Pythagoras: WJEC GCSE Numeracy Higher November 2021 Unit 2 Q9

Numeracy Higher November 2021 Unit 2 Q9

WJECHigherCurrent spec7 marksPythagoras

9. The entrance to a new hotel is to have two equal-sized sloping glass panels, symmetrically placed on either side of the main doors.

The glass panels, ABC and DEF, will be in the shape of right-angled triangles.

The diagrams below show some of the dimensions.

Diagrams not drawn to scale

(a) Calculate the length of AB. [5]

(b)

Metal edging strips are needed along the edges AB and DE.
The metal edging strips come in 45 cm lengths and can be cut to any length.

What is the minimum number of edging strips needed to cover the two edges AB and DE? [2]

Mark scheme (a)

Scheme	Marks	Comments
(Hzntl distance from C to A =) 450 (cm)	B1
(AB =) \(\sqrt{400^2 + 450^2 + 480^2}\)	M3	May be seen in stages FT ‘their 450’ provided < 600 AND provided not an underived 300 or 400 or 480 M2 for \(\sqrt{400^2 + \text{‘their }450\text{’}^2 + 480^2}\) where 600 ⩽ ‘their 450’ < 1200 OR ‘their 450’ = an underived 300 or 400 or 480, or 400\(^2\) + 450\(^2\) + 480\(^2\) with the same FT as for M3 M1 (may be embedded in further working), with the same FT as for M3, for 400\(^2\) + 450\(^2\) OR 450\(^2\) + 480\(^2\) OR 400\(^2\) + 480\(^2\) or \(\sqrt{400^2 + 450^2}\) (= \(\sqrt{362500}\)) (=602.0(7…)) OR \(\sqrt{450^2 + 480^2}\) (= \(\sqrt{432900}\)) (=657.9(5…)) OR \(\sqrt{400^2 + 480^2}\) (= \(\sqrt{390400}\)) (=624.8(1…))
(AB =) 770 (cm)	A1	CAO. Must be from \(\sqrt{592900}\) Note: an answer of 770.0 (cm) is evidence of rounding an incorrect answer and is awarded A0

Scheme

Marks

Comments

(Hzntl distance from C to A =) 450 (cm)

(AB =) \(\sqrt{400^2 + 450^2 + 480^2}\)

May be seen in stages
FT ‘their 450’ provided < 600 AND provided not an underived 300 or 400 or 480

M2 for

\(\sqrt{400^2 + \text{‘their }450\text{’}^2 + 480^2}\) where
600 ⩽ ‘their 450’ < 1200 OR ‘their 450’ = an underived 300 or 400 or 480, or
400\(^2\) + 450\(^2\) + 480\(^2\) with the same FT as for M3

M1 (may be embedded in further working), with the same FT as for M3, for

400\(^2\) + 450\(^2\) OR 450\(^2\) + 480\(^2\) OR 400\(^2\) + 480\(^2\)
or
\(\sqrt{400^2 + 450^2}\) (= \(\sqrt{362500}\)) (=602.0(7…)) OR
\(\sqrt{450^2 + 480^2}\) (= \(\sqrt{432900}\)) (=657.9(5…)) OR
\(\sqrt{400^2 + 480^2}\) (= \(\sqrt{390400}\)) (=624.8(1…))

(AB =) 770 (cm)

CAO. Must be from \(\sqrt{592900}\)
Note: an answer of 770.0 (cm) is evidence of rounding an incorrect answer and is awarded A0

Mark scheme (b)

Scheme	Marks	Comments
2 × 770 ÷ 45 (=34.222…) (Number of strips =) 35	M1 A1	FT ‘their 770’ from (a) Needs to be correctly rounded up If FT ‘their 770’, must come from doubling then rounding, not rounding then doubling Note: if 2 × ‘their 770’ ÷ 45 results in an integer, then award M1A0