202110219-TRIUMPH-STUDENT-WORKBOOK-MATHEMATICS-G07-PART1

(ii) [AS2] In the given figure, ∠B = ∠D = 90◦ and AB = DE. Prove that CD = BC. 7(i) [AS2] Write the congruence of the triangles in the correct correspondence. a) b) (ii) [AS1] In the given figure, X is the midpoint of side BC and AX ⊥ BC. Prove that △AXB is congruent to △AXC and hence AB = AC. 8(i) [AS2] Given here are the measurements of some parts of two triangles. Examine whether the two triangles are congruent or not. In △ABC, ∠A = 90◦, AC = 5 cm and BC = 9 cm △PQR, ∠Q = 90◦, PR = 8 cm and PQ = 5 cm EXERCISE 8.4. RIGHT –ANGLE HYPOTENUSE SIDE CONGRUENCY (RHS) 147

(ii) [AS2] In the adjoining figure, DA ⊥ AB, CB ⊥ AB and AC = BD. State the three pairs of equal parts in ABC and DAB. Which of the following statements is meaningful? a) ABC BAD b) ABC ABD 9(i) [AS2] Given here are the measurements of some parts of two triangles. Examine whether the two triangles are congruent or not. △ABC, ∠B = 90◦, AC = 8 cm and AB = 3 cm △PQR, ∠P = 90◦, PR = 3 cm and QR = 8 cm (ii) [AS1] In the adjoining figure, LR = QM and ∠QLR = ∠QMR = 90◦. Prove that △MQR △LRQ. Long Answer Type Questions 10 [AS2] In a right–angled triangle ABC, right angled at A, AB = 8 cm and BC = 10 cm. In another right–angled triangle DEF, right angled at E, DE = 8 cm and DF = 10 cm. Are thesetriangles congruent? If so, write the congruence of the triangles in correct corresponding order. EXERCISE 8.4. RIGHT –ANGLE HYPOTENUSE SIDE CONGRUENCY (RHS) 148

11 [AS2] In the figure, the perpendiculars OP and OQ from the ray AO to AB and AC respectively are congruent. Prove that AO is the angle bisector of ∠CAB. EXERCISE 8.4. RIGHT –ANGLE HYPOTENUSE SIDE CONGRUENCY (RHS) 149

CHAPTER 9 CONSTRUCTION OF TRIANGLES EXERCISE 9.1 CONSTRUCTION OF A TRIANGLE WHEN MEASUREMENTS OF THE THREE SIDES ARE GIVEN 9.1.1 Key Concepts i. A triangle can be drawn if any three of its elements are known. ii. Steps to construct a triangle when the measures of its three sides are given: a. To construct a triangle when lengths of three sides are given, take any one side (name the two vertices). b. With one of the other sides as radius, draw an arc. c. Again, with the third side as radius, draw another arc intersecting the first one. This is the third vertex. d. Join the point of intersection of the arcs to the other vertices. 9.1.2 Additional Questions Objective Questions . 1. [AS3] If the lengths of all the sides of triangle are equal then it is called a / an (A) Isosceles triangle (B) Scalene triangle (C)Equilateral triangle (D)Obtuse triangle 2. [AS3] If the lengths of any two sides of a triangle are equal then it is called a/an . (A) Isosceles triangle (B) Scalene triangle (C)Equilateral triangle (D)Acute triangle EXERCISE 9.1. CONSTRUCTION OF A TRIANGLE WHEN MEASUREMENTS OF. . . 150

3. [AS3] If the lengths of all sides of a triangle are different then it is called a/ an . (A) Isosceles triangle (B) Scalene triangle (C)Equilateral triangle (D)Right triangle 4. [AS3] The sum of the lengths of any two sides of a triangle is always the third side. (A) Greater than (B) Less than (C)Equal to (D)None of these 5. [AS3] The difference of the lengths of any two sides of a triangle is always the third side. (A) Greater than (B) Less than (C)Equal to (D)None of these Long Answer Type Questions 6 [AS2] Which of the measures given can be used to construct a triangle? If not, give reasons. (i) 8 m, 4 m, 2 m (ii) 9 cm, 9 cm, 4 cm (iii) 7 cm, 20 cm, 6 cm (iv) 7 cm, 20 cm, 8 cm (v) 4 cm, 4 cm, 10 cm 7 [AS5] Construct ∆PQR, given PQ = 3.5 cm, PR = 4.5 cm and QR = 5.5 cm. 8 [AS5] Construct a triangle ABC which has sides AB = 6 cm, BC = 3 cm and CA = 5 cm. 9 [AS5] Construct a △ABC in which BC = 6.2 cm, AB = 5 cm, and AC = 4.3 cm. 10 [AS5] Construct a △PQR in which PQ = 5.3 cm, PR = 4.6 cm and QR = 3.8 cm. 11 [AS5] Construct a △ABC in which BC = 3.6 cm, AB = 5 cm and AC = 5.4 cm. EXERCISE 9.1. CONSTRUCTION OF A TRIANGLE WHEN MEASUREMENTS OF. . . 151

