Unit 6
4 marks · Easy(a) The distance a cyclist travels, d (in km), is directly proportional to the time t (in hours) he cycles. The cyclist travels 24 km in 2 hours. (b) The cyclist records the distances for several trips as the sequence 12, 24, 36, ... each day.
Write down the formula linking d and t, and find how far the cyclist will travel in 3.5 hours.
Write down the nth term of the sequence 12, 24, 36,...
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) d = 12t; d = 42 km when t = 3.5 km
(b) nth term is 12n
Common mistakes: using an incorrect multiplier for direct proportion; stating wrong nth term
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Finds constant of proportionality (12) or states correct formula.
A1 (a) · 1 mark · Calculates correct distance for t = 3.5 hours (42 km). (follow-through)
M1 (b) · 1 mark · Recognises sequence is arithmetic with common difference 12.
A1 (b) · 1 mark · Gives nth term as 12n.
Worked solution
(a) Since d ∝ t, d = kt. When t = 2, d = 24, so 24 = k × 2, so k = 12. The formula is d = 12t.
For t = 3.5: d = 12 × 3.5 = 42 km.
(b) It's an arithmetic sequence with first term 12 and common difference 12, so nth term = 12n.