Revision Algebra
1) A company declares a dividend of 14% on shares of Rs 50. If the rate of interest on investment is 10%, find the market value of the shares.
2) Mohan bought Rs 100 shares at Rs 50 above par. He invested Rs 18000.
a) What is his annual income, if dividend is 6% ?
b) He sells 50% of his shares when the price rises to Rs 200. What is his gain on this transaction ?
3) Ramji invested Rs 16000 and Rs 20000 in buying shares of two companies. these companies declared dividend of 12% and 8% re. He collects the dividends and sells out all his shares at a losss of 2% and 3% respectively on his investment. Find his total gain from these two transactions ?
4) A man bought 4000 shares each of face value Rs 10 at Rs 14 per share . At the end of the yr, the company declares dividend of 16 percent. Calculate
a) The amount of money invested by him.
b) the percentage yield on his outlat. Give answer in two significant figures..
Algebra - Test
1) Mr Desai opens a recurring deposit of Rs 2000 per month for 31 months paying simple interest of 12% p.a. Calculate the amount receives at the time of maturity. 69300
1) Mr Desai opens a recurring deposit of Rs 2000 per month for 31 months paying simple interest of 12% p.a. Calculate the amount receives at the time of maturity. 69300
2) Which is better investment ---12% shares at 90 or 15% at 120? 12%
3) A man invests a sum of money in Rs 20 shares, paying 15% dividend, quoted at 20% premium . If his annual dividend is Rs 720, find
a) his total investment
b) the rate of interest on his investment. Rs 5760, 12.5%
4) A man bought 3200 shares of Rs 10 paying 15% per annum. He sold them when the price rose to Rs 28 and invested the proceeds in Rs fifty shares paying 11% per annum at 12% premium . Find the annual change in his income. Rs 4000
FACTOR THEOREM
1) Show that x³- 7x²+ 14x -8 is the factor of x -1, then find other factors also.
2) Using factor theorem, find out whether polynomial g(x) is a factor of f(x) or not:
a) Given f(x)= x²+ 3x -10, g(x)= x -2.
b) Given f(x)= 6x² - 5x - 6, g(x)= 2x -3.
c) Given f(x)= 2x² - 5x -12, g(x)= x - 4.
d) Given f(x)= 3x² - 2x -8, g(x)= 3x +4.
e) Given f(x)= 9x²- 4a²+ 4ay - y², g(x)= 3x +2a - y.
f) Given f(x)= x²- 3x²+ 4x -2, g(x)= x -1.
g) Given f(x)= x²(x -14)+ 37x -60, g(x)= x - 2.
h) Given f(x)= x³+ x²- 2x -30, g(x)= x -3.
3) Find the value of k when f(x)= x³ - 3x² - x + k, if g(x)= x +1 is a factor of f(x).
4) Find the values of p and q if g(x)= x +2 is the factor of f(x)= x²- px + x + q and , f(2)= 4.
5) For what value of a is x-2 a factor of f(x)= x² - ax + 6.
6) Find the values of p and q if x+3 and x-4 are factors of x³ - px²- qx + 24.
7) Factorise x³- 7x² + 14x - 8completely.
8) Find the values of p and q if g(x)= x -4 is a factor of f(x)= 4x³- px² + qx -216 and f(-1)= -225.
9) Find the values of a and b if p(x)= x +2 is a factor of q(x)= ax³- bx² + 2(x -2) and q(2)= 20.
10) Find the value of a if x+ a is a factor of f(x)= x³ + a(x² +1) - 2x + 4.
11) Find the remainder, if f(x)= x³- 2x² + x - 3 is divided by g(x)= x +2.
12) Find the remainder, if f(x)= 2x³- 3x² -4x - 5 is divided by g(x)= 2x + 1.
13) If g(x)= 2x -3 is a factor of f(x)= 2x³- 9x² + x + p, find the value of p. Hence find all the factors.
14) If g(x)= 3x - 2 is a factor of f(x)= 3x³ + x² + px + 12, find the value of p. Hence find all the factors of f(x).
15) Find the value of p if the polynomial f(x)= x³- 3x² - px + 24 is divisible by g(x)= x + 3. Hence find all the factors.
16) Find the value of q if the polynomial f(x)= 2x³ + qx² - 7x -12 is divisible by g(x)= x + 4. Hence find all the factors of f(x).
