Basic Trigonometry: WJEC GCSE Numeracy Higher November 2021 Unit 2 Q5

Numeracy Higher November 2021 Unit 2 Q5

WJECHigherCurrent spec10 marksBasic Trigonometry Pythagoras

5. Mr Read is building a shelter against his house.

(a)

The length of the shelter is 6 m.

Photo of the shelter against the house, with its length along the house wall labelled 6 metres

He has drawn a sketch of the side view of the shelter, as shown below.

Mr Read has started to place some panels on his roof.
When fitted to the roof, each panel needs to slightly overlap the next panel.
The plan view of placing the first 3 panels is also shown below.

Side view: a roof panel slopes up from the top of a post to the house outside wall, horizontal distance 4·2 m, rise 1·1 m, Length of panel along the slope. Incomplete plan view showing first 3 panels: 1 metre wide panels, each of length Length of panel, slightly overlapping

Diagram not drawn to scale

The shelter roof panels are 1 metre wide and can be bought in different lengths.

Length of panel	4·1 m	4·2 m	4·3 m	4·4 m	4·5 m	4·6 m
Cost per panel	£21	£22	£23	£24	£25	£26

Mr Read bought the cheapest suitable panels to build his shelter roof.
Calculate the cost of all of the panels Mr Read bought.
You must show all your working. [6]

(b)

Side view: the roof slopes up to the outside wall of the house; horizontal 4·2 m, vertical 1·1 m; the angle between the roof and the outside wall of the house is marked

Diagram not drawn to scale

Calculate the size of the angle between the shelter roof and the outside wall of the house.
Give your answer correct to 3 significant figures. [4]

Mark scheme (a)

Scheme

Marks

Comments

(Length\(^2\) =) 4.2\(^2\) + 1.1\(^2\)

Or alternative full method

Length\(^2\) = 18.85 or (Length =) √18.85

(Length) 4.3(416…m)

FT from M1, A0 for the correctly evaluated square root of ‘their 18.85’ provided ‘their answer’ > 4.2 (m)
If 4.3(4...) not seen, this A1 may be implied by the sight of choice of panel 4.4(m)
Do not accept an unsupported answer of 4.3 (m)

Selects 4.4 m length

May be implied by use of £24 in further working
FT where possible the length immediately > ‘their 4.3416...’ provided M1 previously awarded and ‘their 4.3416...’ has not been rounded down or truncated to give a different length from the table

(Number of panels needed is ) 7 (panels)

Allow B1 for 8 (panels) (thinking overlap may be as much as approximately ¼ of the width of a panel)
Do not award B1 for 7 or 8 panels if incorrect logic from misinterpretation seen, e.g. working with area 26.05m\(^2\) so buy 7 of the 4.1m panels with area 28.7m\(^2\)

(Cost of the shelter roof £24 × 7) (£) 168

FT provided B1 previously awarded
FT ‘their derived 4.4’ provided > 4.2 m

4.3 m	23 × 7	(£)161
4.5 m	25 × 7	(£)175
4.6 m	26 × 7	(£)182

Allow for 8 panels:

4.3 m	23 × 8	(£)184
4.4 m	24 × 8	(£)192
4.5 m	25 × 8	(£)200
4.6 m	26 × 8	(£)208

Mark scheme (b)

Scheme	Marks	Comments
tan angle between roof and wall = \(\dfrac{4.2}{1.1}\)	M1	Or alternative full method
75.3(°)	A3	Ignore incorrect units Must be to 3 significant figures A2 for 75.32(3…°) or 75(°) OR A1 for tan\(^{-1}\) \(\dfrac{4.2}{1.1}\) From an alternative full method, award A2 maximum for ‘their accurate answer’ with errors due to rounding or truncation in stages of working, if the final answer is given correct to 3 significant figures, or A1 otherwise Note: Use of tan angle between roof and wall = 1.1/4.2 is awarded M0 A0 If no marks, award SC1 for ‘their derived angle’ given correctly to 3 significant figures (tan\(^{-1}\) 1.1/4.2 = 14.7(°) to 3 significant figures)