Answer the following
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CBSE 8th Mathematics- Square and Square root
1. Show that 500 is not a perfect square.
2. Express 81 as the sum of first nine consecutive odd numbers.
3. Using prime factorisation, find the square roots of (a) 11025 (b) 4761
4. Find the square root of the following by long division method.
(a) 1369 (b) 5625
5. Find the square root of the following by long division method. :
2. Express 81 as the sum of first nine consecutive odd numbers.
3. Using prime factorisation, find the square roots of (a) 11025 (b) 4761
4. Find the square root of the following by long division method.
(a) 1369 (b) 5625
5. Find the square root of the following by long division method. :
(a) 27.04 (b) 1.44
6. What is the least number, that should be subtracted from 1385 to get a perfect square?
7. What is the least number that should be added to 6200 to make it a perfect square?
8. Find the least number of four digits that is a perfect square.
9. Find the least square, number, which is exactly divisible by 3, 4, 5, 6 and 8
10. A decimal number is multiplied by itself. If the product is 51.84, then find the number.
7. What is the least number that should be added to 6200 to make it a perfect square?
8. Find the least number of four digits that is a perfect square.
9. Find the least square, number, which is exactly divisible by 3, 4, 5, 6 and 8
10. A decimal number is multiplied by itself. If the product is 51.84, then find the number.
11. A General wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out?
12. Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.
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12. Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.
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IGCSE Mathematics Worksheet - Venn Diagrams 2
Answer the following
1. Kim collected data on 40 people’s enjoyment of sport.P is the set of people who play sports regularly, and
W is the set of people who watch sports regularly.
3. Jack asked 60 people which sports they liked from rugby, football and cricket.
8 people like all three sports.
17 people like rugby and football.
13 people like football and cricket.
19 people like rugby and cricket.
35 people like football.
27 people like cricket
30 people like rugby.
4. Jenny asked 80 people which sports they enjoy from Football, Hockey and Rugby.
Find the probability of:
(a) How many people enjoy all three sports?
(b) How many people enjoy football and hockey but not rugby?
(c) How many people enjoy football and rugby but not hockey?
(d) Work out which sport is enjoyed by the most number of people.
R = red cars
J = cars manufactured in Japan
32 of the people she asked watch sports regularly.
An incomplete Venn diagram for her data is shown below.
a) Complete the Venn diagram.
b) Work out P(W∪P) for someone picked at random.
c) Work out the probability that someone picked at random watches sports regularly but not play sports regularly
All 50 people like at least one of the drinks
19 people like all three drinks.
16 people like tea and coffee but do not like milk.
21 people like coffee and milk.
24 people like tea and milk.
40 people like coffee.
1 person likes only milk.
Sami selects at random one of the 50 people.
Draw a Venn Diagram and Work out the probability that this person likes tea.
a) Complete the Venn diagram.
b) Work out P(W∪P) for someone picked at random.
c) Work out the probability that someone picked at random watches sports regularly but not play sports regularly
2. Sam asked 50 people which drinks they liked from tea, coffee and milk.
All 50 people like at least one of the drinks
19 people like all three drinks.
16 people like tea and coffee but do not like milk.
21 people like coffee and milk.
24 people like tea and milk.
40 people like coffee.
1 person likes only milk.
Sami selects at random one of the 50 people.
Draw a Venn Diagram and Work out the probability that this person likes tea.
3. Jack asked 60 people which sports they liked from rugby, football and cricket.
8 people like all three sports.
17 people like rugby and football.
13 people like football and cricket.
19 people like rugby and cricket.
35 people like football.
27 people like cricket
30 people like rugby.
Draw a Venn Diagram and Work out the probability that people liked neither rugby or football or cricket?
4. Jenny asked 80 people which sports they enjoy from Football, Hockey and Rugby.
Find the probability of:
(a) How many people enjoy all three sports?
(b) How many people enjoy football and hockey but not rugby?
(c) How many people enjoy football and rugby but not hockey?
(d) Work out which sport is enjoyed by the most number of people.
