ST GEORGE’S GIRLS’ SECONDARY SCHOOL, NAIROBI
FORM 2 MATHEMATICS ADDITIONAL HOLIDAY ASSIGNMENT
NOVEMBER/DECEMBER 2016
1. Factorize x2-y2. Hence find the exact value of
a) 46652-46552.
2. Simplify the expression a)
b) 15.42 – 4.62
3𝑥 2 +4𝑥𝑧+𝑧 2
4𝑥 2 +3𝑥𝑧−𝑧 2
b)
3𝑎+2𝑎𝑏−12−8𝑏
2𝑏+4𝑎𝑏+3+6𝑎
4𝑥 2 − 𝑦 2
c) 2
3𝑦 −7𝑥𝑦+2𝑥 2
√3
3. Given that Cos (90-x) 0 =
, find without using mathematical tables:
2
a) Cos X0
b)Tan (90-x)0
4. Find the equation of the mirror line which maps point A (-2,6) onto A’ (4, 8) in double intercept form.
5. A cone of slant height 8cm is formed from a sector which subtends an angle of 108 0. Find the base area of
the cone.
6. A cylindrical container of radius 6cm contains some water. Calculate the rise in water level when a spherical
steel ball of radius 4.5cm is completely submerged into the water.
7. From a window 8m above the ground, the angle of depression of the foot of a telephone post is 25 0 and the
angle of elevation of the top of the post is 400. Find the height of the post.
8. A Solid frustum made from a cone has radii 1.5cm and 5cm at the top and bottom respectively. Given that
the slant edge of the frustum is 7cm, determine;
a) the height of the frustum
b) the volume of the frustum
c) the Surface Area of the frustum
9. A container of height 30cm has a capacity of 1.5litres. What is the height of a similar container of capacity
3.0m3.
10. A scale model of a building is such that the ratio of the area of the model to the actual area is 1:400.
a) If the height of the actual building is 15m, what is the height of the model?
b) A certain section of the model has a volume of 3cm3, find the actual volume of the corresponding section of
the real building.
11. Use logarithms to evaluate:
a)√
(0.6984)3 𝑥 249.5
85.77
b)√
(35.69)2 𝑥 2.563
4897
1
12. A metallic sphere of radius 7cm is recast into a cone of height 7cm. Calculate the diameter of the cone.
13. A metal bar is in the shape of a pentagonal prism whose length is 30cm. The cross-section is a regular
hexagon of side 6cm. Find
a) the area of the pentagonal face
b) the volume of the metal bar
14. A solid consists of a cone mounted on a hemisphere. The common diameter of the cone and the
hemisphere is 12cm and the slant height of the cone is 10cm.
a) Calculate, correct to 2 decimal places;
i) the surface area of the solid
ii)the volume of the solid
b) If the density of the material used to make the solid is 1.3g/cm3, calculate its mass (in kgs).
15. Solve the inequalities ; 3-2x < 5 and 4-3x > -8 and;
a) Give the range of values of x that satisfies them
b) Represent the solution on the number line
c) State the integral values of x that satisfy them
16.a) A flower bed is x meters long by (x-3) m wide is rectangular in shape. A path 1 meter wide is constructed
all around it. If the area of the flower bed is 28cm2 , calculate the dimensions of the flower bed.
b)The area of a rectangle is 108cm2 and its length is 3cm greater than the width. Find the dimensions of the
rectangle.
17.Two circles of radii 8cm and 6cm intersect . The distance between their centers is 12cm. Calculate their
common area of intersection.
18. Solve for the unknowns given that
𝑎𝑥
𝑎𝑦
= 𝑎3
19. Expand and Simplify: a) (3a+2b)(2a-3b)
20.Solve for x in the equations:
and
3𝑥
3−𝑦
= 243
(3marks)
b) (3x+2y)(2x-5y)
a) (3x+4)2-(2x-3)2= 5x2+10
b) (5x+5)2-(4x-2)2= (3x-3)2
c) 30x2-11x+1=0
d) x2-5tx+6t2=0
21. a)Find the integral values of x which satisfy the inequalities 2(2-x)< 4x-9<x+11
b) Solve the following inequalities and represent your solution on a number line
3-2x< x <
2𝑥+5
3
2
22. Find the value of x in the equation
a) 49(𝑋+1) + 72𝑋 = 350
1
b) ( )𝑚 𝑥 (81)−1 = 243
27
c)
812𝑥 𝑥 27𝑥
9𝑥
= 729
23. Find the equation of the image of the line y=3x+5 under reflection in the line y=x.
24. Lines L1 and L2 intersect at P. L1 passes through the points (-4,0) and (0,6). Given that L2 has the equation :
y=2x-2, find by calculation, the co-ordinates of P.
25. a) Plot triangle ABC with vertices A(-2,1), B(-2,5) & C(0,5) on grid.
b) A1B1C1 is the image of ABC with co-ordinates A1(0,9), B1(4,9) & C1(4,7), under a rotation. Find the Centre and
Angle of Rotation.
c) A2B2C2 with co-ordinates A2(2,-3), B2(6,-3) & C2(6,-1) is the image of ABC under a reflection along the line L.
Write down the equation of L.
26. A rectangle ABCD has vertices A(1,2),B(5,2),C(5,4)& D(1,4).
i) Find its image AIBICIDI after a reflection in the line y=o and state its co-ordinates.
ii)AIBICIDI is reflected onto AIIBIICIIDII along the line y=x. Find the image AIIBIICIIDII and state its co-ordinates.
Plot ABCD and its images on the same grid.
27. Given that log3=0.4771, log5=0.6990 and log 7=0.8451, find without using mathematical tables or
calculator:
a) log 1575
b) log 2205
HAVE A BLESSED HOLIDAY
MERRY CHRISTMAS & A PROSPEROUS 2017
MATHEMATICS DEPARTMENT.
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