Yuen Long Public Secondary School - Yearly Examination 2016-2017
S.4 MATHS PAPER I
TIME ALLOWED: 2 HRS 15 MINS
MAX MARK: 105
Section A(1) (35 marks)
Answer ALL questions in this section and write your answers in the space provided.
1. Simplify
and express your answer with positive indices.
(3 marks)
2. Make t the subject of the formula Mt = (2t – K)L .
3. (a)
(b)
(3 marks)
Factorize p2 – 2pq – 8q2.
Factorize p2 – 2pq – 8q2 + 4p – 16q.
(3 marks)
4. The marked price of a tool is $80, but it is sold at a discount of 25%.
(a) Find the selling price of the tool.
(b)
If the profit percentage is 20%, find the cost of the tool.
(4 marks)
5. Solve the quadratic equation x2 + 8x + 17 = 0.
Express your answer in form of a + bi if necessary.
6. Form a quadratic equation in x whose roots are
(3 marks)
and
.
(3 marks)
7. It is given that f (x) = x2 + 2x + k and f (3) = 10.
(a) Find the value of k.
(b) Hence, find the value(s) of x such that f (x) = 3.
(5 marks)
8. Solve the equation 3x+6 = 81x.
(3 marks)
9. It is given that y varies inversely as
. When x = 144, y = 81.
(a) Express y in terms of x.
(b) If the value of x is increased from 144 to 324, find the change in the value of y.
(5 marks)
10. Solve the equation
S4 Math I/ YE 2016-17 / Page 1
5 tan x = 1 for 0  x  360.
(3 marks)
Section A(2) (35 marks)
Answer ALL questions in this section and write your answers in the space provided.
11. Let f (x) = (x – 2)2 (x + h) + k, where h and k are constants. When f (x) is divided by x – 2, the
remainder is –5. It is given that f (x) is divisible by x – 3.
(a) Find the values of h and k.
(3 marks)
(b) Someone claims that all the roots of the equation f (x) = 0 are integers.
Do you agree? Explain your answer.
(3 marks)
12. The cost ($C) of producing a steel cylinder varies jointly as the square of its base
radius (r cm) and its height (h cm). When r = 4 and h = 6, C = 480.
(a)
(b)
Express C in terms of r and h.
(3 marks)
Originally, a factory produces steel cylinders with a certain base radius and height 8 cm.
Now the factory produces new steel cylinders with base radius increased by 25% but
at the same cost. What will be the height of the new steel cylinder?
(3 marks)
13. A man paid $800 for N magazines last month. This month, the price of each magazine is increased by
$5, and he can buy (N – 8) magazines with the same amount of money. Find the value of N.
(5 marks)
14. The number of customers (N) visiting a restaurant on the x-th day since opening is estimated
by N = 200 log (5x + 10).
(a) Find the number of customers on the 3rd day since opening.
(Correct your answer to the nearest integer.)
(2 marks)
(b) If the number of customers on the k-th day is 400, find the value of k.
(3 marks)
15. Figure 1 shows the graph of
y = a cos (x + 60) for 0  x  390.
(a) Find the value of a.
(b) Find
(2 marks)
(i) the maximum value; and
(ii) the minimum value;
of the function y = a cos (x + 60).
(3 marks)
Figure 1
16. The coordinates of the points A and B are (2, 11) and (10, 7) respectively.
(a) (i) Write down the mid-point of AB.
(ii) L passes through the mid-point of AB and perpendicular to AB.
Find the equation of L.
(5 marks)
(b) The coordinates of C is (2, 3). Find the circumcenter of ABC.
(3 marks)
(Hint: The circumcenter of a triangle is the intersection of perpendicular bisectors of its sides.)
S4 Math I/ YE 2016-17 / Page 2
Section B (35 marks)
Answer ALL questions in this section and write your answers in the space provided.
17. Let a and b be constants. Denote the graph of y = a + logb x by G. The x-intercept of G is 9 and
G passes through the point (243, 3). Express x in terms of y.
(4 marks)
18. Solve the equation 10 sin2 x – 3 sin x – 1 = 0 for 0  x  360.
(5 marks)
19. The number (N) of people waiting for organ transplants in a country can be approximated
by the formula N = abt, where t is the numebr of years since the beginning of 2010.
At the beginning of 2011, there are 3300 people waiting for organ transplants.
At the beginning of 2013, there are 3993 people waiting for organ transplants.
(a) Find the values of a and b.
(b) Find the percentage increase in the number of people waiting for organ transplant
from the beginning of 2010 to the beginning of 2020
20. The selling price of a certain luggage tag is $x. The total profit ($P) on the sale of the
luggage tags partly varies directly as x and partly varies directly as x2.
When x = 20, P = 60000. When x = 30, P = 75000.
(a) Find an equation connecting P and x.
(b)
(c)
Find the total profit if the selling price of each luggage tag is $35.
Write down
(i) the maximum total profit from selling the luggage tag; and
(ii) the corresponding selling price of each luggage tag.
21. The equation of the quadratic curve U is y = x2 – 6x + 7.
The equation of the straight line L1 is y = 2x.
(a) Find the intersections of U and L1.
(b) Another straight line L2 is parallel to L1 and touches U at one point P.
(i) Find the equation of L2.
(Hint: You may let L2: y = mx + c.)
(ii) Find the coordinates of P.
(3 marks)
(4 marks)
(2 marks)
(2 marks)
(4 marks)
(7 marks)
End of Paper
S4 Math I/ YE 2016-17 / Page 3
(4 marks)