Higher January 2022 Paper 1R Q10
10 Jonty has a storage container in the shape of a cuboid, as shown in the diagram.
Diagram NOT accurately drawn
Jonty is going to paint the outside of his storage container, apart from the base which is shown shaded in the diagram.
He needs enough paint to cover the four sides and the top.
Each tin of paint covers an area of 15 m2
The cost of each tin of paint recently increased by 10%
After the increase, the cost of each tin of paint is £26.95
Jonty says
“Before the increase, I could have bought enough paint for less than £200”
Show that Jonty is correct.
Show your working clearly.
(6)
| Scheme | Marks |
|---|---|
| 3 × 2.5 (= 7.5) oe or 2 × 3 × 2.5 (= 15) oe or 12 × 3 (= 36) oe or 2 × 12 × 3 (= 72) oe or 12 × 2.5 (= 30) | M1 |
| (2 × 3 × 2.5) + (2 × 12 × 3) + (12 × 2.5) (= 117) or (2 × 7.5) + (2 × 36) + (12 × 2.5) (= 117) or 15 + 72 + 30 (= 117) | M1 |
1 + 0.1 (= 1.1) or 100(%) + 10(%) (= 110(%)) or \(\dfrac{26.95}{110}\) (= 0.245) oe | M1 |
| 26.95 ÷ “1.1” (= 24.5(0)) or 26.95 ÷ “110” × 100 (= 24.5(0)) or 26.95 × 100 ÷ “110” (= 24.5(0)) oe or “0.245” × 100 (= 24.5(0)) oe | M1 |
| “117” ÷ 15 (= 7.8 or 8) and “8” × “24.50” (= 196) or “117” ÷ 15 (= 7.8 or 8) and 200 ÷ “24.5” (= 8.1...) or “117” ÷ 15 (= 7.8 or 8) and 200 ÷ “8” (= 25) | M1 |
| Working required Answer: Correct figures to show that Jonty is correct | A1 |
| (6) | |
| (6 marks) |
Notes
M1: for area of rectangle
M1: for a complete method to find the surface area
M1: dep on previous M1
M1: for working with a whole number of tins (rounded up) to reach figures where a decision can be made
A1: e.g. 196
7.8 or 8 and 8.1...
24.5 and 25