Grade 8(Mathematics) EV 4( )

Chapter-2 (Number system) Grade 8(Mathematics) EV 4(2016-17) Q. Find the three rational numbers between 3/5 and 3/4. Sol:- let,, be the required rational numbers. = ½ (3/5 + 3/4) = ½ ( ) = ½ 27/20 = 27/40 = ½ (27/40 + 3/4) = ½ ( )= 57/80 q 3 = ½ (57/80 + 3/4) = ½ ( ) = 117/160 3/5 < 27/40< 57/80 < 117/160 < ¾ Exercise :- Find the three numbers between 1/5 and 1/3. Q. Simplify by rationalizing, 4/. Sol:- 4/ / = 4/ Q. Simplify by rationalizing Sol:- = = Exercise:- 1/, simplify by rationalization. Exercise:-, simplify by rationalization. Q. Simplify by rationalization. (a) = = Exercise:- Exercise :-, simplify by rationalization. simplify by rationalization. = 1/6 8() = 4()/3 Q. Arrange in descending order, -1/2, -3/7, -5/14, -25/28 Sol:- LCM of 2,7,14,28 = 28-1/2 = -1/2 14/14 = -14/28-3/7 4/4 = -12/28-5/14 2/2 = -10/28-25/28-14/28, -12/28, -10/28, -25/28-25/28, -14/28, -12/28, -10/28

Q. Arrange in ascending order, (a) -1/5, -3/10, -11/15, 13/20 (b) 3/11, 3/9, 3/6, 3/10 (c) 2/5, 6/15, 5/20, 8/25 (d) -5/6, -7/12, 8/9, 6/15 Chapter-4 (Fractions) Q. Arrange 4/5, 6/15 and 7/20 in ascending order by (a) Making denominators equal (b) Making numerators equal Sol:- (a) To make denominators equal we take the LCM of denominator 5, 15 and 20 LCM = 5 3 4 = 60 So 4/5 = = 6/15 = = 7/20 = = So 21/60 < 24 < 48/60 =) 7/20 < 6/15 < 4<5 (b) To make numerator equal, we take LCM of numerators i.e. 4,6 and 7 so LCM = 84 4/5 = = 84/105 6/15 = = 84/210 7/20 = = 84/240 i.e. 84/240 < 84/210 < 84/105 so 7/20 < 6/15 < 4/5 Exercise:- Arrange the fractions in the ascending order of magnitude by making numerators equal. (a) 2/3, 4/5, ¾, 5/7 (b) 5/6, 10/13, 6/20 Exercise:- Arrange the fractions in the descending order of magnitude by making numerators equal. (a) ¾, 7/8, 11/24,13/42 (b) 2/11, 9/22, 7/33, 6/55 Q. Compare 16/21 and 20/31 Sol :- =) 16x31 > 20x21 =) 496 > 420

Exercise :- Compare the given fractions. (a) 6/25 and 10/19 (b) 15/26 and 11/15 (c) 19/14 and 17/21 of Q. Simplify :- 4 - x 2 + Sol :- 7/2 2/3 x 13/6 + 8/25 of 15/24 =) 21/5 7/2 2/3 x 13/6 + 8/25 x 15/24 =) 21/5 7/2 2/3 x 13/6 +1/5 =) 21/5 2/7 2/3 x 13/6 +1/5 =) 6/5 13/9 + 1/5 = Exercise:- Add the following: (a) 5/9 + 11/15 + 3/10 (b) + 2 + 17/44 = - 2 /45 Exercise :- Subtract the following : (a) 11/12 5/6 (b) 11/57 3/38 Exercise :- Simplify :- (a) 8/9 1/5 + 3/5 + 1/6 ¾ (b) 2 + 4 - Exercise :- Multiply : (a) 11/42 x 28/55 (b) x Exercise :- Simplify : (a) (2 ) (2 + ) (b) 3/5 8/9 5/8 + of 11/12 Exercise :- Divide : (a) 11 (b) 4 6 (c) 9/11 4 Chapter 6(Squares and square root) Q. Is 900 a perfect square? Sol:- 900 = 2x2x3x3x5x5 So 900 = (2x3x5) x (2x3x5) = 30 x 30

