N5 Applications of Maths · SQA past paper
At a school, pupils voted to elect a head prefect.
Fraser received of the votes.
Gracie received of the votes.
Alison received the rest of the votes.
Calculate the fraction of the votes that Alison received.
Laura is buying a picture.
She looks on 3 websites to find the best deal.
| Website A | Website B | Website C |
|---|---|---|
| Picture £21.50 Postage £3.49 |
Picture £35 Offer: 30% off all pictures Postage Free |
Picture £30 Offer: off all pictures Postage £2.80 |
Determine the website which offers the best deal to buy the picture and get it posted to Laura.
Use your working to justify your answer.
Website A: £21.50 + £3.49 = £24.99
Website B: 30% of £35 = £10.50, so £35 − £10.50 = £24.50 (postage free)
Website C: of £30 = £7.50, so £30 − £7.50 + £2.80 = £25.30
Website B is the best deal, at £24.50.
A company produced the following table to show all the tasks involved in manufacturing and packaging chocolate eggs.
| Activity | Description | Preceding activity | Time (seconds) |
|---|---|---|---|
| A | Melt chocolate and stir ingredients | H | 600 |
| B | Wrap the egg | C, I | 30 |
| C | Cool the chocolate | D | 1800 |
| D | Pour chocolate into egg mould | A | 105 |
| E | Construct the cardboard box | G | 60 |
| F | Place wrapped egg into box | B, E | 45 |
| G | Print cardboard | H | 240 |
| H | Collect materials and ingredients | none | 120 |
| I | Print foil | H | 180 |
(a) Complete the diagram below to show the tasks and times.
(b) Calculate the minimum time taken to manufacture and package a chocolate egg.
(a) H (120) splits into A (600), I (180) and G (240). A leads to D (105), then C (1800). G leads to E (60). C and I lead to B (30). B and E lead to F (45).
(b) 2700 seconds
Harris recorded the time, in minutes, that it took him to drive to work over eight days.
22, 21, 37, 25, 32, 28, 36, 24
(a) For this data, calculate: the median, the lower quartile, the upper quartile.
(b) Construct a box plot for this set of data.
(c) Calculate the interquartile range for the number of minutes it took Harris to drive to work.
His colleague Lewis also recorded the number of minutes it took him to drive to work over eight days.
The interquartile range for the number of minutes that Lewis took is 9 minutes.
(d) Make one valid comment comparing the number of minutes Harris and Lewis took to drive to work.
(a) Median = 26.5, Lower Quartile = 23, Upper Quartile = 34
(b) A box plot from the five-figure summary: whiskers to 21 and 37, and a box from 23 to 34 with the median at 26.5.
(c) 11
(d) The number of minutes Lewis took to drive to work was more consistent.
Harris noticed that his journey times were affected by the time he departed.
The table shows his journey time in minutes.
| Departure time (am) | 7:32 | 7:36 | 8:10 | 7:40 | 8:02 | 7:50 | 8:04 | 7:45 |
|---|---|---|---|---|---|---|---|---|
| Journey time (minutes) | 22 | 21 | 37 | 25 | 32 | 28 | 36 | 24 |
(e) On the grid below draw a scattergraph to show this data.
(f) Draw a line of best fit on your scattergraph.
(g) Tomorrow, Harris plans to depart at 7:55 am. Use your line of best fit to estimate his journey time.
(e) Plot (7:32, 22), (7:36, 21), (7:40, 25), (7:45, 24), (7:50, 28), (8:02, 32), (8:04, 36) and (8:10, 37).
(f) A straight line through the middle of the points, with roughly as many points above it as below.
(g) From 7:55 on the departure time axis, go to your line, then read off the journey time. Any answer consistent with your line, approximately 30 minutes.
Julie scored 78% in her science test.
She also scored 32 out of 40 in her maths test.
Determine which subject she performed better in. Justify your answer.
Maths: 80% is more than 78%, so she performed better in Maths.
Ramani works as a sales person for a car company.
She is paid a basic monthly salary of £1870 plus commission of 3% on her monthly sales over £58,000.
In April, her sales totalled £96,000.
Calculate Ramani's gross pay in April.
£3010
A school is designing a playpark.
It is in the shape of a rectangle and a semi-circle.
(a) Calculate the area of the playpark. Take
The school plans to cover some of the playpark with bark.
(b) Calculate the cost of the bark.
(a) 397
(b) £136
Lesley ran a game stall at her local gala.
The game requires two spinners to be spun and allowed to come to rest.
The spinners are fair and are shown below.
To win a prize, spinner B must land on a larger number than spinner A.
(a) Calculate the probability of winning a prize.
(or , 25%, 0.25)
Catriona runs a different game at the gala.
Players who win receive a £5 prize.
When playing this game, the probability of a player winning a prize is 0.15.
The game was played 80 times.
Catriona gave out a total of £70 in prizes.
(b) Determine if this is more or less than expected.
Expected wins , so expected prizes £70 is more than expected.
A farm has 3 different types of animal.
It has sheep, pigs and cows in the ratio 9:7:4 respectively. There are 180 more sheep than there are cows.
Calculate the total number of animals on the farm.
720