Numeracy Foundation November 2020 Unit 1 Q5
5.
A plan for a new housing estate includes 2 roads crossing, as shown below.
One of the angles is 35°.
Diagram not drawn to scale
What is the size of angle \(x\)? [1]
\(x\) = …………………… °
The housing estate includes a park for children.
This park is triangular in shape.
A sketch of the park is shown below.
Diagram not drawn to scale
Complete a scale drawing of the park.
Use a scale of 1 cm represents 10 m.
The 90 m line has been drawn for you.
Use your scale drawing to find the actual length of the other 2 sides of the park. [6]
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
Actual lengths of the other 2 sides of the park are:
…………………… m and …………………… m
| Scheme | Marks | Comments |
|---|---|---|
| 35˚ | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 53˚ drawn (±2˚) in correct place 78˚ drawn (±2˚) in correct place | B1 B1 | If B0, B0 but 53˚ (±2˚) and 78˚ (±2˚) swapped, award SC1 |
| Triangle completed | B1 | Award this B1 provided at least one previous B1 or SC1 awarded |
| Two sides measured correctly (9.5 cm and 11.7 cm) | B2 | B1 for each line. Allow ±2 mm. (Range is: 9.3cm to 9.7cm and 11.5cm to 11.9cm) FT their completed triangle This may be implied by their final answers |
| 95 (m) and 117 (m) | B1 | (Range is 93m to 97m and 115m to 119m) FT ‘their measurements’ provided a triangle drawn If previous B2 is awarded B0 or B1 then FT for the final B1 for at least one of ‘their measurements’ × 10 or at least one of ‘their measurements rounded to the nearest whole number of cms’ × 10 eg for 8.4cm award final B1 for 80 or 82 to 86 Note: the 2 answers given must correspond in size to the sides of the triangle. |
Corrected by Westie's Workshop
- The board's mark scheme printed “115m to 117m”. Changed to “115m to 119m” because the line above gives 11.5 cm to 11.9 cm, and ten times that is 115 to 119, so the upper end must be 119.
Original: see the board's mark scheme PDF (link above).