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456/1
MATHEMATICS
Paper 1
July 2012
2½ hrs
U.C.E. MOCK EXAMINATIONS
MATHEMATICS 456/1
Paper 1
Time: 2hrs 30mins
INSTRUCTIONS TO CANDIDATES:
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Answer all questions in Section A and choose FIVE questions from Section B.
All working must be shown clearly and neatly in the answer booklets provided.
All necessary calculations must be done on the same page as the rest of the answer.
Mathematical tables with lists of formulae and squared paper are provided.
Silent, non-programmable scientific calculators may be used.
©2012 Mathematics Department, Gayaza High School
SECTION A (40 marks)
1.
Evaluate:
18  3of (2)  8  24
 4  6 2
2.
A sales woman earns a basic salary of Ush. 300,000 per month plus commission of
4% of all the sales above Ush.1,500,000. What is her gross income for a month in
which she makes sales of Ushs.2, 700, 000?
3.
Given that
4.
The figure below shows part of a regular polygon not drawn to scale.
2 3
3

 a  b c Find the values of a, b and c.
1 3 1 3
a) Determine the number of sides of the polygon.
b) Calculate the sum of interior angles of the polygon.
5.
Solve the equation
64 3x – 1 ÷ 16 x + 2 = 256 x x 4 2x.
6.
Find the equation of the perpendicular bisector of the line joining the points P (-1, 4)
and Q (-7, 8)
.
7.
8.
A quantity Y is partly constant and partly varies inversely as X. Given that Y=10
when X=1.5 and Y=20 when X = 1.25 find the value of Y when X= 0.5.
Given that tan α = -12/5 and that α is an obtuse angle. Find without using tables or
calculator the value of sin α + cos α
2
9.
Two consecutive odd numbers are such that the difference between thrice the larger
number and twice the smaller number is 21. Find the product of the numbers.
a  2
Under a transformation whose matrix is T  
 a
10.
 2
a figure whose area is
a 
2.5 cm 2 is mapped onto a figure whose area is 10cm2. Find two possible values of a
and hence write down two possible matrices.
SECTION B (60 marks)
11.
a) i) Construct a parallelogram PQRS in which PQ = 7cm, QR = 4cm and
PQR = 1200.
ii) Measure length PR
b) Two straight roads intersect at an angle of 300. A hut is built so that it is
equidistant from the two roads and 30m from the point of intersection. Using a
scale of 1cm to 10m, show all possible positions of the hut.
12.
A lampshade is in the form of a frustum of a cone. Its bottom and top diameters
are 12cm and 8cm respectively. Its height is 6cm.
8cm
6cm
12cm
a)
b)
Find the area of the curved surface of the lamp shade
The material used for making the lampshade is sold at sh.8000 per square metre.
Find the cost of ten lampshades if a lampshade is sold at twice the cost of the
material.
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13.
ABC is a triangle with vertices A( 2, -1), B (4, -1) and C(3,2).
a) A1B1C1 is the image of ABC under the transformation represented by the matrix
, determine the coordinates of A1B1C1.
b) On the same axes, draw triangle ABC and its image A1B1C1 and fully describe
the transformation that maps ABC onto A1B1C1.
c) A11B11C11 is the image of A1B1C1 under reflection along the line y=0. State the
coordinates of A11B11C11 and draw it on the same axes.
d) Determine the matrix representing a single transformation that maps ABC onto
A11B11C11.
14.
The figure below shows a cuboid ABCDEFGH.
Given that AB = 12cm, BC=8cm and BF = 4cm
a)
b)
c)
d)
15.
Draw the net of the figure
State the projection of AG on the plane EFGH.
Determine the angle between the line AG and the plane EFGH.
Given that M is the mid-point of FG, determine the angle between the planes
AMD and ABCD.
a) Copy and complete the table below giving your values correct to 1 decimal place.
x
cosx
2 cos
½x
00 300 600 900
1.0 0.9 0.5
2.0 1.9
1.4
1200 1500 1800 2100 2400 2700 3000 3300 3600
-0.9 -1.0
-0.5
0.5
1.0
0.5 0.5
-1.0
-1.7
-2.0
b) Using a scale of 1cm to represent 300 on the x axis and 2cm to represent 1 unit in
the y axis, draw, on the same axes, the graphs of y = cos x and y =2cos ½ x
c) Use the graph to find the value of x for which
i) cos x0 – 2 cos ½ x0 = 0
ii) 2 cos ½ x0 - 1.3 = 0
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16.
The table below shows the income tax of a certain country for government
employees. This is applied after the allowances have already been deducted.
Taxable Monthly Income in Shs.
1 – 100,00
100,001 – 200,0000
200,001 – 300,000
300,001 – 450,000
450,001 – 550,000
550,001 and above
Tax Rate % per
Month
0
5
10
20
30
50
A married employee has a gross monthly income of Shs.600,000 and is entitled to
the following allowances.
Marriage Shs120,000 per annum
Housing and transport 10% of the gross monthly income
Medical care Shs.240,000 per annum.
Calculate;
a)
his taxable income
b)
his monthly income tax
c)
his net monthly income.
17.
a) Given two sets A and B such that n(A) = 12, n(B) = 13, n(Ɛ) = 24 and
n (A´n B´) = 4, Using a Venn diagram, find:
i)
n(AnB´)
ii)
n(AuB´)
b) A bag contains green and red pens of the same type in the ratio 2:5 respectively.
Two pens are picked at random without replacement and their colours noted.
Using a tree diagram, determine the probability that
(i) the two pens picked are both red.
(ii) Only one of the two pens picked is red.
(iii) the second pen is not red.
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