5. The Venn diagram shows information about the cars in a car park.
ξ = 150 cars in the car parkR = red cars
J = cars manufactured in Japan
A car is chosen at random.
Work out the probability that it is red.
Work out the probability that it is red.
CBSE Class 9 Mathematics-Important Questions-Surface Area and Volume
Answer the following
1. The total surface area of a cube is 726 cm2. Find the length of its edge. [11cm]
2. How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm ? [154cm3]
3. Find the area of the sheet required to make closed cylindrical vessel of height 1 m and diameter 140 cm. [7.48m2]
4. If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. [1000000]
5. How many balls, each of radius 2 cm can be made from a solid sphere of lead of radius 8 cm ? [64]
6. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere [2.1cm]
7. A school provides milk to the students daily in cylindrical glasses of diameter 7 cm. If the glass is filled with milk up to a height of 12 cm, find how many litres of milk is needed to serve 1600 students. [739.2 litres]
8. A rectangular piece of paper is 22 cm long and 10 cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder. [385cm3]
9. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find it volume. If 1cm3 wheat cost is Rs 10, then find total cost. [Rs866.25]
10. The curved surface area of a cylinder is 176 cm2 and its area of the base is 38.5 cm2. Find the volume of the cylinder. [Ans:98 cm3]
CBSE 9th Mathematics Worksheet - Probability
Answer the following
1. A bag contains 50 coins and each coin marked from 51 to 100. One coin is
picked up at random. The probability that the number on the coin is not a prime
number is…………………
2. Eleven bags of wheat flour, each marked 5 kg actually contained the following weights of flour (in kg):
4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
3. The record of a weather station shows that out of the past 250 consecutive days,
its weather forecast correct 175 times. What is the probability that on a given
day.
(i) it was correct.
(ii) it was not correct.
4. A die having six faces is tossed 80 times and the data is as below:
Outcome 1 2 3 4 5 6
Frequency 10 20 10 28 8 4
Find (i) P (1) (ii) P (4) (iii) P (6) (iv) P (5).
5. The blood groups of 30 students of class IX are recorded as follows:
(i) A (ii) B (iii) AB (iv) O
6. Given below is the frequency distribution of wages (in Rs.) of 30 workers in a certain factory
Wages
(in Rs.) 110-130 130-150 150-170 170-190 190-210 210-230 230-250
No. of
workers 3 4 5 6 5 4 3
A worker is selected at random. Find the probability that his wages are:
(i) less than Rs. 150
(ii) at least Rs. 210
(iii) more than or equal to 150 but less than 210.
7. Three coins tossed simultaneously 100 times with the following frequencies of
different outcomes.Out come No head one head two head three head
Frequency 14 38 36 12
If the coin tossed again then find the probability.
(i) two heads coming up
(ii) 3 heads coming up
(iii) getting more tails than heads
(iv) at least one head coming up
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IGCSE Mathematics Worksheet - Differentiation (Calculus) -1
Answer the following
1.
Find the maximum value of A.
2.
(c) State whether the turning point is a maximum or a minimum.
3.
4.
Find the coordinates of the point of y=f(x) where the gradient is 8
5.
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(c) State whether the turning point is a maximum or a minimum.
3.
4.
Find the coordinates of the point of y=f(x) where the gradient is 8
5.
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IGCSE Mathematics Worksheet - Vectors-2
Answer the following
1.
OPQ is a triangle. T is the point on PQ for which PT : TQ = 2 : 1.
= a and = b.
= a and = b.
(a) Write down, in terms of a and b, an expression for .
(b) Express in terms of a and b. Give your answer in its simplest form.
2.
ABCD is a parallelogram. AB is parallel to DC. AD is parallel to BC. = p = q
Express, in terms of p and q
(i)
(ii)
= 2b = 2a = 6a
M is the midpoint of PQ and N is the midpoint of OR.
(a) Find the vector 
in terms of a and b.
in terms of a and b.
X is the midpoint of MN and Y is the midpoint of QR.
(b) Prove that XY is parallel to OR.
4. (a)Express in terms of a and/orb
(i) 
(ii)
X is the midpoint of BC.
(b) Express in terms of a and/or b
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