12 [AS5] Construct an equilateral triangle each of whose sides measures 6.2 cm. 13 [AS5] Construct a △PQR in which PQ = PR = 4.8 cm and QR = 5.3 cm 14 [AS5] Construct a triangle ABC with AB = 5 cm, BC = 6.5 cm and CA = 4 cm. Construct another triangle PQR with PQ = 5 cm, QR = 6.5 cm and RP = 4 cm. Are these triangles congruent? 15 [AS5] Construct ∆ PET, with PE = 4.5 cm, ET = 5.4 cm and TP = 6.5 cm. Construct another triangle ABC, in which AB = 5.4 cm, BC = 4.5 cm and CA = 6.5 cm. Are these triangles congruent? EXERCISE 9.1. CONSTRUCTION OF A TRIANGLE WHEN MEASUREMENTS OF. . . 152

EXERCISE 9.2 CONSTRUCTION OF A TRIANGLE WHEN TWO SIDES AND THE INCLUDED ANGLE ARE GIVEN 9.2.1 Key Concepts i. A triangle can be drawn if any three of its elements are known. ii. To construct a triangle when two sides and the included angle are given, draw a side first. iii. Construct a ray with the measurement of the included angle. iv. Mark the third vertex along the ray with the measurement of the second side. 9.2.2 Additional Questions Objective Questions 1. [AS3] A triangle has _________. (A) 3 sides and 2 angles (B) 2 angles and 3 sides (C)3 sides and 3 angles (D)3 sides and many angles 2. [AS1] △ ABC is an isosceles triangle with ∠C = 90◦and AC = 5 cm. Then, AB = _______. (A) 2.5 cm (B) 5 cm (C)10 cm √ (D)5 2 cm 3. [AS1] In ABC, ∠ B = 90◦, AB = 5 cm and AC = 13 cm. Then, BC = ________. (A) 8 cm (B) 18 cm (C)12 cm (D)None of these EXERCISE 9.2. CONSTRUCTION OF A TRIANGLE WHEN TWO SIDES AND T. . . 153

4. [AS1] △ ABC is right angled at A. If AB = 24 cm and AC = 7 cm then BC = ________. (A) 31 cm (B) 17 cm (C)25 cm (D)28 cm 5. [AS3] In ABC, the inequality that holds good is ________. (A) AB + BC > AC (B) AB + BC < CA (C) AB − BC < CA (D) Both (A) and (C) Long Answer Type Questions 6 [AS5] Construct a triangle ABC with AB = 7 cm, BC = 3 cm and ∠B = 60◦. 7 [AS5] Construct △PQR, given PQ = 3.5 cm, PR = 3 cm and ∠RPQ = 120◦ . 8 [AS5] Construct a △ ABC in which AB = 5 cm, AC = 4.3 cm and ∠A = 60◦. 9 [AS5] Construct a △ PQR in which QR = 4.2 cm, ∠ Q = 120 ◦ and PQ = 3.5 cm. 10 [AS5] 11 [AS5] Construct a △ ABC in which AB = 3.8 cm, ∠ A = ◦ and AC = 5 cm. 60 Construct a △ LMN in which LM = 5 cm, MN = 4 cm and ∠M = 60◦. 12 [AS5] Construct a △ ABC in which AB = AC = 5.2 cm and ∠ A = 120◦. 13 [AS5] Construct a △ABC with AB = 5 cm, BC = 6.5 cm and ∠B = 60◦. Construct another△PQR with PQ = 5 cm, QR = 6.5 cm and ∠Q = 60◦. EXERCISE 9.2. CONSTRUCTION OF A TRIANGLE WHEN TWO SIDES AND T. . . 154

EXERCISE 9.3 CONSTRUCTION OF TRIANGLE WHEN TWO ANGLES AND THE SIDE BETWEEN THE ANGLES ARE GIVEN 9.3.1 Key Concepts i. To construct a triangle, when two angles and the included side between them are given, construct the included side. ii. Construct two rays at the ends of the line segment with the given measurements of the angles. iii. The rays of these angles will meet to give the third vertex. 9.3.2 Additional Questions Objective Questions 1. [AS3] The sum of angles of a triangle is _________. (A) 90◦ (B) 180◦ (C) 270◦ (D) 360◦ 2. [AS2] The triangle formed by BC = 7.2 cm, AC = 6 cm and ∠ C = 120◦ is _______. (A) An acute angled triangle (B) An obtuse angled triangle (C)A right angled triangle (D)An equilateral triangle 3. [AS2] In the given figure, if AD = BC and AD BC, then __________. (A) AB = AD (B) AB = DC (C)BC = CD (D)AD = CD EXERCISE 9.3. CONSTRUCTION OF TRIANGLE WHEN TWO ANGLES AND TH. . . 155

