NAME:……………………………………………………………………………
MARIST SECONDARY SCHOOL
2015/2016 FORM FOUR MOCK EXAMINATION
Mathematics PAPER II
(100 MARKS)
Time Allowed: 2 hrs 30 mins
Wednesday, 16th March, 2016.
Instructions:
1. This paper contains 15 pages. Please check.
2. Write your name on each page of the question paper.
3. This paper has two sections A and B. Answer all the questions in Section A and any
three questions from Section B.
4. Show your working.
5. Marks will be deducted for untidy work.
6. Use of calculators is allowed.
© MARIST
Page 1 of 16
NAME:……………………………………………………………………………
SECTION A
Answer all the six questions in this section
5 3(t−3)
1. a. Simplify 2
− 2
t −3 t −9
(4 marks)
(x)
2
a
b. Given that log a x=0.5488 , evaluate log a
(4 marks)
c. The quantity q is partly constant and partly varies as p. When q = 5, P = 1 and
when q = 26, p = 2. Find g when p = -2.
Page 2 of 16
NAME:……………………………………………………………………………
(4 marks)
2. a. Show that points A(2, 3), B(6, - 1) and C (12, -7)are collinear.
(4 marks)
b. If (x +3) is a factor of x 3 +3 x 2 + 4 x−d . Find the value of d.
Page 3 of 16
NAME:……………………………………………………………………………
(5 marks)
2
3. a. Chimwemwe travels to work by a car or minibus. There is a probability of 3
That he travels by minibus on Monday. If he travels by minibus on any one
3
day, there is a probability of 4 that he will travel by car the next day. If he
5
travels by car on every one day, there is a probability of 6 that he will travel
by minibus the next day. Use a tree diagram to find the probability that he
travels by minibus on Wednesday.
(6 marks)
b. If sin y = 0.6 find without using a calculator the value of tan y.
Page 4 of 16
NAME:……………………………………………………………………………
(4 marks)
4. a. A vehicle travels from point P to Q in 8 hours. It starts from rest at P
increasing its speed steadily to 200km/h in 2 hours. It then travels at that
speed for 1 hour. Finally the vehicle reduces its speed steadily until when it
stops at Q, 5 hours later.
i. Draw a speed –time graph of the vehicle on the graph paper provided.
(3 marks)
ii. Using the graph in (i), calculate the distance the vehicle has travelled
from P to Q.
(3 marks)
b. In Figure 1ABCD is a circle and DE is a tangent to the circle at D. AC is
parallel to the tangent DE.
Page 5 of 16
NAME:……………………………………………………………………………
Prove that:
i. Triangle ADC is isosceles
(3 marks)
ii. Angle ABC is twice angle DAC.
(3 marks)
5. a. Given that ( 4 x 2−9 ) (m x +d ) is identical to 16 x 3+ 24 x 2−54, Calculate
the values of m and d.
Page 6 of 16
NAME:……………………………………………………………………………
(4 marks)
b. Figure 2 shows a parallelogram ABCD in which ⃗
AB = b and ⃗
BC = c
1
AQ = ⃗
If ⃗ AC , Find ⃗
BQ in terms of b and c
4
(5 marks)
6. Ulemu running at a speed of y meters per second crosses a bridge which is 50
25
meters long. If Ulemu takes y−1 seconds to cross the bridge, calculate the value of
y.
Page 7 of 16
NAME:……………………………………………………………………………
(3 marks)
SECTION B
Answer any three questions from this section.
7. a. A quantity P varies directly as q and inversely as q 2+ 1. When p = q = 2.
Express p in terms of q only.
(4 marks)
o
b. An aeroplane leaves airport A on bearing of N23 E and flies for 340km to
another airport B. It then leaves airport B and flies on a bearing of N600W to
another airport C. If the airport A and C are 680 km apart, calculate the
bearing of airport A from C.
Page 8 of 16
NAME:……………………………………………………………………………
(6 marks)
c. Solve the equation
3 2
2 x −5 x + x +2=0
(5 marks)
8. a. Point P and Q have position vectors (3, 7) and (9,15) respectively.
Find
i. ⃗
PQ
(3 marks)
iii. |⃗
PQ|
Page 9 of 16
NAME:……………………………………………………………………………
(3 marks)
b. The bus fare per passenger F is partly constant and partly inversely
proportional to the number n of passengers. The fare per passenger for 40
passengers is K240, and for 50 passengers is K200. Calculate the fare per
passenger if there are 100 passengers.
(6 marks)
x x−1
4 ×8
c. Simplify x
32
Page 10 of 16
NAME:……………………………………………………………………………
(3 marks)
9. a. The sum of the first n terms of a Geometric progression, G.P, is
2 −1, Calculate the common ratio of the G.P.
n +1
(5 marks)
b. Innocent wants to make 6 litres of local juice using two types of fruits:
Oranges and Lemons. An orange produces 0.3 litres while a lemon produces
0.2 litres. He plans to use not less than 4 oranges to prepare the juice.
i. Taking x to represent number of oranges and y to represent number of
lemons, write down all inequalities in x and y that satisfy the above
information.
Page 11 of 16
NAME:……………………………………………………………………………
ii. Using a scale of 2cm to represent 5 units on both axes, draw graphs to
show the region represented by the inequalities, shading the unwanted
region.
iv. Use your graphs to find the maximum number of lemons that can be
used to make the juice.
(10 marks)
10. a. Figure 3 shows a triangle ABC with vertices A (2, 3), B (3, 10) and C (8, 7)
Page 12 of 16
NAME:……………………………………………………………………………
AB + ⃗
Show that ⃗ BC = ⃗
AC
(5 marks)
b. At Marist Secondary school, a French Club has 5 short students and 7 tall
students. The club wants to form a committee of 3 members by electing a
member at a time from the club.
i. Draw a tree diagram to show all possible outcomes of selecting the
three members.
Page 13 of 16
NAME:……………………………………………………………………………
iii. Use the tree diagram to calculate the probability of having two short
students and one tall students in the committee.
(6 marks)
c. Given that matrix:
( 3 5)
M = −1 1 and N = 0 (−1 12) . Find MN –M
(4 marks)
11. (a) Table below shows the results of a test which 30 students sat for
2 9 7 14 12 3 19 7 13 19
Page 14 of 16
NAME:……………………………………………………………………………
8 14 7 23 18 9 9 14 8 22
17 9 18 12 14 18 13 12 24 4
i. Using the class intervals of the marks as 1-5, 6-10, 11-15,…. Construct
a frequency table for the marks.
ii. Use your frequency table, to draw a frequency polygon on the graph
provided.
(7 marks)
(b) Draw a circle centre O with radius 3 cm. Construct another circle radius 4 cm
passing through point O. Label its centre C. Label one of the intersection
points of the two circles A. Using a ruler only, construct a tangent to the circle
centre O at point A. Measure and state angle AOC.
(6 marks)
Page 15 of 16
NAME:……………………………………………………………………………
(c) Calculate the value of y if 10y = 0.001
(2 marks)
END OF QUESTION PAPER
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