IB DP Math MAA SL : IB Style Mock Exams – Set 9 Paper 2

The following table shows the number of skateboards y that are sold x days after the shop opened.

Time after opening (x days)	2	4	6	8	10	12
Skateboards sold (y)	10	19	28	36	45	55

This data can be modelled by the regression line with equation y = ax + b.

(a) (i) Write down the value of a and the value of b.

(ii) Explain what the gradient a represents.

(b) Use the model to estimate the number of skateboards sold in 5 days after the shop opened. Round your answer to the nearest integer.

Answer/Explanation

Ans:

(a) (i) a ≈ 4.44 and b ≈ 1.07 [ by using G.D.C.]

(ii) 4.44; each day after the shop opened the number of skateboards sold increases by 4.44

(b) Evaluating y = 4.44x + 1.07 for x = 5, we get

y = 4.44(5) + 1.07

= 23.27

≈ 23 skateboards

Let f(x) = x³ and g(x) = 5(x – 2)³, for x ∈ R.

The graph of g can be obtained from the graph of f using two transformations.

(a) Give a full geometric description of each of the two transformations.

The graph of g is translated by the vector \(\binom{4}{-1}\) to give the graph of a function h.

The point P(1, 1) on the graph of f is translated to point Q on the graph of h.

(b) Find the coordinates of Q.

Answer/Explanation

Ans:

(a) We have

Transformation 1 : vertical stretch by a factor of 5

transformation 2 : translation by the vector \(\binom{2}{0}\)

(b) We have

transformation 3: translation by the vector \(\binom{4}{-1}\)

If we apply the transformations 1, 2 and 3 to P, we find

Hence the coordinates of Q are (7, 4)