Higher November 2017 Paper 2 Q22
22 The cross section of an earring is a semicircle, centre \(C\), radius 25 mm
The earring is black and white.
The shaded area is black.
Not drawn accurately
Sector \(BCD\) is white and has radius 12 mm
Not drawn accurately
Is more than 20% of the semicircle white?
You must show your working. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (\(\dfrac{1}{2} \times\)) \(\pi \times 25 \times 25\) or \(625\pi\) or \(312.5\pi\) or [1962.5, 1964] or [981, 982] or \(\pi \times 12 \times 12\) or \(144\pi\) or [452, 452.45] | M1 | oe Area of circle or semicircle radius 25 or area of circle radius 12 |
| \(\dfrac{150}{360}\) or \(\dfrac{5}{12}\) or 0.41(6…) or 0.417 or 0.42 or \(\dfrac{360}{150}\) or \(\dfrac{12}{5}\) or 2.4 | M1 | May be seen in two steps eg \(\times\, 150 \div 360\) |
| their \(\dfrac{150}{360} \times \pi \times 12 \times 12\) or \(\pi \times 12 \times 12 \div\) their \(\dfrac{360}{150}\) or \(60\pi\) or [188.4, 188.52] | M1dep | oe dep on M2 Area of sector |
| \(\dfrac{\text{their } [188.4, 188.52]}{\text{their } [981, 982]}\) (\(\times\, 100\)) or [0.19, 0.1922] or [19, 19.22] | M1dep | oe dep on M3 their [981, 982] must be the area of semicircle radius 25 |
| [19, 19.22] and No or [0.19, 0.1922] and 0.2 and No | A1 | |
| Alternative method 2 | ||
| (\(\dfrac{1}{2} \times\)) \(\pi \times 25 \times 25\) or \(625\pi\) or \(312.5\pi\) or [1962.5, 1964] or [981, 982] or \(\pi \times 12 \times 12\) or \(144\pi\) or [452, 452.45] | M1 | oe Area of circle or semicircle radius 25 or area of circle radius 12 |
| \(\dfrac{150}{360}\) or \(\dfrac{5}{12}\) or 0.41(6…) or 0.417 or 0.42 or \(\dfrac{360}{150}\) or \(\dfrac{12}{5}\) or 2.4 | M1 | May be seen in two steps eg \(\times\, 150 \div 360\) |
| their \(\dfrac{150}{360} \times \pi \times 12 \times 12\) or \(\pi \times 12 \times 12 \div\) their \(\dfrac{360}{150}\) or \(60\pi\) or [188.4, 188.52] | M1dep | oe dep on M2 Area of sector |
| their \([188.4, 188.52] \times 5\) or [942, 942.6] | M1dep | oe dep on M3 |
| [942, 942.6] and [981, 982] and No | A1 | oe eg \(300\pi\) and \(312.5\pi\) and No |
| Alternative method 3 | ||
| (\(\dfrac{1}{2} \times\)) \(\pi \times 25 \times 25\) or \(625\pi\) or \(312.5\pi\) or [1962.5, 1964] or [981, 982] or \(\pi \times 12 \times 12\) or \(144\pi\) or [452, 452.45] | M1 | oe Area of circle or semicircle radius 25 or area of circle radius 12 |
| \(0.2 \times\) their [981, 982] or \(62.5\pi\) or [196.2, 196.4] | M1dep | oe dep on 1st M1 their [981, 982] must be the area of semicircle radius 25 |
| \(\dfrac{150}{360}\) or \(\dfrac{5}{12}\) or 0.41(6…) or 0.417 or 0.42 or \(\dfrac{360}{150}\) or \(\dfrac{12}{5}\) or 2.4 | M1 | May be seen in two steps eg \(\times\, 150 \div 360\) |
| their \(\dfrac{150}{360} \times \pi \times 12 \times 12\) or \(\pi \times 12 \times 12 \div\) their \(\dfrac{360}{150}\) or \(60\pi\) or [188.4, 188.52] | M1dep | oe dep on 1st M1 and 3rd M1 Area of sector |
| [188.4, 188.52] and [196.2, 196.4] and No | A1 | oe eg \(60\pi\) and \(62.5\pi\) and No |
Additional guidance
Alt 3 20% of [981, 982] does not score 2nd M1 unless evaluated correctly