Foundation June 2022 Paper 2 Q15
15 The scale drawing shows a tree and a student.
The actual height of the tree is 4.2 metres.
Work out the actual height of the student. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 Using the given values | ||
| \(4.2 \div 7\) or 0.6 or \(7 \div 4.2\) or 1.66… or 1.67 or \(2.5 \div 7\) or 0.357… or 0.36 or \(7 \div 2.5\) or 2.8 | M1 | implied by \(1 \rightarrow 0.6\) or \(0.5 \rightarrow 0.3\) |
| \(2.5 \times 4.2 \div 7\) | M1dep | oe eg \(2.5 \div (7 \div 4.2)\) or \(2.5 \div 1.67\) or \(4.2 \div (7 \div 2.5)\) or \(4.2 \div 2.8\) or full build-up eg \(0.6 + 0.6 + 0.3\) or \(0.3 \times 5\) or \(4.2 \div 2 - 0.6\) |
| 1.5 | A1 | oe fraction or decimal SC2 answer with digits 15 |
| Alternative method 2 Working consistently in centimetres | ||
| \(4.2 \times 100 \div 7\) or 60 or \(7 \div (4.2 \times 100)\) or 0.0166… or 0.0167 or \(2.5 \div 7\) or 0.357… or 0.36 or \(7 \div 2.5\) or 2.8 | M1 | oe eg \(420 \div 7\) or \(7 \div 420\) implied by \(1 \rightarrow 60\) or \(0.5 \rightarrow 30\) |
| \(2.5 \times 420 \div 7\) or 150 | M1dep | oe eg \(2.5 \div (7 \div 420)\) or \(2.5 \div 0.0167\) or \(420 \div (7 \div 2.5)\) or \(420 \div 2.8\) or full build-up eg \(60 + 60 + 30\) or \(30 \times 5\) or \(420 \div 2 - 60\) |
| 1.5 | A1 | oe fraction or decimal SC2 answer with digits 15 |
Additional guidance
| Up to M1 may be awarded for correct work with no, or incorrect answer, even if this is seen amongst multiple attempts | |
| Answer 1.5 with no working | M2A1 |
| 150 is M2A0 but Answer 150 cm with m crossed out would be M2A1 | |
| 4.2 : 1.5 or 420 : 150 | M2 |
| For consistent working in millimetres or metres apply the principles of Alt 2 | |
| Incorrect or inconsistent change of units must be recovered for M2A0 or M2A1, otherwise score 0 or SC2 | |
| eg1 \(42 \div 7 = 6\), \(6 \times 2.5 = 15\), Answer 1.5 (units recovered) | M2A1 |
| eg2 \(4200 \div 7 = 800\), \(800 \times 2.5 = 2000\), Answer 2 (arithmetic slip but method shown and units recovered) | M2A0 |
| eg3 \(42 \div 7 = 6\), \(6 \times 2.5 = 15\), Answer 15 (units never recovered) | SC2 |
| NB Correct values from incorrect methods | |
| eg1 \(7 - 4.2 = 2.8\) with no other creditworthy work | M0M0A0 |
| eg2 \(2.5 \div 4.2 = 0.6\) (1 dp) with no other creditworthy work | M0M0A0 |
| If rounded or truncated values are used, the final answer must be exactly 1.5 | |
| eg1 \(2.5 \div 1.66\) Answer 1.5 (may have kept full value on calculator) | M2A1 |
| eg2 \(2.5 \div 1.66 = 1.506\) Answer 1.5 (comes from further rounding) | M2A0 |