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Maths 2 JMW

The document is a mathematics test paper from JMW Institute of Sciences, consisting of 15 questions divided into two sections, A and B, with a total time allowance of 2 hours. The questions cover various mathematical concepts including probability, matrices, simultaneous equations, geometric progressions, and constructions. Students are instructed to answer all questions and follow specific guidelines provided in the paper.

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24 views8 pages

Maths 2 JMW

The document is a mathematics test paper from JMW Institute of Sciences, consisting of 15 questions divided into two sections, A and B, with a total time allowance of 2 hours. The questions cover various mathematical concepts including probability, matrices, simultaneous equations, geometric progressions, and constructions. Students are instructed to answer all questions and follow specific guidelines provided in the paper.

Uploaded by

ksimwaka84
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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JMW INSTITUTE OF SCIENCES

Mathematic Test 2 Time allowed: 2 hours


Instructions
1. The paper contains 7 pages, please check
2. There 15 questions in this paper, answer all questions
3. There are 2 sections in this paper, section A and B, all have
compulsory questions
4. Follow the instructions when you are answering your
questions
1.A fair dice is rolled once, what is the probability of obtaining
a. a prime number

(3 marks)
b. perfect square

( 3 marks)
2 1
2. T and R are two matrices. Given that T = −1 3

0 3
And R =−1 1 ,find 3R-T2

(5 marks)
3. Solve the following simultaneous equations
Y = x2 – 1
4x = y – 4

(6 marks)
4.The 3rd and 9th term of an arithmetic progression are 29 and 8
respectively. Calculate the 20th term of the progression
(7 marks)
5. Using a ruler and a pair of compass only, construct in the
same diagram; a circle centre O of radius 3cm, a tangent to
the circle at P from a point T which is 8cm from the centre
of the circle

(6 marks)
6. A box contains 5 red balls, 8 white balls and 7 black balls. If
one ball is selected at random, calculate the probability
that it is white or black
(5 marks)
6 8 w −4 1 0
7. Given that 2 3 −1 3 = 0 1 , find the value of w

(5 marks)
8.Solve the following silmutaneous equations
9x2 – y2 = 15
3x – y = 5

(8 marks)
9. A geometric progression has 6 terms. If its first term is 3
And the last term is 96, calculate the common ratio

(6 marks)
10. Figure 1 shows a circle KLMN centre O. Line LON is a
diameter, KL = LM and angle LNM = 43

Calculate angle KMO

(6 marks)

Section B(40 marks)


11. Figure 1 shows a circle ABC centre O. OCP is a straight
line and AP is a tangent to the circle at A

(6 marks)
12. A man drives from his village to town, a distance of 40km on
a bearing of 046°. He then drives from the town to a lake 60km
away on a bearing of 107°.
a. How far apart is the lake from his house?

(4 marks)
b. What is the bearing of his house from the lake?

(4 marks)
13. The probability of having an early lunch at a boarding school
2 7
is 3 .When the lunch is early, the probability of having beef is 10
1
and when late the probability of having beef is 8 . Draw the tree
diagram to represent this information completing all branches
(6 marks)

14. The expression 2x3 + ax2 + bx – 6 is exactly divisible by x – 1


and leaves a remainder of 9 when divided by x + 2. Find the
values of a and b.

(8 marks)

15. If B = [ ] and B = [ ],calculate the value of x


x 2
2 −y 2
5 0
0 5
(7 marks)
16. The sum of the first eleven terms of an arithmetic
progression AP is 66. Given that the first term is -9, calculate

the last term of the progression.

(5 marks)
SUCCESS FOR ALL!!!!!!!!!!!!!!!!!
By Juma Mayamiko Wizaford
(0995913776)

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