17) Find the value of q if the polynomial f(x)= x³ + 2x² - 13x + q is divisible by g(x)= x -2. Hence find all the factors f(x).
18) Find the value of p if the polynomial f(x)= x³ - px² - x +3 is divisible by g(x)= x² -1. Hence find all the factors.
19) Find the value of p and q if the polynomial f(x)= px³ - 8x -12 + qx² is divisible by g(x)= x² - 4. Hence find all the factors.
Find the value of p and q if the polynomial f(x)= px³ + qx² - 8x -12 is divisible by g(x)= x² - 4. Hence find all the factors.
20) Find the value of p and q if the polynomial f(x)= px³ + 6x² + qx + 6 is divisible by g(x)= x²+ 4x + 3. Hence find all the factors of f(x).
21) Find the value of p for which the polynomial f(x)= x³ + px² - 16x +8 has g(x)= x -2 as one of the factors. Hence find the remaining two factors.
22) Find the value of q for which the polynomial f(x)= 2x³ + qx² - x -15 has g(x)= 2x + 3 as one of the factors. Hence find all the remaining factors.
23) Factorise 6x³ - 11x² - 3x +2. Completely.
MEAN
1) Find the arithmetic mean of the numbers 5, 3, 8, 7, 6, 1. What is the new mean if 3 is added to each number?
2) The table below gives the expenditure (in rupees) on water consumption of 70 houses in a locality. Find the average expenditure (in rupees) per house.
Expenditure no of house
15-20 7
20-25 5
25-30 7
30-35 8
35-40 9
40-45 11
45-50 7
50-55 5
55-60 4
60-65 4
65-70 3
3) Find the mean by the short cut method of the following table:
X: 5 6 7 8 9 10
F: 10 12 15 11 7 5
4) Find the mean of the following frequency table by step deviation method:
Class frequency
10-15 5
15- 20 6
20-25 8
25-30 12
30-35 6
35-40 3
5) Weights of 50 eggs were recorded as given below :
Weight(in gms) no of eggs
80-84 5
85-89 10
90-94 12
95-99 12
100-104 8
105-109 2
110-114 1
Calculate the mean weight to the nearest geams.
6) Find the mean of the following data:
a) 12, 15 , 10, 9, 11, 14, 6.
b) 200, 230, 18รณ, 210, 240.
7) a) if 8 is the mean of 4, 7, a, 8, 10, 12, find a.
b) if 7 is the mean of 5, 3.5, 4.5, b, 8.5, 9.5; find b.
8) Following at the height of (in inches) of 10 girls:
52, 55 , 48, 51, 47, 46, 47, 46, 50, 51
Find the mean height. If 3 each are added to each of the above height, find the new mean height.
9) Following are the runs scored by three batsman, in 6 completed innings:
A: 15, 25, 0, 32, 35, 65
B: 24, 36, 12, 14, 18, 30
C: 18, 45, 37, 3, 40, 32
Find who is the best batsman, using the above data.
10) From the following table find the mean height:
Height: 60 61 62 63 64
no of boys: 2 3 5 8 7
11) From the following table, find the mean mark:
Mark number of students
0 1
1 1
2 3
3 6
4 8
5 8
6 6
7 4
8 7
9 4
10 2
12) Find the mean weight of 70 students from the following data :
Weight (kg) no of students
50 8
52 10
54 15
56 20
58 8
60 6
62 2
64 1
13) The daily salaries of 60 workers are given below. Find the mean salary.
Salary: 10 15 20 25 30 35
Workers: 20 12 8 10 9 1.
