Higher November 2020 Paper 1 Q12
12 Two wire shapes make an earring.
The shapes are
a circle with radius 21 mm
and
a quarter circle.
Not drawn accurately
| radius of circle : radius of quarter circle \(= 7 : 2\) |
(a) Show that the radius of the quarter circle is 6 mm [1 mark]
(b) Work out the total length of the wire in the earring.
Give your answer in the form \(\quad a\pi + b \quad\) where \(a\) and \(b\) are integers. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(21 \div 7 \times 2\ (= 6)\) or \(21 \div 3 = 7\) and \(6 \div 3 = 2\) or \(21 \div 7 = 3\) and \(6 \div 2 = 3\) or \(7 \times 3 = 21\) and \(2 \times 3 = 6\) | B1 | oe eg \(6 \div 2 = 3\) and \(7 \times 3 = 21\) |
Additional guidance
| \(3 \times 2\ (= 6)\) | B0 |
| \(7 : 2\ (=)\ 21 : 6\) with no other working | B0 |
| \(7 : 2\ (=)\ 21 : 6\) with multiplication by 3 shown by arrow(s) | B1 |
| \(7 : 2\ (=)\ 14 : 4\ (=)\ 21 : 6\) | B1 |
| Do not condone incorrect representation of a division eg \(7 \div 21 = 3\) | B0 |
| Do not condone incorrect mathematical representation eg \(21 \div 7 = 3 \times 2 = 6\) | B0 |
| \(21 \div 6 = 3.5\), \(3.5 \times 2 = 7\) | B1 |
| \(21 \times 2 = 42\), \(42 \div 7 = 6\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(2 \times \pi \times 21\) or \(\pi \times 42\) or \(42\pi\) or [131.88, 132] | M1 | oe condone [3.14, 3.142] for \(\pi\) |
| \(2 \times \pi \times 6 \div 4\) or \(\pi \times 12 \div 4\) or \(3\pi\) or [9.4, 9.43] | M1 | oe arc length of quarter circle condone [3.14, 3.142] for \(\pi\) |
| \(2 \times \pi \times 6 \div 4 + 2 \times 6\) or \(3\pi + 12\) or [21.4, 21.43] | M1dep | oe dep on 2nd M1 this does not imply M1M1M1 |
| \(45\pi + 12\) | A1 | |
| Alternative method 2 | ||
| \(2 \times \pi \times 21\) or \(\pi \times 42\) or \(42\pi\) or [131.88, 132] | M1 | oe condone [3.14, 3.142] for \(\pi\) |
| \(2 \times \pi \times 21\) and \(2 \times \pi \times 6 \div 4\) or \(42\pi\) and \(3\pi\) or \(2 \times \pi \times 21 + 2 \times 6\) or \(42\pi + 12\) or [143.88, 144] | M1dep | oe eg \(42\pi\) and [9.4, 9.43] or [131.88, 132] and \(3\pi\) |
| \(2 \times \pi \times 21 + 2 \times \pi \times 6 \div 4\) or \(42\pi + 3\pi\) or \(45\pi\) or [141, 141.43] or [153, 153.43] | M1dep | oe eg \(42\pi +\) [9.4, 9.43] or [131.88, 132] \(+ 3\pi\) |
| \(45\pi + 12\) | A1 | |
Additional guidance
| Condone \(\quad 3(15\pi + 4)\) | M1M1M1A1 |
| Condone, for example, \(\pi 42\) for up to M1M1M1 | |
| \(21\pi + 3\pi + 12\) | M0M1M1A0 on alt 1 |
| \(441\pi + 3\pi + 12\) | M0M1M1A0 on alt 1 |
| \(42\pi + 36\pi + 12\) | M1M1M0A0 on alt 2 |
| \(441\pi + 36\pi + 12\) | M0M0M0A0 |
| Using \(\pi r^2\) instead of \(2\pi r\) throughout | M0M0M0A0 |
| \(45\pi + 12\) in working with incorrect further work, eg \(45\pi + 12 = 57\pi\) | M1M1M1A0 |