= 0 So 30 is a square root of 900 Exercise :- Find the square root of 7225. Exercise :- Find the square root of the fractions : (a) 196/484 (b) 1225/2025 (c) 0.01 Q. Simplify :- 5 4 Sol:- 5 4 =) 256 =) 9 = 3 Exercise :- Simplify : (a) 5 +2 (b) (-8) 2-64 Q. Find the square root of 1227.8016. Sol :- 22.806 =) 35.04 35.04 3 1227.8016 9 65 327 325 7004 28016 28016 0 Exercise :- Find the square root :- (a) 235.3156 (b) 81.5409 (c) 794.6761 (d) 291.7264 Chapter 8( Ratio and Proportion) Q. Express the ratios in simplest form 560 to 7200 Sol :- 560 : 7200 =) 560/7200 = 7/90 Exercise :- Express the ratios in simplest form (a) 65m : 2m 60cm (b) 90 sec : 1 minute 15sec Exercise :- Simplify the ratio 6 : Sol :- 6 : =) 27/4 : 18/5 =) 27/4 18/5

=) 27/4 x 5/18 =) 15/8 = 15 : 8 Exercise :- Simplify the ratios :- (a) 4 : 5.6 (b).2 : 1.6 Q. Which ratio is greater? (6 : 7) or (3 : 5) Sol :- (6 : 7) or (3 : 5) =) =) 30 > 21 So 6/7 is greater Exercise :- which ratio is greater? (a) (½ : 1/5) or (1/7 : 1/8) (b) (2/5 : 4/10) or (0.6 : 0.7) Q. Two numbers are in the ratio 11:13. If their sum is 192, find the numbers. Sol :- let the two numbers be 11x and 13x. Given 11x + 13x = 192 =) 24x = 192 =) x = 8 So no.s are 11x = 11x8 = 88 13x = 13x8 = 104 Exercise :- Two numbers are in the ratio 9 : 13. If the large number is 390, find the smaller. Q. Find the value of x in the proportion, 4.5 : 0.09 : : x : 1.8 Sol:-, 4.5 : 0.09 : : x : 1.8 Product of extremes = product of mean 4.5 x 1.8 = 0.09 x 8.10 = 0.09 x X = 8.10/0.09 X = 90 Exercise :- Find the value of x in proportions: (a) 3/4 : x : : 1/5 : 2/3 (b) 42 : 1.2 : : 5.6 : x Q. Find the fourth proportional to 3.6, 6.4 and 1.8. Sol:- let the fourth proportional to 3.6, 6.4 and 1.8 be x. then 3.6 : 6.4 : : 1.8 : x 3.6 x = 6.4 1.8 X = 3.2 Exercise :- Find the fourth proportional to (a) 31, 124, 0.12

(b) 3/5, 2/3, 2 (c) 43, 64.5, 13 Q. Find the mean proportional between 4 and 9. Sol:- let x be the mean proportional between 4 and 9. then X 2 = 4 9 = 6= 6 Exercise :- Find the mean proportional between : (a) 0.25 and 0.36 (b) 1/96 and 1/24 (c) 5 and 175 Chapter 12 (unitary method and its Application) Direct variation: Q. 26 iron rods of the same size weigh 312 kg. What will be weight of 42 such iron rods? Sol:- the weight of 26 iron rods = 312 kg So, the weight of 1 iron rod = 312 / 26 So, The weight of 42 iron rods = x 42 = 504 kg Exercise :- If a man working for 56 hours earns rs 1876, how much will he earn for working 27 hours? Exercise :- 4 men makes 4 cupboards in 4 days, how many cupboards can 14 men make in 14 days? Inverse variation : Q. 120 men had food provision for 200 days. After 10 days, 40 men dies due to an epidemic. How long will the remaining food last? Sol :- After 10 days 40 men died So, the remaining food is sufficient for 120 men. We have to find how long the remaining food will last for 80 men. For 120 men, the food is sufficient for 200 days So, for 1 men, the food last (200 x 120) (less men, more days) For 80 men, the food last for = = 300 days (more men, less days ) Exercise :- How many days would it take 59 men to build a wall which 118 men can build in 3 weeks? Exercise :- Ram has enough money to buy 75 machines worth rs 200 each. How many machines can he buy if he gets a discount of rs 50 on each machine? Compound Variation:- Q. 26 horses eat 5 bags of corn in 12 days, how much will 10 horses eat in 18 days?

