GILI SECONDARY SCHOOL
FORM TWO HOLIDAY ASSIGMENT DECEMBER 2015
BASIC MATHEMATICS
1. a) Given express this fraction into decimals with
i) Three significant figures
ii) three decimal places
iii) Standard from correct to 2 significant figures
b) Change into fraction form.
2. a) List the elements of the set named below
D = is an odd number less than 10
b) Given the angles and if two angles are
complementary, find
i) The value of x
ii) The size of each angle
3. a) Given that Log solve for X
b) Rationalize the denominator
4. a) Given the equation of a straight line 18y – 15x + 10 = 0 find
i) the slope of the line
ii) the value of y – intercept and X – intercept
b) If
Make v the subject of the formula
5. a) If = , find the value of
b) Given that Sin and x is an acute angle, Find the value of
i) tan X ii) Cos
6. a) A regular polygon has exterior angle of 40. Find
i) the number of sides of the regular polygon
ii) Size of each interior angles
iii) sum of interior angles of the polygon
b) Show the solution of the following inequality on the number line
7. a) Given two lines and Find the value of K if the
line are
i) Perpendicular
ii) parallel
b) Pamela deposited Tsh. 2,000,000/= in a bank at a compound interest 8%
semi – annually for 2 years. Calculate the amount she received at the
end of the period
8. The fifth term of an arithmetic progression (AP) is zero and the tenth term
is 10
Find
i) the first term
ii) the common difference
b) Draw the graph of R = for -
9. a) show the following operations on the numberline
i) 7 – 4
ii) -4 x 3
iii) -6 + 2
b) Doto scored 55 out of 80% marks in Mathematics test what percentage
was this?
10. The table below shows the time taken by a car to cover a distance of
120km at different speeds
SPEED(km/h / 10 / 20 / 30 / 40 / 50 / 60 / 80 / 100
TIME
(Hour) / 12 / 6 / 4 / 3 / 2.4 / 2 / 1.5 / 1.2
i) Find the equation relating S and t
ii) Draw the graph of S against t
b) Factorize completely
i)
ii)
iii)
SECTION B
Attempt any four (4) questions from this section
11. a) A ladder 7.m long rests against a vertical wall so that the distance
between the foot of the ladder and the wall is 3m. Find
i) the angel the ladder makes with the wall
ii) the height above the ground at which the upper end of the ladder
touches the wall
b) The volume of a sphere is given by the formula
V =
Find the volume of a sphere with radius 20.06cm (take )
[ use mathematical table calculation using logarithms ]
12. Given
-2 if x < -2
F(x) = x + 1, if -2 £ x < -1
if x ³
a) Sketch the graph of f(x)
b) State the domain and range of f(x)
c) Use the graph to find
i) ii) f( -2) iii) f(0) iv) f(-1)
13. the table below shows the distribution of scores of 45 students in a physics
examination
Marks % / 45 – 55 / 56 – 66 / 67 – 77 / 78 – 88 / 89 – 99Number of students / 7 / 11 / 20 / 5 / 2
i) Draw the Histogram and find the mark scored by many students
ii) Find the median class of score
iii) Find the mean score
b) Draw the cumulative frequency curve and determine from it the median score
14. a) Given the balances below, prepare a profit and loss account for the year
ended 31st December 2010
Gross porift shs 900,000/=
Wages and salaries shs 100,000/=
Rent shs 50,000/=
Insurance shs 120,000/=
Discount received shs. 80,000/=
Discount allowed shs 300,000/=
Transport shs 130,000/=
Commission received shs 400,000/=
Office expenses shs 200,000/=
Bad debts shs 20,000/=
Advertising shs 70,000/=
Sundry expenses shs 150,000/=
b) find the inverse of the relation
R = and hence determine its domain and range.
15. a) In a certain examination, 80 students take mathematics 73 students take
physics and 45 students take chemistry, 15 students take Mathematics
and chemistry, and 18 students take chemistry and physics 20
students take physics and Math and 6
students take all three subjects Represent this information in Venn
diagram and find the number of students who take
i) Mathematics Only
ii) Chemistry only
iii) At least two subjects
b) If the universal set
A = and B = Find
i)
ii)
iii)
16. a) Use tables to calculate given your answer to three significant figures.
(4 marks)
b) Change to a fraction. (2 marks)
17. a) Given that find.
b) Determine the value of if .
18. a) Rationalize the denominator .
b) Make the subject .
19. All of 60 different vitamin pills contain at least one of the vitamins A, B and C. Twelve have A only, 7 have B only, and eleven have C only. If 6 have all three vitamins and there having A and B only, B and C only and A and C only. How many pills contain vitamin A.
20. 80 machines can produce 4800 identical pens in 5 hours. At this rate.
a. How many pens would a machine produce in one hour?
b. How many pens would 25 machines produce in 7 hours?
21. P(-2, 1), Q(4,3), R(5, 0), S(-1, -2) is a rectangle. Calculate:-
a. Its area,
b. The length of one of its diagonals,
c. The coordinates of the point where the diagonals cross.
22. A ship starts at (40°S, 30°N) and sails due west for 1000nm. Find its new latitude and longitude. (6 marks)
23. a) Evaluate
b) Express as a square root of a single number.
