Fractions: WJEC GCSE Intermediate June 2023 Unit 1 Q10

Intermediate June 2023 Unit 1 Q10

WJECIntermediateCurrent spec4 marksFractions

10. A number machine is shown below.

Number machine: INPUT, arrow, box 'Decrease the number by 1/4 of its value.', arrow, OUTPUT

For a given INPUT number, there will be an OUTPUT number.
The OUTPUT is then put back in the number machine as the next INPUT.
This process is then repeated many times.

The first INPUT number is 512.
What will be the first OUTPUT number that is less than 300? [4]

First OUTPUT number that is less than 300 = ……………………

Mark scheme

Scheme	Marks	Comments
\(\dfrac{3}{4}\) × 512 OR 512 – \(\dfrac{1}{4}\) × 512 or equivalent	M1	Award M1 for full method for calculating the OUTPUT.(Note: 512 – 128).
= 384	A1
\(\dfrac{3}{4}\) × 384 OR 384 – \(\dfrac{1}{4}\) × 384 or equivalent	M1	Award M1 for full method for calculating the OUTPUT.(Note: 384 – 96). FT ‘their 384’ if greater than 300.
(OUTPUT =) 288 ISW	A1	FT if ‘their 288’ < 300, or further evaluation correctly carried out until their output < 300. If no marks gained allow SC1 for sight of 128. Award M2 for \(\dfrac{9}{16}\) × 512 with answer of 288 is awarded A2.