Sol:- In 12 days 25 horses eat 5 bags of corn In 1 day 25 horses eat 5/12 bags of corn (less days, less corn) In 1 day 1 horse eat bags of corn (less horses, less corn) In 1 day 10 horses will eat x 10 bags (more horses, more corn) In 18 days 10 horses will eat bags of corn = 3 bags (more days, more corn) Exercise:- In how many days of working 8 hours each day can 12 men do the same work as 10 men working 9 hours a day do in 16 days? Exercise :- 3 pumps working 8 hours a day can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day? Time and Work:- Q. A can do a piece of work in 12 days, which A and B working together can do it in 8 days. how long will B take working alone? Sol:- (A+B)`s 1 day`s work = 1/8 A`s 1 day work = 1/12 B`s 1 day work = (A+B)`s 1 day work A`s 1 day work = (1/8 1/12) = = 1/24 So B working alone will finish the work in 24 days. Exercise :- A can do a piece of work in 30 days and B can do it in 6 days. How long will A and B take to do work, working together? Exercise :- A and B can polish the floor in 12 days. A can do alone 1/5 of this job in 4 days. In how many days can B alone polish the floors? Chapter 23 (Quadrartic equations) :- Q. Solve :- x 2 3x -10 = 0 Sol:- x 2 3x -10 = 0 =) x 2 5x + 2x -10 = 0 =) x(x - 5) + 2 (x - 5) = 0 =) (x - 5)(x + 2) = 0 X= 5 or x= - 2 Exercise :- (1) Solve : x 2 25 (2) Solve : x 2 49 (3) Solve : 4 = 100 y 2 (4) solve : 2 x 2 = 8 (5) Solve : x 2 7x +12 = 0 (6) Solve : x 2 5x -6 = 0 (7) Solve: 2x 2 10x +12 = 0 Q. Solve : - =

Sol:- = = = (By cross multiplication) =) x 2 + 2x 15 = 48 =) x 2 + 2x 15 48 = 0 =) x 2 + 2x 63 = 0 =) x 2 + 9x 7x 63 = 0 =) x(x +9) 7(x +9) = 0 =) (x+9) (x-7) = 0 X=- 9 or x = 7 Exercise :- Solve : (1) = 2 (2) + = 6 (3) - = (4) + = (5) + = Chapter 24 (Linear Inequations) :- Q. solve the inequality : 23 4x < 7 Sol:- 23 4x < 7 =) 23 7 < 4x =) 16 < 4x x > 4 Exercise :- find the solution set for inequality: (a) x-8 < 30 where x is a square number. (b) 17x 119 where x is a positive odd number. Q. Solve the inequality 3n +8 < 29 if n W and graph the solution set. Sol:- W = set of whole numbers = {0,1, 2, 3, } =) 3n + 8 < 29 =) 3n < 29 8 =) 3n < 21 N < 7 So the solution set = all whole numbers less than 7 = {0,1,2,3,4,5,6} -1 0 1 2 3 4 5 6 7 8

Exercise :- Solve the inequation and show the solution on a number line: (1) 6 + 3t > 27 for even numbers less than 15. (2) 13 y < 9 for prime numbers less than 20. (3) y + 3 > - 4 for real numbers. Q. Solve the inequalities and the solution on number line from - 4 to 4. - 1 2x + 1 < 5 Sol:- -1 2x + 1 2x + 1 < 5 = -1 1 2x 2x < 5-1 = - 2 2x 2x < 4 = -1 x x < 2 i.e. 1 x < 2-1 0 1 2 Exercise :- Solve the inequalities & show on number line :- (1) 4 3x + 2 11 (2) 2 < 4 x 6 (3) 8 3x + 1 10 (4) 9 > 3 (2 - x) - 3 (5) 1 2x + 4 < 5 (6) 8 4x 12 Chapter 29 (Construction of special types of Quadrilaterals) :- Q. Construct a Quadrilateral:- ABCD in which AB = 3.6 cm, BC = 5.5 cm, CD = 4.9 cm, DA = 5.3 cm and AC = 7.2 cm. D 5.3 cm 4.9 cm A 7.2 cm 7 C 3.6 cm 5.5 cm B Steps :- (1) Draw AC = 7.2 cm (2) with center A and AB = 3.6 cm as radius, draw an arc on any side of AC. (3) Same with C and draw C line BC to intersect arc of step (2). (4) Similarly with AD = 5.3 cm and CD = 4.9 cm (5) Join AB, BC, CD, and AD. then ABCD is the required quadrilateral.

