There are 8 street lights in Ffordd Alwyn. Each light is fitted with an 80 watt light bulb.
Each of the 8 street lights is usually on from 6 p.m. to 6 a.m.
It costs 32.4p per hour for each kilowatt of electricity used.
How much would be saved per week if the 8 street lights were only on from 7 p.m. to 5 a.m.? Give your answer in pounds, correct to the nearest penny. You must show all your working. [5]
(b)
A lamp post is vertical and stands on horizontal ground. The angle of elevation of the top of the lamp post is 68° when measured from a point 3.3 m from the centre of the base of the lamp post.
Diagram not drawn to scale
Calculate the height of the lamp post. [3]
Mark scheme (a)
Scheme
Marks
Comments
Method not directly working with a stated or omitted number of hours difference
Methods may be shown in stages or be embedded Use this method if 2 separate numbers of hours are used, which may not be correct, i.e. ≠12 and ≠10, with or without indication of subtraction
Penalise every additional spurious term by reducing the count of correct terms by 1*
0.324 × 8 × (10 or 12) × 7 × 80 ÷ 1000
M3
Allow ‘× 32.4’ for ‘× 0.324’ M2 for any 4 or 5 correct terms* M1 for any 3 correct terms*
0.324 × 8 × (12 or 10) × 7 × 80 ÷ 1000 with the intention to subtract
m1
Must be an indication of the intention to subtract, in either order FT from 5 (or 6) consistent correct terms for use of
the other value 10 or 12 respectively
‘their number of hours’ are 13 and 11 (incorrect)
Award m0 if inconsistent, i.e. not an equal number of consistent correct terms* between the expressions. Mark ‘their better stated calculation’ first if both are given
(Saving is 17.418… – 14.515…=) (£) 2.90
A1
CAO All working must be checked, do not award 5 marks for £2.90 from incorrect working.
Alternative
Scheme
Marks
Comments
Alternative method: Method directly working with a stated or omitted number of hours difference
Methods may be shown in stages or be embedded Use this method if a single number of hours is used, which may not be correct, i.e. ≠2, or if the number of hours is omitted
Do not allow 2 hours as a correct term from incorrect working, e.g. 13 – 11 = 2
Penalise every additional spurious term by reducing the count of correct terms by 1*
0.324 × 8 × 2 × 7 × 80 ÷ 1000
M4
Allow ‘× 32.4’ for ‘× 0.324’ M3 for any 5 correct terms* M2 for any 4 correct terms* M1 for any 3 correct terms*
(Saving is) (£) 2.90
A1
CAO All working must be checked, do not award 5 marks for £2.90 from incorrect working.
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