14) If the mean of the following distribution is 7.5, find the missing frequency f of the following data :
variable frequency
5 20
6 17
7 16
8 10
9 f
10 6
11 7
12 6
15) if the mean of the following distribution is 58.2, find the missing frequency f
salary no of person
45 6
50 8
55 10
60 f
65 6
70 5
75 2
80 1
16) Find the mean for the following frequency distribution, using direct method
Marks students
0- 10 5
10-20 8
20-30 12
30-40 10
40-50 5
17) Find the mean, using direct method
Weight students
30-34 6
34-38 8
38-42 12
42-46 9
46-50 5
18) Find the mean by shortcut method :
weight student
11-15 8
16-20 12
21-25 13
26-30 16
31-35 12
36-40 9
41-45 8
46-50 2
19) Find the mean by step deviation method
weight students
10-20 6
20-30 8
30-40 12
40-50 15
59-60 10
60-70 9
20) Find the mean by step division method :
variate frequency
10-20 12
20-30 15
30-40 16
40-50 19
50-60 12
60-70 6
21) compute the mean of the following frequency table by i) direct method and ii) shortcut method
class frequency
05-10 10
19-15 6
15-20 4
20-25 12
25-30 8
30-35 4
35-40 2
40-45 1
45-50 3
22) Find the mean of the following frequency distribution:
Class frequency
00-10 6
10-20 8
20-30 12
30-40 8
40-50 6
23) Find the mean for the following distribution:
class frequency
1-10 3
11-20 5
21-30 8
31-40 6
41-50 3
24) Find the mean for the following distribution:
Class frequency
00-10 6
10-20 12
20-30 18
30-40 20
40-50 25
50-60 32
70-80 18
80-90 6
90-100 1
25) Find the mean for the following distribution:
Class frequency
01-10 8
11-20 15
21-30 16
31-40 17
41-50 20
51-60 18
61-70 11
71-80 8
81-90 2
91-100 1
26) The frequency distribution of marks obtained by 40 students as under. Calculate the arithmetic mean:
Marks student
00-08 5
08-16 3
16-24 10
24-32 16
32-40 4
40-48 2
27) find the missing frequency for the following distribution, if the mean is 12.9.
Class frequency
0-5 3
5-10 f
10-15 8
15-20 5
20-25 4
28) a box contains nails of different lengths, measured to nearest half centimetre. The frequency distribution is as follows:
Length: 2.5 3.0 3.5 4.0 4.5 5.0
F: 10 35 50 45 35 25
i) state the upper boundary of the last class.
ii) state the class size.
iii) calculate the mean.
29) The following table shows the marks of 120 students at ICSE examination in mathematics. Calculate the mean marks:
Marks no of students
30-39 1
40-49 3
50-59 11
60-69 21
70-69 43
80-89 32
90-99 9
If the marks of each student are increased by 5%. Find the new mean marks.
30) Marks obtained by 40 students in Mathematics were as follows:
23 36 54 60 65 45 40 41 21 29 35 38 68 58 47 42 75 89 95 30 34 74 78 22 84 62 46 49 37 39 66 78 25 50 91 44 37 37 48
Construct the frequency table for the above marks, against the following class intervals with 21-30......
Find mean.
Test paper -23
1) a)
b) If (-6, n+2) on reflection in origin gives (m+3, -4). Find the values of m and n. (2)
c)
d) Given that x +2 and x-3 are factors of x²+ ax + b. Calculate the values of a and b. (2)
e) If A= 2 4
2. 1
then show that A⅖- 3A - 6I= 0 (2)
2) a) Find the equation of a line passing through the points (7, -3) and (2,-2). If this line meets x-axis at point P and y-axis at Q, find the coordinate of P and Q. (3)
b)
c)
3) a)
b)
c)
4) a) In the adjoining figure, a circle touches the side AC of a ∆ ABC at point P. BC produced at Q and BA produced at R. Show that the length of tangent BQ is equal to half the perimeter of ∆ ABC. (3)
b) The result of an examination are tabulated below:
Marks(less than) no of candidates
10 0
20 25
30 42
40 65
50 95
60 120
70 128
80 135
90 148
100 150
find median. (3
c) The time taken by a person to cover 150 km was 2.5hrs more than the time taken in return journey. if he returned at a speed of 10 kmph more than the speed of going. what was the speed per hour in each direction ? (3)
5) a)
b) A man invests Rs 8000 in buying shares of a company of face value of Rs 100 each at a premium of 10%. If he earns Rs1200 at the end of the year as dividend, find
i) the number of shares he has in the company.