Exercise :- Construct quadrilaterals ABCD of : (1) AB = 4.5 cm, BC = 3.5 cm, AD = 3 cm, AC = 5 cm and BD = 4.5 cm. (2) AB = 5 cm, BC = 4 cm, CD = 6 cm, AD = 7 cm and B = 80. (3) PQ = 3.5 cm, QR = 5.5 cm, QS = 5.5 cm, PS = 4.5 cm, SR = 4.5 cm (4) PQ = QR = 3.5 cm, PS = RS = 5.2 cm, PQR = 120. Q. Construct a rectangle ABCD, AB = 5 cm, BC = 3 cm. Sol :- D 5 cm C 3 cm 3 cm A 5 cm B Steps :- (1) draw AB = 5 cm. (2) At A draw AX AB. (3) From AX cut of AD = 3 cm. (4) With 3 cm radius and center B draw an arc. (5) With radius 5 cm and center D, draw another arc cutting the arc of step (4) at C. (6) Join BC and DC, ABCD is the required rectangle. Q. Construct a square ABCD, one side = 4 cm. D 4 cm C 4 cm 4 cm A 4cm B Steps :- (1) Draw AB = 4 cm. (2) At A, draw AX AB. (3) From AX, cut of AD = 4 cm. (4) With B and D centers and radii 4 cm each, draw two arcs cutting each other at C. (5) Join BC and DC, ABCD is the required square. Exercise : Construct a rectangle ABCD : (1) AB = 6 cm, BC = 5 cm (2) AB = 5.8 cm, BC = 4.6 cm (3) AB = 6.4 cm, AC = 7.8 cm Exercise :- Construct a square ABCD : (1) of side 4.5 cm. (2) of side 5.4 cm.

(3) one diagonal = 7 cm. Q. Construct a Parallelogram ABCD, AB = 4 cm, BC = 3 cm, A = 60. D C 3 cm 60 A 4 cm B Steps :- (1) Draw AB = 4 cm. (2) Through A, draw AX making BAX = 60. (3) From AX, cut off AD = 3 cm. (4) With center D and radius 4 cm, draw an arc. (5) Join BC and DC, required ABCD parallelogram done. Exercise :- Construct a parallelogram ABCD of : (1) AB = 6.5 cm, BC =5.2 cm, B = 45. (2) AB = 6.8 cm, AC = 8 cm, BD = 7.3 cm (3) AB = 7 cm, BC = 5.8 cm, A = 120. Chapter 33 (Rotation) :- Q. State the co- ordinates of image of P (5, 2), Q (- 7, 4), R (9, - 4), T (- 5, - 3) after reflection in x axis.

After reflection in x- axis, P` (5, -2), Q`(-7,- 4), R`(9, 4), T` (- 5, 3). Exercise : - (1) state the co-ordinates of image of each of the following points : A (11, 14), B(- 10, 15), C (17, -12), D(- 6,8) after reflection in y- axis. (2) Write down the co-ordinates of image of each points E (- 7, - 13) and F (16, - 21) when (a) reflected in x- axis (b) reflected in y- axis (3) The vertices of a ABC are A (- 5,9), B (- 10,5), C(- 2,3). Find the co-ordinates of the vertices of the image of this triangle after reflection in the x- axis. Draw the figure and its image. (4) On a graph paper plot the ABC, where A (4,4), B(10,10) and C (18,2). Now draw the image of ABC under the reflection on y- axis. Q. Plot the point on graph and show its image under indicated rotation A (4,6), 90 clockwise. Sol:- A(4,6) through 90 clockwise. (1) Plot the point A(4,6). (2) join OA (3) construct AOA` = 90, OA` = OA Then A`(6, - 4) is the image of A.

Exercise :- Plot the points on a graph and show their images under the given rotation. (1) B (-8,- 10) through 90 clockwise. (2) P(5, - 9) through 90 clockwise. (3) D (7, - 11) through 90 anticlockwise. (4) K (6, 4) through 90 anticlockwise. (5) F (-7, - 4) through 90 anticlockwise. (6) Construct an image of a ABC with A (5, - 6), B (5, - 9), C (8, - 9) under an anticlockwise rotation of 90 about the origin. Chapter 35 (Circumference and Area of a Circle) :- Q. Find the circumference and area of a circle of radius = 10.5 cm. Sol:- Radius (r) = 10.5 cm Area of circle = = 22/7 x 0.5 = 693/2 = 346.5 cm 2 Circumference = 2r = 2 x 22/7 x 10.5 = 66 cm Exercise :- Find the circumference and area of circle of : (1) radius = 35 cm (2) diameter = 9.8 cm (3) diameter = 56 cm Q. Find the diameter of a circle whose circumference is 66 cm. Sol:- circumference = 66 cm Circumference of circle = 2r 66 = 2 x 22/7 x r

