Algebra 6
4 marks · HardThe time, T seconds, for a chemical reaction is directly proportional to the square of the temperature, t °C. The reaction takes 32 seconds at 40°C.
a) Write down the formula for T in terms of t.
b) Calculate the time for the reaction at 70°C.
c) Find the temperature if the reaction takes 50 seconds.
Write your answer in the form T = k t^2.
Give your answer to 1 decimal place if necessary.
Find t, the temperature, when T = 50.
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) T = 0.02 t^2
(b) 98 s
(c) 50 0C
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Writes T = k t^2 and finds k using 32 = k 0^2
A1 (b) · 1 mark · Correct substitution for t = 70; correctly uses the formula T = 0.02 70^2 (follow-through)
A2 (b) · 1 mark · Correct value for T (accept 98) (follow-through)
A3 (c) · 1 mark · Solves 50 = 0.02 t^2 for t; answer correct to the nearest integer (follow-through)
Worked solution
a) Since T is directly proportional to t squared, T = k t^2.
When T = 32, t = 40: 32 = k 40^2, so k = 32 / 1600 = 0.02.
So, T = 0.02 t^2.
b) When t = 70: T = 0.02 70^2 = 0.02 4900 = 98.
c) When T = 50: 50 = 0.02 t^2, so t^2 = 50 / 0.02 = 2500, so t = 50.