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Q1. Write the base and exponent of the following numbers. Also write the expanded form and the value. (i) 3 4 (ii) (-4) 3 (iii) 1 8 Solution Number Base Exponent Expanded form Value 3 4 3 4 3 x 3 x 3 x 3 81 (-4) 3 -4 3 -4 x -4 x -4 -64 1 8 1 8 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 1 Q2. Write the following in standard form. (i) 458000 (ii) 1780000 (iii) 85000 Solution (i) 458000 = 4.58 x 100000 = 4.58 x 10 5 . (ii) 1780000 = 1.78 x 1000000 = 1.78 x 10 6 . (iii) 85000 = 8.5 x 10000 = 8.5 x 10 4 . Q3. Express the following numbers in exponent form. (i) 343000 (ii) 2048 Solution (i) 343000 = 343 x 1000 = 7 x 7 x 7 x 10 x 10 x 10 = 7 3 x 10 3 . (ii) 2048 = 2 x 1024 = 2 x 2 x 512 = 2 x 2 x 2 x 256 = 2 x 2 x 2 x 2x 128 = 2 x 2 x 2 x 2 x 2 x 64 = 2 x 2 x 2 x 2 x 2 x 2 x 32 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 16 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 8 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2 11 Q4. Express the number...
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12

Q1. Classify the following as monomial, binomial or trinomial: (i) 2x + 3y (ii) 2x 3 + 3y 2 - 1 (iii) 2xy + 10 (iv) -9x 4 yz Solution (i) 2x + 3y : Binomial (ii) 2x 3 + 3y 2 - 1 : Trinomial (iii) 2xy + 10 : Binomial (iv) -9x 4 yz : Monomial Q2. Identify like terms in the followings: -xy 2 , -7yx 2 , -6x 2 z 2 , -18z 2 x 2 , 3x 2 y, 2xy 2 Solution -xy 2 and 2xy 2 are like terms. -7yx 2 and 3x 2 y are like terms. -6x 2 z 2 and -18z 2 x 2 are like terms. Q3. An electrician charges Rs 45 per hour and spends Rs 20 a day on gasoline. Write an algebraic expression to represent his earnings for one day. Solution Let x represent the number of hours the electrician works in one day. Since charges is Rs 45 per hours. So the charges for x hours is RS 45x. Now Rs 20 is spend on gasoline, therefore The electrician's earning can be represented by the following algebraic expression 45x - 20 Q4. Add the following expressions: 6m - 7...
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11

Q1. If the area of a rectangle is 243 square m and the length is 27 m, what is the breadth of the rectangle? Solution Area of a rectangle is given by Area = length x breadth = l x b Now, area is given as 243 m 2 and its length = 27 m Thus, Area = l x bi.e. 243 = 27 x b Or 27 x b = 243 Taking 27 to the RHS and dividing 243 by it, we get b = 9 Thus, breadth of the rectangle = 9 m Q2. The area of a square is 16 square centimetres. What is the length of each side? Solution A Square has 4 equal sides. Thus, given the area = 16 cm 2 , we get length of each side as: Area = side x side = s x s Or s x s = Areai.e. s 2 = 16 = 4 2 Therefore, s = 4 cm Thus, length of each side of the square is 4 cm. Q3. A rectangle whose area is 24 m 2 has a length that is 2 m longer than the width. What are the dimensions of the rectangle? Solution Given that area of the rectangle = 24 m 2 Let the width of the rectangle be 'b' m Thus, length (l) of the rectangle = (b +...
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6