4. [AS3] The sum of the exterior angles of a triangle is ______. (A) 360◦ (B) 180◦ (C) 720◦ (D) 540◦ 5. [AS2] The triangle formed by PQ = 5.8 cm, QR = 5 cm and ∠ Q = 60◦ is _______. (A) An acute angled triangle (B) An obtuse angled triangle (C)A right angled triangle (D)An isosceles triangle Long Answer Type Questions 6 [AS5] Construct a triangle ABC with ∠A = 60◦, ∠B = 30◦ and AB = 5.6 cm. 7 [AS5] Construct ∆PQR, given ∠RPQ = 30◦, PR = 4.5 cm and ∠PQR = 45◦. 8 [AS5] Construct a △ ABC in which BC = 4.8 cm, ∠ B = 60◦ and ∠ C = 75.◦ 9 [AS5] Construct a △ ABC in which BC = 5.3 cm, ∠B = 45◦ ◦ and ∠A = 75 . 10 [AS5] Construct a △ ABC in which AB = 3.8 cm, ∠A = 60◦ and ∠B = 70◦. 11 [AS5] Construct a △ ABC in which BC = 6.2 cm, ∠B = 60◦ and ∠C = 45 ◦. 12 [AS5] Construct a △ ABC in which BC = 5.8 cm, ∠ B = ∠ C = 30◦. Measure AB and AC. What do you observe? 13 [AS5] Construct △ABC with BC = 6 cm, ∠B = 55◦ and ∠C = 40◦ and construct another △PQR with QR = 6 cm and ∠Q = 55.◦ 14 [AS5] Draw a triangle ABC with BC = 3 cm, ∠ B = 70◦ and ∠ C = 60◦. Draw another triangle PQR with QR = 5 cm, ∠ Q = 70◦. EXERCISE 9.3. CONSTRUCTION OF TRIANGLE WHEN TWO ANGLES AND TH. . . 156

EXERCISE 9.4 CONSTRUCTION OF RIGHT ANGLED TRIANGLE WHEN THE HYPOTENUSE AND THE SIDE ARE GIVEN 9.4.1 Key Concepts i. To construct a right angled triangle when the hypotenuse and a side are given, first draw the side. ii. Then draw a ray, perpendicular to the side (to get a right angle). iii. At the other end of the side, with radius as hypotenuse, draw an arc. iv. This arc intersects the ray at the third vertex. 9.4.2 Additional Questions Objective Questions 1. [AS1] In the adjoining figure, x = _______. (A) 7 (B) 5 (C) 4 (D) 10 2. [AS3] The side opposite to the right angle in a right angled triangle is called its _______. (A) Median (B) Altitude (C) Hypotenuse (D)None of these EXERCISE 9.4. CONSTRUCTION OF RIGHT ANGLED TRIANGLE WHEN THE . . . 157

3. [AS2] For the adjoining figure, the true statement among the following is _________. (A) y2 = x2 + z2 (B) x2 = y2 + z2 (C)z2 = x2 + y2 (D)z2 = x2 − y2 4. [AS1] In PQR, if ∠ Q = 90◦and ∠ R = 45◦then ∠ P = ________. (A) 30◦ (B) 20◦ (C) 50◦ (D) 45◦ 5. [AS1] In △ LMN, if LM = LN, ∠ L = 90◦, then ∠ M = _______. (A) 30◦ (B) 60◦ (C) 90◦ (D) 45◦ EXERCISE 9.4. CONSTRUCTION OF RIGHT ANGLED TRIANGLE WHEN THE . . . 158

