Section A

Answer all questions in the boxes provided. Working may be continued below the lines if necessary.
1. [Maximum mark: 7]
The following table shows the average number of hours per day spent watching television by seven mothers and each mother’s youngest child.

The relationship can be modelled by the regression line with equation y = ax + b .


  • (i) Find the correlation coefficient.
  • (ii) Write down the value of a and of b

Elizabeth watches television for an average of 3.7 hours per day.

(b) Use your regression line to predict the average number of hours of television watched per day by Elizabeth’s youngest child. Give your answer correct to one decimal place.


2.[Maximum mark: 5]
Consider the expansion of  .
(a) Write down the number of terms in this expansion. [1]
(b) Find the term in x³ .


3. [Maximum mark: 6]
In an arithmetic sequence  .

(a) Write down the value of the common difference. [1]

(b) Find the first term. [3]

(c) Find the sum of the first 50 terms of the sequence.


4. [Maximum mark: 7]
Let f(x)=2x-6/1-x, for x ≠ 1 .
(a) For the graph of f
(i) find the x-intercept;
(ii) write down the equation of the vertical asymptote;
(iii) find the equation of the horizontal asymptote. 

(b) Find .


5. [Maximum mark: 6]
Let G (x) =  + 40 , for 20 ≤ x ≤ 200 .
(a) On the following grid, sketch the graph of G .

(b) Robin and Pat are planning a wedding banquet. The cost per guest, G dollars, is modelled by the function G (n) = + 40 , for 20 ≤ n ≤ 200 , where n is the number of guests.

Calculate the total cost for 45 guests.


6. [Maximum mark: 7]
Let f(x) = ln (4)/X, for 0 < x ≤ 5 .

Points P (0.25 , 0) and Q are on the curve of f . The tangent to the curve of f at P is perpendicular to the tangent at Q . Find the coordinates of Q .


7. [Maximum mark: 7]
The following diagram shows part of the graph of f (x) = −2x³ + 5.1x² + 3.6x − 0.4.

(a) Find the coordinates of the local minimum point.

(b) The graph of f is translated to the graph of g by the vector . Find all values of k so that g(x) = 0 has exactly one solution.


Section B部分省略。。。。。



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