Numeracy Intermediate June 2019 Unit 1 Q5
5. Rupert Shoes sells shoes online.
Diagram not drawn to scale
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
She takes the sketch to the printers.
The table shows the costs for printing 100 labels.
| Area of label, to the nearest cm2 | Cost to print 100 labels |
|---|---|
| Up to 80 cm2 | £1.15 |
| 81 cm2 to 85 cm2 | £1.25 |
| 86 cm2 to 89 cm2 | £1.50 |
| 90 cm2 or more | £1.75 |
How much will it cost to have 500 of the designer’s label printed?
You must show all your working. [4]
The dimensions of the shoebox used are given on the diagram below.
Diagram not drawn to scale
Circle your answer. [1]
40 cm2 225 cm2 375 cm2 800 cm2 1000 cm2
The package for sending the shoes to the customer is made by:
- placing one box on top of the other, and
- taping the two boxes together.
This is shown in the diagram.
The cost for sending the package is calculated using the formula below. All dimensions are measured in cm.
Cost in £ = \(\dfrac{1}{5}\) × (S + F) × 0·02
S = value of the sum of the 3 dimensions of the package
F = value of the area of one of the largest faces of the package
How much does it cost Rupert Shoes to send the package?
Give your answer in pounds.
You must show all your working. [5]
| Scheme | Marks | Comments | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (Area) ½ × 8 × (10 + 12) or 10 x 8 + ½ × 8 × (12-10) | M1 | |||||||||||
| 88 (cm2) | A1 | |||||||||||
| (Cost) 5 × 1.5(0) | M1 | Strict FT for ‘their derived area’ used with the table of charges A ‘derived area’ is a value obtained form any calculation which a candidate considers as ‘their area’ | ||||||||||
| (£)7.5(0) | A1 | FT for ‘their derived area’ used to select the charge
|
| Scheme | Marks | Comments | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (i) 375 (cm2) | B1 | |||||||||||||||||||||
| (ii) (Value sum dimensions) 40+25+30 (S = 95) | B1 | |||||||||||||||||||||
| (Value area largest face) 30 × 40 (F = 1200) | B1 | |||||||||||||||||||||
For sight of any 1 of the following:
| B1 | Not a FT mark | ||||||||||||||||||||
| Any correct substitution into the given formula, e.g. (Cost) 1/5 × (95 + 1200) × 0.02 (= 259 × 0.02) or ⅕ × 95 × 0.02 + ⅕ × 1200 ×0.02 (= 0.38 + 4.8(0)) | M1 | FT ‘their derived S’ + ‘their derived F’ (‘derived’ meaning not taken from the diagram) Allow intention of brackets, provided not contradicted For a single calculation or may be seen in stages Allow M1 for ⅕ ×1295 × 2 or ⅕ × 95 × 2 + ⅕ × 1200 ×2 | ||||||||||||||||||||
| (=) (£) 5.18 | A1 | Examples of possible FT answers:
|