Long Answer Type Questions 6 [AS5] Construct a right angled triangle △MNP in which MP = 10 cm and hypotenuse NP = 13 cm. 7 [AS5] Construct a right-angled triangle ABC, right angled at B in which AB = 5.4 cm and BC = 4 cm. 8 [AS5] Construct a △ ABC in which base BC = 4.8 cm, ∠ B = 90,◦ and hypotenuse AC = 6.2 cm. 9 [AS5] Construct a right angled triangle whose hypotenuse measures 5.6 cm and one of whose acute angles measures 30 ◦. 10 [AS5] Construct △ ABC in which BC = 4.8 cm, ∠ C = 90◦ and AB = 6.3 cm. 11 [AS5] Construct a right angled triangle one side of which measures 3.5 cm and the length of whose hypotenuse is 6 cm. 12 [AS5] Construct a right triangle having hypotenuse of length 7 cm and one of whose acute angles measures 40◦. 13 [AS5] Draw a △ ABC with ∠ B = 90◦ AB = 6 cm and hypotenuse AC = 10 cm. Draw , an other △ PQR with ∠ Q = 90 ◦ PQ = 6 cm and hypotenuse PR = 10 cm. Are these triangles , congruent? 14 [AS5] Construct the following right-angled triangles and check whether they are congruent. (i) ∆PQR in which PQ = 7 cm and hypotenuse QR = 12 cm. (ii) ∆ABC in which hypotenuse AB = 9 cm and side AC = 6 cm. EXERCISE 9.4. CONSTRUCTION OF RIGHT ANGLED TRIANGLE WHEN THE . . . 159

EXERCISE 9.5 CONSTRUCTION OF TRIANGLE WHEN TWO SIDES AND THE NON-INCLUDED ANGLE ARE GIVEN 9.5.1 Key Concepts i. To construct a triangle when two sides and the non–included angle are given, draw the side which has the given angle. ii. Construct a ray with the measurement of the given angle. iii. On the other end of the line segment, taking a radius equal to the second side, draw an arc. iv. This arc intersects the ray at the third vertex. 9.5.2 Additional Questions Objective Questions 1. [AS2] In △ PQR, if PQ = PR then _______. (A) ∠ Q = ∠ R (B) ∠ P = ∠ Q (C)∠ R = ∠ P (D)∠ Q = 2 ∠ P 2. [AS1] In △ LMN, if LM = LN and ∠ L = 60◦ then ∠ M = _____. (A) 30◦ (B) 60◦ (C) 90◦ (D) 20◦ 3. [AS1] In △ ABC, if AB = BC = CA = 5 cm then ∠ B = ______. (A) 30◦ (B) 60◦ (C) 90◦ (D) 45◦ 4. [AS1] In △ PQR, if PQ = QR and ∠ P = 70◦ then ∠ Q = ______. (A) 30◦ (B) 50◦ (C) 40◦ (D) 20◦ EXERCISE 9.5. CONSTRUCTION OF TRIANGLE WHEN TWO SIDES AND THE. . . 160

5. [AS1] In △ ABC, if BC = CA and ∠ A = 80◦ then ∠ B = _____. (A) 30◦ (B) 100◦ (C) 80◦ (D) 20◦ Very Short Answer Type Questions 6 [AS2] Answer the following questions in one sentence. Which of the following can be constructed as a triangle? Why or why not? i) ∠A = 120◦, ∠B = 90◦ and AB = 8 cm ii) ◦ ∠B = 30◦ and AB = 7 cm ∠A = 120 , iii) ◦ ∠Q = 90◦ and PQ = 9 cm ∠P = 90 , iv) ∠A = 70◦, ∠B = 40◦ and AB = 4 cm v) ∠X = 110◦, ∠Y = 95◦ and XY = 8 cm Long Answer Type Questions 7 [AS5] Construct XYZ such that XY = 4.5 cm, XZ = 3.5 cm and ∠Y = 70°. EXERCISE 9.5. CONSTRUCTION OF TRIANGLE WHEN TWO SIDES AND THE. . . 161

CHAPTER 10 ALGEBRAIC EXPRESSIONS EXERCISE 10.1 INTRODUCTION 10.1.1 Key Concepts i. Variable: The quantity that takes different values, x, y, z, a, b, c, m etc are variables. ii. Constant: The value of a constant is fixed. e.g.,1, 2, 3 etc are constants. iii. Algebraic expression: An algebraic expression is a single term or a combination of terms connected by the symbols ‘+’ (plus) or ‘–’(minus). iv. An algebraic expression containing one term is called a monomial. v. An algebraic expression containing two unlike terms is called a binomial. vi. An algebraic expression containing three unlike terms is called a trinomial. vii. An algebraic expression containing more than three unlike terms is called a multinomial. 10.1.2 Additional Questions Objective Questions . 1. [AS3] The number of match sticks required to make 6 “H” shapes is (A) 12 (B) 13 (C) 14 (D) 30 2. [AS3] The expression for '7 is added to twice the sum of x and y’ is . (A) (x + y) + 7 (B) 7(x + y) (C)2(x + y) + 7 (D)(2x + y) + 7 EXERCISE 10.1. INTRODUCTION 162