r = so diameter = 2r = 2 x 15.5 = 31 cm = 15.5 cm Q :-The circumference of a flower bed is 88 cm. Find its area. Sol :- circumference = 88 cm Area of circle = Circumference of circle = 2r 88 = 2r r = 88/ 2 r = = 2 x 7 = 14 cm so area = = / x 14 x 14 = 616 cm2 Exercise :- (1) find the area of a circle whose circumference is 44 cm. (2) Find the area of circle whose circumference is 110 cm. Q. Find the perimeter of 5 cm 17 cm Sol :- length of rectangle = 17 cm Breadth = 5 cm Diameter of half circle = 17 cm Radius of half circle = 17/2 cm Perimeter of half circle = r + 2r = x + 2 x = + 17 = = cm Perimeter of rectangle = 2 (l + b) = 2 (17 + 5) = 2 x 22 = 44 cm So perimeter of shape = + 44 = Exercise :- (1) Find the perimeter of shape = = 87.7 cm 6 cm

(2) Find the perimeter of the shape. Q. Find the area of the shape. Sol:- length of rectangle = 4 cm Breadth of rectangle = 3 cm Area of rectangle = l x b Area of half circle = Radius = 2 cm Area of the shape = (l x b) + = (4 x 3) + x 22/7 x 2 x 2 = 12 + 44/7 = = 128 /7 = 18.2 cm 2 Exercise :- (1) Find the area of the shape correct to 1 d.p. (2) Find the area of the shaded region of the shape correct to 1 d.p.

Chapter 37 (Data Handling) :- Q. find the mean : x 5 15 25 35 45 f 7 8 20 10 5 Sol:- mean = X f fx 5 7 35 15 8 120 25 20 500 35 10 350 45 5 225 Total 50 1230 Mean = 1230/ 50 Mean = 24.6 Exercise :- (1) Find the mean of first ten natural numbers. (2) find the mean of first ten prime numbers. (3) find the mean of the following: X 4 6 9 10 15 F 5 10 10 7 8 Q. find the mean : Marks 0-10 10-20 20-30 30-40 40-50 50-60 No.of 12 18 27 20 17 6 students Sol :- marks frequency X fx 0-10 12 5 60 10-20 18 15 270 20-30 27 25 675 30-40 20 35 700 40-50 17 45 765 50-60 6 55 330 total 2800

Mean = = 2800 /100 = 28 marks Exercise :- (1) Find the mean : x 25-35 35-45 45-55 55-65 65-75 f 6 10 8 12 4 (2) Find the mean : Class 0-8 8-16 16-24 24-32 32-40 interval frequency 5 6 4 3 2 Median :- Q. Find the median of 4, 8, 12, 16, 20, 24, 28, 32 Sol:- Arrange them in ascending order 4, 8, 12, 16, 20, 24, 28, 32 Median = = = 18 Exercise :- Find the median : (1) 60, 33, 63, 61, 44, 48, 51 (2) 13, 22, 25, 8, 11, 19, 17, 31, 16, 10 (3) 15 students got marks in test of mathematics. Find the median marks : 35, 28, 13, 17, 20, 30, 19, 29, 11, 10, 29, 23, 18, 25, 17 Mode :- Find the mode of size 2 3 4 5 6 7 frequency 4 6 2 5 3 1 Sol:- size Frequency 2 4 3 6 4 2 5 5 6 3 7 1 So highest frequency is 6 hence 3 is the mode. Exercise :- (1) Find the mode :

Size of shoes No. of persons 6 7 8 9 10 12 20 40 15 7 (2) Find the mode : (a) 5,3,5,2,3,5,1,7 (b) 4,6,8,4,8,4,8,4,12,6,10 Histogram & Bar Graphs :- Exercise :- (1) Represent the data by a bar graph : English Hindi Science Math Social science 75 60 80 95 85 (2) Represent the data by bar graph : scooter Bike Car Van Bus 25 40 20 15 10 (3) Represent the data by histogram graph : Age(in years) 25-30 30-35 35-40 40-45 45-50 No. of teacher 12 11 8 1 3 (4) Draw histogram graph for the data : size 0-10 10-20 20-30 30-40 40-50 frequency 5 10 20 25 30 -----------------------------------------