Numeracy Foundation November 2023 Unit 1 Q8
8.
(a)
Rita gives some money to charity.
She decides to share this money between 3 different charities.
Rita gives $40 to a children’s charity.
This is \(\dfrac{1}{5}\) of the total amount of money she gives to the 3 charities.
Rita gives \(\dfrac{1}{4}\) of the total amount of money to an animal charity.
She gives the remaining money to a medical research charity.
Calculate how much money Rita gives to the medical research charity.
You must show all your working. [5]
(b)
Last year, Rita’s total income before tax was $30 000.
No income tax was payable on any income below $10 000.
Income tax had to be paid at a rate of 22% on any income between $10 000 and $30 000.
How much income tax did Rita pay last year? [3]
| Scheme | Marks | Comments |
|---|---|---|
| (\(\dfrac{1}{5}\) is $40, total amount of gift is) 40 × 5 or 40 ÷ \(\dfrac{1}{5}\) | M1 | Ignore $ written as £ or €, etc |
| ($)200 | A1 | ISW |
| (Amount gifted to animal charity is ¼ × 200) ($)50 | B1 | FT ¼ × ‘their 200’ correctly evaluated, provided
|
| (Gift to medical research is) ($) 200 – 40 – 50 | M1 | FT ‘their derived 200’ – 40 – ‘their 50’, provided > 0 |
| ($) 110 | A1 | FT provided both M marks previously awarded If no marks, award SC1 for (40 – \(\dfrac{1}{5}\) × 40 – ¼ × 40 = 40 – 8 – 10 =) ($)22 |
8(a) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Total amount of gift is) 40 × 5 or 40 ÷ \(\dfrac{1}{5}\) | M1 | Ignore $ written as £ or €, etc |
| ($)200 | A1 | ISW |
| (Proportion given to medical charity) (1 – \(\dfrac{1}{5}\) – \(\dfrac{1}{4}\) =) \(\dfrac{11}{20}\) or (1 – 0.2 – 0.25 =) 0.55 or (100 – 20 – 25 =) 55 (%) | B1 | Allow for proportion given to children’s and animal charity clearly shown as \(\dfrac{9}{20}\) , 0.45 or 45 (%) |
| (Gift to medical research is) \(\dfrac{11}{20}\) × 200 or 200 – \(\dfrac{9}{20}\) × 200 | M1 | FT ‘their incorrectly evaluated 1 – \(\dfrac{1}{5}\) – \(\dfrac{1}{4}\) ’ or ‘their incorrectly evaluated \(\dfrac{1}{5}\) + \(\dfrac{1}{4}\) as appropriate and ‘their derived 200’, provided
|
| ($) 110 | A1 | FT provided both M marks previously awarded |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 30 000 – 10 000 or 20 000 | B1 | Ignore incorrect units given throughout |
| (30 000 – 10 000) × 0.22 or 20 000 × 0.22 or equivalent | M1 | Any repeated addition method of 10% and 1% must clearly show addition to 22% |
| ($) 4400 | A1 | CAO. Mark final answer |