3. [AS3] '9 is multiplied by x and 7 is added to it’ is written as . (A) 9x + 7 (B) 9(x + 7) (C)9x − 7 (D)7x + 9 4. [AS4] A variable among the following is _________. (A) No. of players in a cricket match (B) Temperature of a city (C) Length of the cricket pitch (D) No. of days in the month of March 5. [AS4] A constant among the following is _____. (A) Temperature of a day (B) Height of a growing plant (C) Length of your classroom (D) All the days of the year Very Short Answer Type Questions 6 [AS1] State true or false. (i) 9x2y is an algebraic expression. (ii) The sign of a variable is always positive. [ ] [ ] [AS1] Fill in the blanks. (iii) 98 + 42 + 11 is a __________ expression. [AS1] Choose the correct answer. (iv) In the expression 11a 2 + 6b2 − 5, the constant term is . (A) 11a2 (B) 6b2 (C)– 5 (D)All of these (v) An expression having a variable and a constant is _______. (A) 4x2 + 9y (B) x2 + 2y (C) x + 3 (D) y + 4x EXERCISE 10.1. INTRODUCTION 163

7 [AS1] State true or false. is 2n. [] (i) The algebraic expression for the pattern [AS1] Fill in the blanks. . (ii) An algebraic expression containing one term is called a (iii) A pattern of letter ‘V’ has two match sticks. The rule which gives the number of match sticks in thepattern is _______________ [AS1] Choose the correct answer. (iv) The rule which gives the number of match sticks required to make a pattern of letter ‘H’ is ____. (A) 2n (B) n (C) 3n (D) None of these [AS1] Answer the following questions in one sentence. (v) If A = 4x2 + 2y2 − 6xy B = 3x2 + 10y2 + 7xy C = 7x2 + 9y2 + 9xy then find a) A + B + C b) A + (B − C). 8 [AS1] Fill in the blanks. . (i) The number of match sticks required to make a square is (ii) The rule which gives the number of match sticks required to make a pattern of the letter ‘B’ is . (iii) The cost of one pencil is Rs. 7. Then the rule for the cost of ‘n’ pencils is . (iv) If the number of sticks required to make a pentagon is 5 then the number of sticks required to make 3 such pentagons is . EXERCISE 10.1. INTRODUCTION 164

[AS1] Choose the correct answer. (v) If the number of match sticks required to make a triangle is 3, then the number of match sticks required to make 3 such triangles is ________ . (A) 3 (B) 6 (C) 9 (D) 12 9 [AS1] State true or false. [ ] (i) 3m + 11 is formed by multiplying m by 3 and adding 11 to the product. [AS1] Fill in the blanks. (ii) The statement ‘8 added to 6 times of m' is expressed as _______. [AS1] Choose the correct answer. (iii) One-fourth of the product of ‘p ’ and ‘q ’ is ______. (A) 1 pq 4 (B) pq 4 (C) p × q 2 2 (D)All the above (iv) 5 subtracted from two times of y is _____. (B) 2(y – 5) (A) 2y – 5 (D) (5 – y2) (C) 5 – 2y (v) 3 more than A is written as ________. (B) 3A (A) 3 + A (D) 3 – A (C) A + 3 EXERCISE 10.1. INTRODUCTION 165

Short Answer Type Questions 10(i) [AS1] Form an expression for 'q is multiplied by –5 and 8 is subtracted from the product'. Form an expression for '8 is multiplied by –p and 6 is added to the product.' Write an expression for the sum of these two expressions. (ii) [AS1] Write in the form of algebraic expression: a) ‘p’ is increased by 6 and the sum is multiplied by 2. b) ‘s’ is multiplied by 4 and the product is divided by 7. c) ‘a’ is 5 more than thrice the value of ‘b’. 11(i) [AS1] m is reduced by 4 and then is multiplied by 6. Write the expression for the given statement. Is the expression the same as (4 – m)6? (ii) [AS1] Write the following statements in the form of algebraic expressions. a) Three times of x added to four times of y. b) Five times of p subtracted from half of q. c) Seven–ninths of b added to three–fourths of a. 12(i) [AS1] Write the given statements as algebraic expressions. a) 8 times x is subtracted from twice y. b) 7 is subtracted from the product of 3 and x. (ii) [AS1] Write the given statements as algebraic expressions. a) One-fourth of the product of a and b. b) 9 is mutiplied by p and the product is added to 7. c) 2 is subtracted from the product of 5 and y. 13(i) [AS1] Write the given statements as algebraic expressions. a) 10 times y is subtracted from k times x. b) 9 is added to p and this result is subtracted from 4 times q. EXERCISE 10.1. INTRODUCTION 166

