Higher November 2022 Paper 2 Q12
12 The length of this rectangle is 6 times the width.
Two of these rectangles are joined, with no overlap, to make this L-shape.
The perimeter of the L-shape is 98.8 cm
Work out the value of the perimeter of one of the rectangles. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6x + x + 5x + 6x + x + 6x + x\) or \(26x\) or \(6 + 1 + 5 + 6 + 1 + 6 + 1\) or 26 | M1 | oe eg \(7x + 6x - x + 6x + x + 6x + x\) \(26x\) or 26 is implied by 3.8 oe if addition not seen |
| their \(26x = 98.8\) or \(98.8 \div\) their 26 or 3.8 or \(\dfrac{19}{5}\) | M1 | oe equation must have terms collected if 1st M1 not awarded their \(26x\) must be \(24x\) or \(25x\) or \(27x\) if 1st M1 not awarded their 26 must be 24 or 25 or 27 |
| their \(3.8 \times 14\) | M1dep | dep on 2nd M1 oe eg \(45.6 + 7.6\) |
| 53.2 | A1ft | oe ft their 3.8 if M0M2 awarded |
| Alternative method 2 | ||
| \(6x + x + 6x\) or \(13x\) or \(6 + 1 + 6\) or 13 | M1 | oe eg \(6x + x + 5x + x\) \(13x\) or 13 is implied by 3.8 oe if addition not seen |
| their \(13x = 98.8 \div 2\) or \(49.4 \div\) their 13 or 3.8 or \(\dfrac{19}{5}\) | M1 | oe equation must have terms collected if 1st M1 not awarded their \(13x\) must be \(12x\) if 1st M1 not awarded their 13 must be 12 |
| their \(3.8 \times 14\) | M1dep | dep on 2nd M1 oe eg \(49.4 + 3.8\) |
| 53.2 | A1ft | oe ft their 3.8 if M0M2 awarded |
Additional guidance
| Up to M3 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts | |
| Follow through must be to at least 1 dp and their 26 or their 13 must be seen For information: \(24 \to 57.6\ldots \quad 25 \to 55.3\ldots \quad 27 \to 51.2\ldots \quad 12 \to 57.6\ldots\) | M0M1M1A1ft |
| Both 2nd and 3rd method marks may be implied by their answer. If not using 24, 25, 26, 27, 12 or 13 you must have seen the first M1. | |
| \(27x = 98.8\) (1st M0, no addition seen, but \(27x\) allowed) \(\dfrac{98.8}{27} \times 14\), answer 51.2 | M0M1 M1A1ft |
| \(7x + 5x + 6x + x + 6x + x = 20x\) (correct terms added with incorrect total) \(98.8 \div 20 = 4.94\) 69.16 (multiplication by 14 implied) | M1 M1 M1A0 |
| \(98.8 \div 20 = 4.94\) (1st M0, no addition seen, and 20 not allowed) \(4.94 \times 14\), answer 69.16 | M0M0 M0A0 |
| \(6x + x + 5x + 6x + x + 6x + x = 26x^7\) | M1M0M0A0 |