Number 6

4 marks · Hard

A car travels s kilometres in t hours. It is known that s is directly proportional to t, and that when t = 2.5, s = 165.

a) Write down the formula connecting s and t.

b) What is the value of the constant of proportionality?

c) Calculate the value of s when t = 6.4.

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(a) s = k t

(b) 66

Also accept: Full method using ratio arguments

Common mistakes: Incorrectly rearranging the formula.; Failure to substitute values properly.

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Marking points

B1 · 1 mark · States or writes correct general formula for direct proportion: s = k t.

M1 · 1 mark · Use data point to substitute into s = k t to find k (i.e., 165 = k × 2.5).

A1 · 1 mark · Solves for k: k = 66. (follow-through)

A2 · 1 mark · Uses found k to calculate s for t = 6.4: s = 66 × 6.4 = 422.4 km. Allow FT on earlier error for k. (follow-through)

Worked solution

a) Since s is directly proportional to t, s = k t.

b) When t = 2.5, s = 165, so 165 = k × 2.5 => k = 165 / 2.5 = 66.

c) For t = 6.4, s = 66 × 6.4 = 422.4 km.