(ii) [AS1] Write the given statements as algebraic expressions. a) Twice the difference of 9 and a number 'n'. b) Three times the sum of n and 5. c) 8 is subtracted from x and this result is added to the product of 9 and p. 14(i)[AS1] Write the given statements as algebraic expressions. a) Six more than a number r. b) The quotient of eleven and p. (ii) [AS1] Write the given statements as algebraic expressions. a) 9 is subtracted from twice the sum of p and q. b) 4 is added to k and the result is divided by 8. c) 5 times x is added to 8 times y. 15(i) [AS1] Write the given statements as algebraic expressions. a) The product of p and q is added to the quotient of x and y. b) 8 times p is added to twice k. (ii) [AS1] Write the given statements as algebraic expressions. a) 8 times k is subtracted from twice the product of a and b. b) 8 times x is added to 5 times y and this result is subtracted from thrice p. c) 11 is added to 8 times the sum of p and q. EXERCISE 10.1. INTRODUCTION 167

EXERCISE 10.2 ALGEBRAIC TERMS AND NUMERIC TERM 10.2.1 Key Concepts i. Numerical expression: If every term of an expression is a constant term, then the expression is called a numerical expression. e.g., 2 + 1, −5 × 3, (12 + 4) ÷ 3 ii. In the expression 2x + 9, 2x is an algebraic term and ‘9’ is called a numeric term. iii. Like terms are terms which contain the same variables with the same exponents. eg., 12x, 25x, −7x are like terms. 2xy 2, 3xy2, 7xy 2 are like terms. iv. Coefficient: In axn, a is called the numerical coefficient and x is called the literal coefficient. v. Types of algebraic expressions: No. of terms Name of the Examples Expression One term Monomial x, 7xyz, 3x3y, 9x2 Two terms Binomial a + 4x, x2 + 2y Three terms Trinomial ax2 + bx + c More than Multinomial 4x2 + 2xy + cx + d, 9p2 − three terms 11q + 7r + t vi. Degree of a monomial: The sum of all exponents of the variables present in a monomial is called the degree of the term or degree of the monomial. e.g., The degree of 9x2y2 is 4. vii. Degree of a constant term is zero. viii. The highest of the degrees of all the terms of an expression is called the degree of the expression. e.g., The degree of the expression ax + bx 2 + cx3 + dx4 + ex5 is 5. EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM 168

10.2.2 Additional Questions Objective Questions and respectively. 1. [AS3] In 6x − 9, algebraic and numeric terms are (A) 9, 6x (B) 6x, 9 (C) x, 6 (D)9, x 2. [AS3] Identify the like terms in the following. (B) 5yz, 7zx (A) 3xy, 4yz (D)9pq, 8pr (C)9xz, −12zx (B) Unlike 3. [AS3] 4xyz and −8xz are terms. (D) Numerical (A) Like . (C) Constant (B) –12 (D) −12yz 4. [AS3] Numerical coefficient of −12x2yz is (A) 12 (B) –9 (D) −9z (C) 12 x 5. [AS3] Literal coefficient of −9z is . (A) 9 (C) z Very Short Answer Type Questions [ ] 6 [AS2] State true or false. [ ] (i) 3xy and 100xy are like terms. (ii) –2p and 3p are unlike terms. EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM 169

[AS2] Fill in the blanks. . (iii) In like terms, the variable is always the (B) x2, y2 [AS2] Choose the correct answer. (D) x2y2, xy (iv) Identify the like terms. (A) x2, 2x2 (C)mno, pqr (v) x2z and xz2 are _____. (B) Unlike terms (D)None of the above (A) Like terms (C) Constants 7 [AS2] State true or false. [ ] (i) a2 + b2 is a binomial expression. [ ] (ii) A multinomial expression has more than one unlike terms. [AS2] Fill in the blanks. expression. (iii) 104 – 14b is a [AS2] Choose the correct answer. (iv) 10xy2 is a . (A) Monomial (B) Trinomial (D) Binomial (C) Constant . (v) ax2 + 9x + 14 is a (B) Trinomial (D)None of these (A) Monomial (C) Binomial EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM 170

8 [AS1] State true or false. [ ] (i) In the expression 12ab, a is the co-efficient of 12b. [AS1] Fill in the blanks. (ii) 14x is the co-efficient of y. This can be written as __________. [AS1] Choose the correct answer. (iii) xy is the coefficient of 9. This can be written as _____. (A) (xy) + 9 (B) 9(x + y) (C) 9 xy (D)None of these (iv) The numerical co-efficient of –y is_____. (B) –1 (A) 1 (C) −y (D) y (v) If 25 is the co-efficient of x and 18 is the co-efficient of y then the terms are _____. (A) 25x, 8y (B) 18x, 25y (C)25x, 18y (D)None of these Short Answer Type Questions 9(i) [AS1] Identify the number of terms in the following algebraicexpressions. a) 2xy + 3x2 + 9 b) 9xy2 − 12xyz + 13y + 3 (ii) [AS1] Identify the algebraical and numerical terms in the following expressions. a) −6xy + 9 b) 3xy + 45y − 5 c) 3x2y3z EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM 171