ii) the dividend percent per share. (3)
6) a)
b) A shopkeeper announces a discount of 15% on his goods. if the marked price of an article is Rs 1850, how much must a customer pay for it, if GST is 9%. (3)
c) solve the graoh the solution set of -2< 2x - 6 or -2x +5≥ 13 where x belongs to R. (3)
c) solve the graoh the solution set of -2< 2x - 6 or -2x +5≥ 13 where x belongs to R. (3)
7) a) Solve : (2x -3)/(x -1) - 4{(x -1)/(2x -3)}= 3. (3)
b)
c) If q is the mean proportional between p and r, prove that p²- q²+ r²= q⁴(1/p²- 1/q²+ 1/r²). (3)
8) a)
b) If A=a 0 & B= 0 - b & C= 1 -1
0 2 1 0. 1 1 and BA= C², find the values of a and b. (3)
c) Show that P(3, m -5) is a point of tricsection of the line segment joining the points A(4,-2) and B(1,4). Hence find the value of m. (3)
9) a) In the given figure, two straight lines AB and CD intersect each other at point P(3,4). AB makes an angle of 45° and CD makes an angle 60° with the positive direction of x-axis. Find the equation of AB and CD. (3)
b)
c) A line PQ is drawn parallel to base of ∆ ABC which meets sides AB and AC at points P and Q respectively. If AP= (1/3) PB , find the value of
i) ar(∆ABC)/Ar(∆APQ)
ii) ar(∆APQ)/ar(teapeziumPBCQ). (3)
10) a) In the given figure, AOB is a diameter and DC|| AB. If angle CAB= x°, find the value of the following in terms of x:
i) angle COB
ii) angle DIC
iii) angle DAC
iv) angle ADC. (3)
b)
c)
11) a) From a solid cylinder whose height is 16 cm and radius is 12 cm, a conice cavity of height 8cm and of a base radius 6 cm is hollowed out. Find the volume and the total surface area of the remaining solid. (3)
b) prove that : tan²A - tan²B= (sin²A - sin²B)/cos²A cos²B. (3)
c) The length of the shadow of a vertical Tower is √3 times its height. Find the angle of elevation of the Sun. (3)
TEST PAPER - 24
1)a) The lines given by ax+ 4y= 8 and 2x+ 3y +2=0 are mutually perpendicular. Find the value of a. (2)
b) AB and CD are two chords of a circle intersecting at a point P outside the circle. Find if PC= 30cm, CD= 14cm and PA= 24cm. Determine AB. (2)
c)
d) Find the total surface area of an open pipe of length 50 cm, external diameter 20cm and internal diameter 6cm. (2)
e)
2)a)
b) Find the equation of the lines which passes through the point (-2,3) and are equally inclined to the co-ordinate axes. (3)
c) If P= 2 6 & Q= 3 x
3 9 y 2
Find x and y such that PQ= null matrix. (3)
3) a) Using remainder theorem, factorise the expression 3x³+ 10x²+ x - 6. (3)
b)
c) If (a²+ b²)+x²+ y²)= (ax + by)², show that a/x = b/y. (3)
4) a) If a= 4√6/(√2+ √3), find the value of
(a+ 2√2)/(a- 2√2) + (a+ 2√3)/(a- 2√3). (3)
b)
c) Mr. Ahuja invests equal sums of money in two companies offering 8% shares of Rs 100 at a premium of Rs 25 at 6% shares of Rs 100 at a discount of Rs 25. He finds that if with his total investment he has bought equal number of shares of each company, his income would have been Rs142 less. Find his total investment . (3)
5) a)
b)
6) a)
b) A recurring deposit account of Rs 1200 per month has a maturity value of Rs 12440.00. if the rate of interest is 8% and the interest is calculated at the end of every month, find the time of the recurring deposit account. (3)
7) a) i(plot the point A(3,5) and B(-2,4).
ii) A' is the image of A when reflected in the x-axis . Write down the coordinates of A'b and plot it.
iii) B' is the image of B when reflected in the y-axis, followed by reflection in the origin, Write down the coordinates of B'.
iv) write down the geometrical name of the figure AA'BB'.
v) Name two invariant points under the reflection in the x-axis . (3)
b) The point P(5,-4) divides the line segment AB as shown
in the figure in the ratio 2:5. Find the coordinates of points A and B. 3
8) a) The vertices of a ∆ ABC are (0,5), B(-1,-2) and C(11,7). Write down the equation of BC . Find
a) i) the equation of line through A and perpendicular to BC.
ii) the coordinates of the point P, where the perpendicular through A as obtained in (i) meets BC. (3)
b)
9) a) Find the mean of the given data:
C. I frequency
63-70 9
70-77 13
77-84 27
84-91 38
91-98 32
98-105 16
105-112 15 (3)
b)
10a)
b) A, B are the points (9,6) and (10,0). O is the origin, OM is a median and OP is an altitude of ∆ OAB. Find the equations of OM and OP. (3)
11) a) prove: (SinA + cosecA)² + (cosA + secA)²= 7+ tan²A + cot²A. (3)
b)
c) If A= -1 1
a b and A²= I, find a, b.
