N5 Applications of Maths · SQA past paper
A lake had a volume of 14,730,000 litres.
Due to decreasing rainfall the volume of the lake is expected to decrease by 2.8% annually.
Calculate the expected volume of the lake after 3 years.
Give your answer to 3 significant figures.
litres
A glazier is edging the perimeter of a window.
The window is in the shape of two rectangles and two identical quarter circles.
Calculate the length of edging required for the perimeter of the window.
(or )
Fiona is having her back garden redesigned.
A new fence is to be put from A to B and from B to C.
Rolls of fencing are 3 m long and cost £22 per roll.
Calculate the cost of the fencing.
£308
The reception area in a hotel features a large mirror.
The mirror is in the shape of a square with identical semi-circles on each side.
The square has sides of length 1.2 metres.
The semi-circles have a diameter of 0.7 metres.
(a) Calculate the area of the mirror.
The hotel bought a different mirror for the ballroom.
The options for mirrors are shown in the table.
| Options | Details and Costs | ||
|---|---|---|---|
| Glass coating | standard: £12 per | anti-glare: £16 per | |
| Fixings | basic: £19 per mirror | standard: £32 per mirror | premium: £42 per mirror |
| Backing | no backing: £0 per mirror | foil backing: £20 per mirror | |
| Glass colour and thickness |
Bronze (per ) 6 mm: £58 4 mm: £36 |
Silver (per ) 6 mm: £66 4 mm: £38 |
Gold (per ) 6 mm: £86.50 |
The hotel bought a mirror with an area of
The hotel chose the following options for the mirror:
(b) Calculate the total cost of this mirror.
£214
Stuart records the chlorine levels in his hot tub.
A sample of the levels is shown below.
| Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
|---|---|---|---|---|---|---|
| 0.8 | 1.9 | 1.1 | 2.6 | 3.1 | 2.4 | 2.1 |
(a) For these levels, calculate:
(i) the mean
(ii) the standard deviation.
His friend Colin's hot tub had a mean chlorine level of 2.2 and a standard deviation of 1.4.
(b) Make two valid comparisons about the chlorine levels in Stuart's and Colin's hot tubs.
(a)(i) Mean = 2.0
(a)(ii) Standard deviation = 0.82 (or 0.816...)
(b) On average, Colin's chlorine levels are higher (since 2.2 > 2.0). Stuart's chlorine levels are more consistent (since 0.82 < 1.4).
Colin had a new hot tub installed in his garden.
It normally takes a team of 4 workers 12 hours to complete the task.
The company sent an additional worker to help complete the task. All workers work at the same rate.
The workers started at 08:00 and they took a 30 minute break for lunch.
(c) Determine the time they finished installing the hot tub.
18:06 (or 6:06 pm)
Lorna is travelling around Europe.
| Rates of exchange | |
|---|---|
| Pounds sterling (£) | Other currencies |
| 1 | 1.15 euros |
| 1 | 4.94 Polish zlotys |
(a) Calculate how many euros she received.
€419.40 (or 419.41)
Lorna visited Switzerland and decided to buy some cheese.
The cost of five types of cheese is shown in the table.
| Type of cheese | Cost per 250 grams in Swiss francs |
|---|---|
| Emmental | 2.50 |
| Gruyere | 7.50 |
| Raclette | 7.00 |
| Edam | 3.00 |
| Mozzarella | 2.00 |
Lorna saw 3 different deals for buying cheese.
| Deal A | Deal B | Deal C |
|---|---|---|
| Buy all 5 for 18.50 Swiss francs | Buy all 5, get the cheapest free | Buy all 5, save 15% |
Lorna is going to buy 250 grams of each cheese.
(b) Determine the best deal for buying all 5 cheeses.
Use your working to justify your answer.
Deal A (Total cost for A is 18.50 CHF, B is 20.00 CHF, and C is 18.70 CHF).
Lorna also purchased a paperweight as a gift.
The paperweight is made in the shape of a cube with a hemisphere on top.
The hemisphere is half of a sphere with a diameter of 6 cm.
(c) Calculate the volume of the paperweight.
Dave has a job in an office typing documents.
He is contracted to work 35 hours per week.
He earns £11.20 per hour.
He is paid time and a half for any overtime he works.
Last week Dave worked 37.5 hours.
(a) Calculate his gross wage last week.
£434
Dave records the number of words per minute that he typed during a 14-minute period.
47 39 51 49 42 44 47 54 48 37 41 46 37 44
(b) For this data, calculate:
- the median
- the lower quartile
- the upper quartile.
(c) Construct a boxplot for this set of data.
(d) (i) Calculate the interquartile range for the number of words Dave can type per minute.
Lynn works in the same office as Dave.
Lynn also records the number of words per minute that she can type.
The interquartile range for the number of words that Lynn can type per minute is 5.
(ii) Make one valid comment comparing the number of words Dave and Lynn can type per minute.
(b) Median = 45, Lower quartile = 41, Upper quartile = 48.
(c) A boxplot drawn with Min = 37, = 41, = 45, = 48, Max = 54.
(d)(i) Interquartile range = 7.
(d)(ii) Lynn's typing speed is more consistent (since 5 < 7).
Lynn earns £1052 a week.
National Insurance is calculated on a person's wage before deductions such as pension contributions.
| National Insurance rates (weekly) | |
|---|---|
| Up to £242 | 0% |
| From £242 to £967 | 13.25% |
| Over £967 | 3.25% |
(e) (i) Calculate Lynn's weekly National Insurance payment.
Lynn pays 4.5% of her weekly wage into her pension.
Her weekly income tax is £52.08.
(ii) Calculate Lynn's weekly net pay.
(i) £98.83 (or £98.82)
(ii) £853.75 (or £853.74 / £853.76)
Jacqueline buys items online and sells them in her shop.
Jacqueline bought a painting for £320 and sold it for £415.
(a) Calculate the percentage profit that she made.
(or )
Eileen wants to buy a new dining table from the shop.
It is advertised at a price of £800.
Eileen wishes to use a payment plan to buy the dining table.
The total price of the payment plan is 14% more than the advertised price.
The payments are calculated as follows:
(b) Calculate the cost of each monthly instalment.
£58.40
Jacqueline owns shops in Edinburgh, New York and Dubai.
Jacqueline wants an item sent from her Dubai shop to her New York shop.
It will be sent from her Dubai shop at 8:45 am local time on 24 November.
The expected delivery time is 90 hours.
New York is 5 hours behind Edinburgh.
Dubai is 4 hours ahead of Edinburgh.
(c) Determine the local time and date the item is expected to arrive at her New York shop.
5:45 pm (or 17:45) on 27 November