10(i)[AS1] a) Write an algebraic expression with 2 terms. b) Write an algebraic expression with 3 terms. (ii) [AS1] a) Write an algebraic expression with 1 term. b) Write an algebraic expression with 4 terms. c) Write an algebraic expression with 5 terms. 11(i) [AS1] Find the degree of each of the given algebraic expressions. a) 3x3yz − 14xyz2 + 13x4y2z2 b) −12x9y + 14xyz (ii) [AS1] Find the degrees of the following expressions: a) 3x5y6 + 6x2y2 b) −8xy6y − 13xyz4 c) 7xy6z6 − 13yz + 23 EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM 172

EXERCISE 10.3 ADDITION AND SUBTRACTION OF LIKE AND UNLIKE TERMS 10.3.1 Key Concepts i. The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms. ii. The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms. 10.3.2 Additional Questions Objective Questions . 1. [AS1] The sum of 3xy and − 8xy is (B) 5xy (A) 11xy (C)− 5xy (D)− 11xy 2. [AS1] 8x2yz + 13x2yz = . (A) 21xy2z (B) 21x2yz (C) 21 xyz2 (D) 21 xyz 3. [AS1] The sum of 4ab, 5ab, −9ab and 12ab is . (A) 30ab (B) 9ab (C) 12ab (D) 12a2b2 4. [AS3] If no two terms of an expression are alike then it is said to be in the form. (A) Simplified (B) Standard (C)Expanded (D)Short EXERCISE 10.3. ADDITION AND SUBTRACTION OF LIKE AND UNLIKE TERMS 173

5. [AS3] The expression that is in the standard form is_______. (A) 3x3 + 5 − 6x (B) 9x2 + 3 − x3 (C)9x3 + 4x2 + 8 (D)6 − 8x2 + x3 Short Answer Type Questions 6(i) [AS1] Simplify the following: a) 9m + 14m – 19m b) –18yz + 17yz – 9yz (ii) [AS1] Simplify the following: a) 3a2 − 4b2 + 9a2 − 7a2 + 8a2b + 6b2a b) 5x2 + 9 + 4x + 6 + 3x + 3x2 − 7x + 9 c) 9ab + 2b + 3a − 4ab + 2b − 3a − 5ab 7(i) [AS1] Simplify by combining the like terms: a) 21b – 32 + 7b – 20b b) p – (p – q) – q – (q – p) (ii) [AS1] Add the following: a) 4x2y, –3xy2, –5xy2, 5x2y b) 3p2q2 – 4pq + 5, –10p2q2, 15 + 9pq + 7p2q2 c) ab − 4a, 4b − ab, 4a − 4b 8(i) [AS1] Find the values of 9x2 if x is –1 and 2x2 − y + 2 when x = 1; y = 0. (ii) [AS1] a) Find the area of a triangle, given that its base, b = 18 cm and height, h = 9 cm. b) Simple Interest is given by I = PT R . 100 If P = Rs.900, T = 2 years and R= 5% find the simple interest. , EXERCISE 10.3. ADDITION AND SUBTRACTION OF LIKE AND UNLIKE TERMS 174

9(i) [AS1] Write the following expressions in the standard form. a) 3x2 + 9x + 3x b) − 2x2 + 16 + 4x c) −2m + 4 + 3m2 d) 8 − 2x2 + 3x (ii) [AS1] Identify the expressions that are in standard form: a) 9x2 + 6x + 8 b) x2y + xy + 3 c) 9x2 + 15 + 7x d) x2 + x2y2 + 16xy e) 9x2 + 7 f) 15x2 + x3 + x2 EXERCISE 10.3. ADDITION AND SUBTRACTION OF LIKE AND UNLIKE TERMS 175

EXERCISE 10.4 ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS 10.4.1 Key Concepts i. Addition and subtraction of algebraic expressions is the same as addition and subtraction of the like terms. ii. Algebraic expressions can be added or subtracted using the following methods: a) Verticalmethod b) Horizontal method iii. Subtracting an algebraic expression is to add its additive inverse. 10.4.2 Additional Questions Objective Questions 1. [AS1] The sum of 5x2 + 6x − 9 and −2x2 + 3x + 8 is _______. (A) 7x2 + 9x + 17 (B) 5x2 + 9x + 17 (C)3x2 + 9x − 1 (D)5x2 + 9x − 1 2. [AS3] Additive inverse of 7x2 − 3x − 9 is ________. (A) 7x2 + 3x − 9 (B) 7x2 + 3x + 9 (C)−7x2 + 3x − 9 (D)−7x2 + 3x + 9 3. [AS1] The difference when 5x2yz subtracted from − 9x2yz is . (A) −14x2yz (B) 14x2yz (C) 4 x2yz (D) −14 xy2z 4. [AS1] The sum of ab and −6ab is _______. (B) 3ab (A) 5ab (D) −5ab (C) −3ab EXERCISE 10.4. ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS 176

