12. Robyn has 5 planks of wood each of length 2 m and width 10 cm.
Diagram not drawn to scale
She lays the 5 planks horizontally on the floor. She leaves a 15 cm gap between each plank, as shown below.
Diagram not drawn to scale
Robyn is planning to make a gate. She uses these 5 planks and one other plank that is to be placed diagonally, as shown below.
Diagram not drawn to scale
(a)
(i) Calculate an estimate of the length of the plank that is to be placed diagonally. Give your answer in metres. [4]
(ii) What assumption did you make in calculating the length of the plank that is to be placed diagonally? [1]
(b) Robyn finishes the gate with two end planks of wood.
Diagram not drawn to scale
The costs of the different sizes of planks of wood are in the following ratio:
cost of 1 horizontal plank : cost of 1 diagonal plank : cost of 1 end plank
= 3 : 4 : 5
An end plank costs £8.55. Calculate the total cost of the planks needed to make the gate. [4]
Mark scheme (a)
Scheme
Marks
Comments
(i) Height of the gate 110 (cm) or 1.1(0 m)
B1
Allow other estimates of height of the gate (100 cm to 110 cm inclusive) If units are given they must be correct If incorrect conversion of units seen later, B0 and FT for possible M1 A1 A1
(Diagonal2 =) 22 + 1.12 or 2002 + 1102
M1
FT ‘their derived 110 or 1.1(0)’ provided units are consistent in the application of Pythagoras’ Theorem Allow use of 190 cm to 200 cm for the width of the gate in calculating the diagonal length
Diagonal2 = 5.21 or (Diagonal =) √5.21 or Diagonal2 = 52100 or (Diagonal =) √52100 or 228.(...cm)
A1
(Diagonal = ) 2.28(...m) or 2.3(m)
A1
Answer must be in metres Allow truncation to 2.2(m) Do not accept truncation to 2(m) FT from M1 for the correctly evaluated square root of ‘their 5.21’ provided ‘their answer’ > 2 (m) for possible A1
(ii) Assumption, e.g. ‘diagonal plank went to each end’, ‘thought of the planks as lines’, ‘that it is a right angle (triangle)’, ‘it goes from corner to corner’
E1
Allow, e.g. ‘no thickness’ (allow as implying width) ‘width (or length) of gate is not exact’ (could mean diagonal plank not quite touching across full width of the gate)
Do not accept, e.g. ‘all planks have the same thickness’ (as not an assumption whether meaning width or not), ‘the gaps are not exact’ (as question defines the gaps) ‘lengths are not exact’, ‘that this diagonal plank is longer than the others’, ‘it’s straight’
Ignore additional spurious comments
Mark scheme (b)
Scheme
Marks
Comments
(Cost of 1 horizontal plank is) (£) 3 × 8.55 ÷ 5 OR (Cost of 1 diagonal plank is) (£) 4 × 8.55 ÷ 5
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