Higher November 2018 Paper 3 Q9
9 A motor racing circuit consists of
two parallel straight sections, each of length 0.75 km
a semicircle of diameter 0.9 km
three equal, smaller semicircles.
Not drawn accurately
The length of a motor race must be greater than 305 km
What is the lowest number of full laps needed at this circuit?
You must show your working. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.9 \times \pi \div 2\) or \(0.9\pi \div 2\) or \(0.45\pi\) or \(0.9 \times [3.14, 3.142] \div 2\) or \([2.82, 2.83] \div 2\) or \(2.8 \div 2\) or 1.4… | M1 | Large semicircle |
| \(0.9 \div 3 \times \pi \div 2\) or \(0.3\pi \div 2\) or \(0.15\pi\) or \(0.9 \div 3 \times [3.14, 3.142] \div 2\) or \(0.94… \div 2\) or 0.47… | M1 | Small semicircle May be implied from using 1.4… for three small semicircles in next mark |
| \(\text{their } 1.4…\) \(+\; 3 \times \text{their } 0.47…\) \(+\; 2 \times 0.75\) or \(0.9\pi + 2 \times 0.75\) or \(2 \times \text{their } 1.4… + 2 \times 0.75\) or 4.3… | M1dep | oe dep on both marks |
| \(305 \div \text{their } 4.3…\) or [70.4, 70.94] | M1dep | dep on previous mark |
| 71 with working | A1 |
Additional guidance
| \(0.9\pi\) or 2.8… with no evidence of incorrect method | M1M1 |
| \(0.45\pi \div 2\) | M0 |