5. [AS1] The sum of 8x2y2z + 9xyz − 9 and −12x2y2z − 7xyz + 3 is . (A) 20x2y2z + 16xyz + 12 (B) −4x2y2z − 2xyz − 6 (C)−4x2y2z + 2xyz + 6 (D)−4x2y2z + 2xyz − 6 Short Answer Type Questions 6(i) [AS1] Add 2 + 3x + 7; 2x + 4x2 and 6 − 5x. 4x (ii) [AS1] Add 3mn + 6m2 + n2 and 8m2 − n2 − 6mn. 7(i) [AS1] Find the additive inverses of the following: a) 3x + 4 b) 6x − 5y (ii) [AS1] Write the additive inverses of the following: a) 7a + 8b – 9c b) 2m – 3n + 5c c) 2p + 6q – 3r 8(i) [AS1] Subtract the second expression from the first. a) 2a + b, a − b b) 6m3 + 4m2 + 7m + 3, 3m3 + 4 (ii) [AS1] Subtract the second expression from the first. a) 3a + 4b, 5a − 3b b) m3 − 8m2 + 17m − 13, 6m3 + 5. 9(i) [AS1] Subtract the sum of 2x2 − 5xy + y2 and 3y2 − 2xy − 6x2 from 9x2 + 15xy − 4y2. (ii) [AS1] Find the sum of 6x2 + 2xy + 4y2 and − 6y 2 + 4xy − x2 . Subtract the sum from the sum of 3x2 − 5xy + y2 and 2xy − 2y2 − x2. EXERCISE 10.4. ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS 177

—— Project Based Questions —— (i) A water tank has steps inside it. A monkey is sitting on the topmost step (i.e. the first step). The water level is at the ninth step. a) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level? b) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step? PROJECT BASED QUESTIONS 178

(ii) Fill the grid by multiplying each number in the first column by each number in the first row. × 6 5 4 3 2 1 0 –1 –2 –3 –4 –5 –6 6 36 5 30 4 24 3 18 2 12 16 00 –1 –6 –2 –12 –3 –18 –4 –24 –5 –30 –6 –36 Observe the table and answer the following the questions: a) Is the product of two positive integers always a positive integer? b) Is the product of two negative integers always a positive integer? c) Is the product of a negative integer and a positive integer always a negative integer? (iii) Mr. Upendra wants to distribute his annual profit of Rs.3,00,000 to all his four partners in the following way. 1 th of the profit to Mr. Nagendra, 1 th of the profit to Mr. Phaneendra, 2 th of the 8 6 5 1 th profit to Mr. Rajendra and 10 to Mr. Raghavendra and the remaining profit for Mr. Upendra. Calculate the shares of profit each person got and represent them pictorially with different colours. PROJECT BASED QUESTIONS 179

(iv) Write any 10 situations of life which involve simple equations. Frame simple equations for all these situations. (v) Write any five pairs of supplementary angles, draw these angles side by side and draw another figure which represents that they are supplementary angles. (vi) Draw three lines and two transversals intersecting them. Name the pairs of angles formed and measure them. What can you conclude?Justify. Repeat the same thrice and note the values in the form of a table. Conclude your observation. (vii) Draw any five triangles say ∆ ABC, ∆ DEF, ∆ PQR, ∆ XYZ and ∆ LMN in your note book. Use your protractor and measure each of the angles of these triangles and also find the sum of all the three angles to prove the angle sum property of a triangle. (viii) Draw any five triangles say ∆ ABC, ∆ DEF, ∆ PQR, ∆ XYZ and ∆ LMN in your note book. Measure the sides of each triangle. Verify that the sum of any two sides of the triangle is greater than the third side and also the difference of any two sides is smaller than the third side. (ix) Draw three triangles such that one is acute angled triangle, obtuse angled triangle and third is a right angled triangle. Without measuring the lengths of the sides and angles draw the congruent triangles to each of them by using any one of these congruency conditions: ASA congruency; SSS congruency; SAS congruency or RHS congruency. (x) Construct a triangle with two sides of lengths of your choice and the non–included angle as anobtuse angle. Can you draw two triangles in this solution? If so, construct them. PROJECT BASED QUESTIONS 180