Q1. Can we form a triangle having angles 58 o  , 80 o  and 90 o  ? Solution Q2. Answer what kind of triangle it is: (a) A triangle has angle measurements of 90 o , 20 o  and 70 o ? (b) A triangle has angle measurements of 14 o , 30 o  and 136 o ? (c) A triangle has angle measurements of 76 o , 68 o  and 36 o ? Solution We know that In an acute-angled triangle, all three angles are less than 90°. In a right-angled triangle, one angle is exactly 90 o . In an obtuse-angled triangle, one angle is greater than 90 o . (a) This triangle is a right-angled triangle because it has a 90 o angle which is a right angle. (b) This triangle is an obtuse-angled triangle because it has a 136 o angle which is an obtuse angle. (c) This triangle is an acute-angled triangle because it has all three angles acute, that is less than 90 o . Q3. Is it possible to have a triangle with the sides having following lengths? 5 cm, 3 cm, 4 cm Solution We k...
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5

Q1. If the degree measure of an angle is 30 o greater than twice the degree measure of its supplementary angle, what is the degree measure of the angle? Solution Let d = the degree measure of the angle. Then, 180 o - d = the degree measure of the supplement of the angle. We now set up an equation according to the question: d = 2 x (180 o - d) + 30 o We now solve for d: d = 360 o - 2d + 30 o (using distributive property) d + 2d = 360 o + 30 o (adding 2d on both sides) 3d = 360 o + 30 o (combining like terms) 3d = 390 o (dividing both sides by 3) d = 130 o Thus, the angle measures 130 o . Q2. What is the measure of complement of each of the angle XYZ = 32o? Solution To find the complement of each of the given angle, we have to subtract them from 90 o , since the sum of two complementary angles is 90 o .Complementary angle the angle XYZ = 90 o - 32 o  = 58 o . Q3. What is the measure of supplement angle of the angle ABC of measure 88 o ? Solution ...
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4

Q1. Evaluate the expression: (a) vw - v = ? ( for v = 6 and w = 3 ) (b) 8z + 5 = ? ( for z = 9 ) Solution Here we have to put the values of the variables given in the bracket. (a) vw - v Put v = 6 and w = 3 i.e. vw - v = (6 x 3) - 6 = 18 - 6 = 12 (b) 8z + 5 Put z = 9 i.e. 8z + 5 = (8 x 9) + 5 = 72 + 5 = 77 Q2. Sumitra has Rs 34 in denominations of 50 paisa and 25 paisa coins. If the number of 25 paisa coins is twice the number of 50 paisa coins, then how many coins of each type does she has in all? Solution Let the number of 50 paisa coins = x Then, number of 25 paisa coins = 2x Total money with Sumitra = Rs 34 = 34 × 100 paise = 3400 paiseFrom the given condition, we have: 50x + 25 × 2x = 3400 50x + 50x = 3400 100x = 3400 x = 34 Number of 50 paisa coins = 34 Number of 25 paisa coins = 2 × 34 = 68 Q3. A sum of Rs. 500 is in denominations of Rs. 5 and Rs. 10. If the total number of notes is 90, find the number of notes of each type? Solution Let ...
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3

Q1. In a cricket match, the runs scored by 11 players are as follows12, 23, 10, 77, 15, 78, 90, 54, 23, 10, xThe average score is 44 runs. Find the value of x. Solution Q2. Find median of the following information:4, 5, 6, 2, 9, 8, 2, 2, 3, 5, 5, 7,1 Solution The numbers in ascending order:  1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8,  9Median is the middle most value.So, median = 5 Q3. Read the given table and answer the questions that follow: City Minimum Maximum Delhi 39 o C 38 o C Mumbai 34 o C 35 o C Kolkata 35 o C 38 o C Chennai 38 o C 40 o C Jaipur 39 o C 42 o C (a) Which cities have equal minimum temperature? (b) Which city has the highest maximum temperature? Solution (a) Delhi and Jaipur have equal minimum temperature i.e. 39 o C (b) Jaipur has the highest maximum temperature of 42 o C Q4. Calculate median and mode for following data : 23, 45, 46, 12, 34, 87, 78, 12, 65, 33, 19, 34, 55, 67, 81, 12, 56, 98, 11, 4...
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