24. a) Find the nth term of the series . . .
b) The fourth, fifth and sixth terms of the series are (2x + 10), (4x – 4) and 8x + 40) respectively. Calculate the value of x and find the sum of the first ten terms when the series is an A.P.
Frequency / 12 / 10 / 15 / 19 / 12 / 14 / 3 / 0 / 4 / 1Marks / 9 / 12 / 15 / 18 / 21 / 24 / 27 / 30 / 33 / 36
25.
The above table shows scores of candidates in a mathematics examination.
a) Find the number of candidates in the examination.
b) Draw a cumulative frequency curve (OGIVE) for the scores.
c) Find the following:-
i) The mean, using an assumed mean of 18 or otherwise, correct to 3 decimal places.
ii) The mode.
iii) The median.
26. a) Write the function in the form where a, b, c are constants.
b) Find the domain and range as well as the turning point of the function
c) If is defined by the function
i. Draw the graph of
ii. Determine the domain and range of.
iii. Find.
27. a) Find if .
b) The angle of elevation of the top of a church from a point due East of it and 96m away from its base is 30°. From another point due West of the church the angle of elevation of the top is 60°. Find the distance of the latter point from the base of the church.
28. A ship leaves town X at 2030 hrs on Monday to town Y with an average speed of 300knots. If town X is at 45°W and town Y is at 75°E and both lie on a circle of latitude 60°N, Calculate when and at what time a ship will reach town Y.
29. Study the given trial balance and answer questions that follow:-
Prepare the following the year ending 31st December 2007.
i) Trading account;
ii) Profit and Loss account;
iii) Balance sheet.
30. Evaluate | ˉ9 | | ˉ2 |².
31. Simplify the expression below:
32. The line 8x + by = 12 crosses the y-axis at the point (0, 2). Find the value of b.
33. Write in the form 1:n the following rations giving n to three significant figures:
a. 3 : 10
b. 5cm : 2km
c. 6cm to 9m
34. a) The points A(5,2), B(1,0), C(c,5) and D(-5,d) lie on the same straight line. Find the values of c and d.
b) Find the equation of the line using points C and D.
35. a) Create a possible greatest number from 5928.
b) Write the created possible greatest number in scientific notation, correct to two significant figures.
36. a) The LCM of the numbers 8, 15, x and 24 is 120. Find in its lowest terms the ratio of the unknown and the LCM.
b) Use listing method to find the HCF of the numbers 27, 18 and 36 and hence find the following: , correct to one decimal place.
37. Write the decimal 0.7232323... in the form where a and b are integers and b ≠ 0. Hence simplify
38. Rationalize the denominator
39. Given that tan A = and A is an acute angle. Find the value of the following:
40. a) A translation T takes the point (0,6) to (0,10). Find where it will take the point
(7,-9).
b) Find the image of the point (6,5) under a rotation through 90º followed by a reflection in the line y + x = 0.
41. The interior angle of a regular polygon is three times the exterior angle. If the sum of the interior angles is 1440º, find:
a. The size of one interior angle,
b. The size of one exterior angle,
c. The sum of exterior angles,
d. The number of sides of the polygon,
e. The name of the polygon.
42. Find the cost of 3tonnes 500kg of cement if each 50kg costs 8,000/=.
43. The surface area if a sphere is 48Лcm². Find the volume of sphere in cm³.
Use Л =
44. Make Q the subject of the formula given that
45. If A * B denotes A²B² - 5A, find (3 * 4) * 5.
46. Find the simple interest and amount at 3½% on 18,250/= from 25th March to 25th September of the same year.
47. Solve for X if
48. Arrange in order of size, largest first, the following numbers:
49. Solve the system of equations.
50. (a) If a = 10.25, b = 8.24 and c = 131, use logarithm to calculate the value of
(b) Use mathematical tables to find the following
51. A building has an angle of elevation of 35º from point A and an angle of elevation of 45º from point B. If the distance between A and B is 30m, what is the height of the building?
52. At a race meeting 120 people were asked what sports newspaper they had bought that day. 70 had bought “The Racing Times” and 37 had bough “The Sporting Press”. If 28 people had bough neither, how many had bought both?
53. The examination results were as follows:-
3 students got marks between 0 and 10,
5 students got marks between 10 and 20,
6 students got marks between 20 and 30,
4 students got marks between 30 and 40,
8 students got marks between 40 and 30,
2 students got marks between 50 and 60,
3 students got marks between 60 and 70,
a. Construct a frequency distribution table for the above information.
b. What is the size of the class interval?
c. Draw a histogram and frequency polygon on the same set of axes.
54. a) Solve graphically the equation 2x² + x – 6 = 0.
b) Use the graph in (a) above to solve the equation here under: 2x² + 3x – 8 = 0.
55. Find the equation of the line passes through the following points:
(a) and
(b) and
(c) and
56. Find the equation of a line which passes through the point:
(a) and has a gradient of -3.
(b) and has a y-intercept of 6
(c) and crosses the x-axis at -5
(d) X-intercept 2, and y-intercept 4
57. Find the coordinate of the point at which a line whose equation is given by crosses the
58. Line both pass through the point. Line has a gradient of and passes through the point , find:
(a) The value of
(b) The equation of given that it crosses the x-axis at -14
59. Show that the equation of the straight line that passes through
60. The line crosses the y-axis at the point find the value of
61. A line passes through write its equation in the form