time of 4 and the remaining boxes are blank

(b) Calculate the minimum time taken to complete all of the tasks.

Show answer

(a) A(4) splits into D(8), E(2) and C(3). D and E lead to F(7), then F to B(6). B splits into H(10) and J(5). C, H and J all lead to I(24), then I to G(12).
(D and E may be swapped, as may H and J.)

(b) The longest path is A(4) + D(8) + F(7) + B(6) + H(10) + I(24) + G(12) = 71 hours.

5

Question 5

Statistics

(2, 2, 1)5 Marks

2026 P1 Q5

Ainzlie recorded the number of cars that she washed each day at a carwash over a period of ten days.

26 9 27 14 31 18 21 7 10 17

(a) For this data, calculate:

the median
the upper and lower quartiles.

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

Grid for drawing a box plot, with a scale from 0 to 35 labelled number of cars washed

(c) Calculate the interquartile range for the number of cars that Ainzlie washed.

Show answer

(a) In order: 7, 9, 10, 14, 17, 18, 21, 26, 27, 31.
Median = $\displaystyle \frac{17+18}{2}=17.5$ , lower quartile = 10, upper quartile = 26.

(b) Box plot drawn from the five-figure summary: minimum 7, $\displaystyle Q_1=10$ , $\displaystyle Q_2=17.5$ , $\displaystyle Q_3=26$ , maximum 31.

(c) IQR = 26 − 10 = 16

6

Question 6

Geometry

2 Marks

2026 P1 Q6

A warehouse has a ramp at its back door.
The dimensions are shown.

Right-angled triangle representing a ramp, with horizontal distance 12 m and vertical height 180 cm

Calculate the gradient of the ramp.
Give your answer as a fraction in its simplest form.

Show answer

12 m = 1200 cm, so gradient $\displaystyle =\frac{180}{1200}=\frac{3}{20}$

7

Question 7

Finance

2 Marks

2026 P1 Q7

Jayanti sells kitchens.
She is paid a basic monthly salary of £1765 plus commission of 5% on her monthly sales over £40,000.
In March her sales totalled £56,000.
Calculate Jayanti's gross pay in March.

Show answer

Sales earning commission = £56,000 − £40,000 = £16,000, so commission = 5% of £16,000 = £800.

Gross pay = £1765 + £800 = £2565

8

Question 8

Probability and Graphical Data

(2, 1, 1)4 Marks

2026 P1 Q8

David is a pilot. He keeps a record of the distances and times of each flight.
The table shows the distances, to the nearest 100 miles, and times taken for the flights.

Distance (miles)	600	700	1100	1800	2000	2100	3300	3600
Flight time (hours)	1.8	2.4	2.6	4.2	4.4	5.6	8.0	7.2

(a) On the grid below draw a scattergraph to show this data.

Blank grid titled distances and times of David's flights, with distance in miles from 500 to 4000 across and flight time in hours from 0 to 9 up

(b) Draw a line of best fit on your scattergraph.

(c) David's next flight is expected to last 3.4 hours.
Use your line of best fit to estimate the distance of this flight.

Show answer

(a) Plot (600, 1.8), (700, 2.4), (1100, 2.6), (1800, 4.2), (2000, 4.4), (2100, 5.6), (3300, 8.0) and (3600, 7.2).

(b) A straight line through the middle of the points, with roughly as many points above it as below.

(c) Read across from 3.4 hours to the line, then down to the distance axis. Any answer consistent with your line, approximately 1450 to 1550 miles.

9

Question 9

Numeracy

2 Marks

2026 P1 Q9

The volume flow rate (VFR) of a liquid is calculated using volume of liquid in m³ and time in seconds.
It is calculated using the formula

$\displaystyle \text{VFR}=\frac{\text{volume}}{\text{time}}$

54 m³ of water flows from a tank in a time of $\displaystyle 1\frac{1}{2}$ minutes.
Calculate the volume flow rate of the water in m³ per second.
Give your answer as a decimal.

Show answer

$\displaystyle 1\frac{1}{2}$ minutes = 90 seconds, so VFR $\displaystyle =\frac{54}{90}=$ 0.6 m³/s

10

Question 10

Numeracy

2 Marks

2026 P1 Q10

Emma sells bath salts.
The price of the bath salts is directly proportional to its weight.
Emma sells 450 grams of bath salts for £4.32.
Calculate the price of 1 kilogram of bath salts.

Show answer

$\displaystyle £4.32\div450\times1000=$ £9.60

11

Question 11

Probability and Graphical Data

3 Marks

2026 P1 Q11

Ann is playing a game which involves rolling a fair dice and flipping a fair coin.

The dice has six sides numbered 1, 2, 3, 4, 5, 6.
The coin has two sides, heads and tails.

There are two possible ways to win the game:

The coin landing on tails and the dice landing on a multiple of 3.
The coin landing on heads and the dice landing on an odd number.

Calculate the probability that Ann will win on her next turn.
Give your answer as a fraction.

Show answer

There are $\displaystyle 6\times2=12$ possible outcomes.

Tails with a multiple of 3 gives 2 outcomes; heads with an odd number gives 3 outcomes.

$\displaystyle P(\text{win})=\frac{2+3}{12}=\frac{5}{12}$

12

Question 12

Geometry

2 Marks

2026 P1 Q12

A garden has been designed in the shape of a square and a quarter circle.
A fence will be built around the garden.
The fence will have a 1 metre-wide gap as shown.

Garden made from a square of side 10 m with a quarter circle of radius 10 m on top; the right-hand side has a 1 m gap near the bottom

Calculate the total length of the fence.
Use $\displaystyle \pi=3.14$

Show answer

Arc $\displaystyle =\frac{1}{4}\times3.14\times20=15.7$ m.

Straight edges: bottom 10 m, right 10 − 1 = 9 m, left 10 + 10 = 20 m.

Total = 10 + 9 + 20 + 15.7 = 54.7 m

13

Question 13

Probability and Graphical DataNumeracy

3 Marks

2026 P1 Q13

A company was interested in customer opinions about a soft drink.
They carried out a survey.
The results are shown in the pie chart.

Pie chart titled results of survey about soft drink, with sectors like 160 degrees, undecided 140 degrees and dislike 60 degrees

Following this survey, the company changed to a new recipe.
They then carried out a second survey.
The results of the second survey are shown in the table.

Like	Dislike	Undecided
280	70	130

Determine if there has been a decrease in the proportion of customers who dislike the soft drink.
Use your working to justify your answer.

Show answer

First survey: $\displaystyle \frac{60}{360}=\frac{1}{6}=\frac{8}{48}$

Second survey: total = 280 + 70 + 130 = 480, so $\displaystyle \frac{70}{480}=\frac{7}{48}$

$\displaystyle \frac{7}{48} < \frac{8}{48}$ , so yes, the proportion who dislike the drink has decreased.