Maths Workbook_7_P_2.pdf 1 18-10-2019 17:36:51 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________
TABLE OF CONTENTS 9 CONSTRUCTION OF TRIANGLES 1 9.1 CONSTRUCTION OF A TRIANGLE WHEN MEASUREMENTS OF THE THREE SIDES 1 ARE GIVEN 4 9.2 CONSTRUCTION OF A TRIANGLE WHEN TWO SIDES AND THE INCLUDED ANGLE ARE GIVEN 6 9.3 CONSTRUCTION OF TRIANGLE WHEN TWO ANGLES AND THE SIDE BETWEEN THE 8 ANGLES ARE GIVEN 11 9.4 CONSTRUCTION OF RIGHT ANGLED TRIANGLE WHEN THE HYPOTENUSE AND THE SIDE ARE GIVEN 13 9.5 CONSTRUCTION OF TRIANGLE WHEN TWO SIDES AND THE NON-INCLUDED ANGLE 13 ARE GIVEN 19 24 10 ALGEBRAIC EXPRESSIONS 27 10.1 INTRODUCTION 29 10.2 ALGEBRAIC TERMS AND NUMERIC TERM 10.3 ADDITION AND SUBTRACTION OF LIKE AND UNLIKE TERMS 29 10.4 ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS 33 12 QUADRILATERALS 40 12.1 QUADRILATERALS 40 12.2 TYPES OF QUADRILATERALS 44 53 14 UNDERSTANDING 3D AND 2D SHAPES 55 14.1 INTRODUCTION 14.2 NETS OF 3–D SHAPES 14.3 DRAWING SOLIDS ON A FLAT SURFACE 14.4 VISUALISING SOLID OBJECTS
15 SYMMETRY 59 15.1 LINE SYMMETRY 59 15.2 ROTATIONAL SYMMETRY 66 15.3 LINE SYMMETRY AND ROTATIONAL SYMMETRY 70 PROJECT BASED QUESTIONS 72 ADDITIONAL AS BASED PRACTICE QUESTIONS 73
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. . . 1
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. . . 2
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. . . 3
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. . . 4
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. . . 5
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. . . 6
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. . . 7
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 . . . 8
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 . . . 9
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 . . . 10
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. . . 11
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. . . 12
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 13
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 14
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 15
[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 16
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 17
(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 18
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 19
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. 20 (ii) –2p and 3p are unlike terms. EXERCISE 10.2. ALGEBRAIC TERMS AND NUMERIC TERM
[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 21
8 [AS1] State true or false. [ ] (i) In the expression 12ab, a is the co-efficient of 12b. 22 [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
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 23
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 24
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 25
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 26
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 27
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 28
CHAPTER 12 QUADRILATERALS EXERCISE 12.1 QUADRILATERALS 12.1.1 Key Concepts i. Quadrilateral: A closed figure bounded by four line segments is called a quadrilateral. ii. A quadrilateral divides a plane into three parts: interior of the quadrilateral, exterior of the quadrilateral and boundary of the quadrilateral. iii. A quadrilateral is said to be a convex quadrilateral if all line segments joining points in its interior also lie in its interior completely. e.g.,– BELT is a convex quadrilateral. iv. A quadrilateral is said to be a concave quadrilateral if all line segments joining any two points in its interior do not necessarily lie in its interior completely. In RING, the line segment ABdoes not lie completely in its interior. So, the quadrilateral RING is a concave quadrilateral. v. Sum of the interior angles of a quadrilateral is 360◦. EXERCISE 12.1. QUADRILATERALS 29
12.1.2 Additional Questions Objective Questions 1. [AS3] The sum of exterior angles of a quadrilateral is . (A) 180◦ (B) 270◦ (C) 360◦ (D) 720◦ 2. [AS3] The line segment joining the opposite vertices in a quadrilateral is called its . (A) Diagonal (B) Altitude (C) Median (D)None of these 3. [AS1] If the angles of a quadrilateral are 2x◦, (3x + 2)◦, (5x − 2)◦, 8x◦ then the angles are . (A) 30◦, 120◦, 170◦, 60◦ (B) 40◦, 62◦, 98◦, 160◦ (C)45◦, 89◦, 121◦, 105◦ (D)120◦, 150◦, 60◦, 30◦ 4. [AS1] If the three angles of a quadrilateral are 69◦, 98◦ and 129◦ then the fourth angle is . (A) 66◦ (B) 69◦ (C) 63◦ (D) 64◦ 5. [AS3] The number of diagonals that can be drawn in a quadrilateral is . (A) 1 (B) 2 (C) 3 (D) 4 EXERCISE 12.1. QUADRILATERALS 30
Very Short Answer Type Questions [ ] 6 [AS2] State true or false. ] (i) Rectangle is a convex quadrilateral. (ii) In a concave quadrilateral a line segment joining any two ponts will lie in its interior. [AS2] Fill in the blanks. [ (iii) In a trapezium ABCD, AB DC. If ∠D = x ◦ then ∠A = . (iv) is a quadrilateral. [AS2] Choose the correct answer. (v) is a ________. (A) Convex quadrilateral (B) Concave quadrilateral (C)Both convex and concave quadrilateral (D)None of these 7 [AS4] State true or false. (i) A parallelogram having all sides equal is called a rhombus. [ ] . [AS4] Fill in the blanks. (ii) A is a quadrilateral with one pair of parallel sides. (iii) If an angle of a parallelogram is a right angle, then it is necessarily a [AS4] Choose the correct answer. (iv) The consecutive angles of a parallelogram are ________. (A) Supplementary (B) Complementary (C)Right angles (D)None of these EXERCISE 12.1. QUADRILATERALS 31
(v) If a pair of opposite sides of a figure are equal and parallel then it is a . (A) Rectangle (B) Square (C) Rhombus (D) Parallelogram Correct Answer: D Short Answer Type Questions 8(i) [AS1] If three of the angles of a quadrilateral are 35◦, 95◦ and 125◦, find the fourth angle. (ii) [AS1] If the adjacent angles of a parallelogram are in the ratio 5 : 4. Then find all the four angles of the parallelogram. 9(i) [AS1] Write the adjacent side of AB and the adjacent angle of ∠A in the following figure. (ii) [AS1] Write the adjacent side of BC and the adjacent angle of ∠C in the following figure. EXERCISE 12.1. QUADRILATERALS 32
EXERCISE 12.2 TYPES OF QUADRILATERALS 12.2.1 Key Concepts i. A quadrilateral in which one pair of opposite sides are parallel is called a trapezium or trapeziod. In the given trapezium ABCD, AB is parallel to DC. ii. A trapezium in which non parallel sides are equal is called an isosceles trapezium or isosceles trapeziod. iii. A kite is a quadrilateral in which exactly two distinct pairs of sides are of the same length. In the kite ABCD, AB = BC and AD = CD. iv. A quadrilateral in which both the pairs of opposite sides are parallel is called a parallelogram. In the quadrilateral ABCD, AB CD and AD BC. Hence, ABCD is a parallelogram. EXERCISE 12.2. TYPES OF QUADRILATERALS 33
v. In a parallelogram, • Opposite sides are parallel and equal [AB = CD and AD = BC]. • Diagonals bisect each other (AO = OC and BO = OD). • Opposite angles are equal (∠A = ∠C and ∠B = ∠D). • Adjacent angles are supplementary (∠A + ∠B = ∠B + ∠C = ∠C + ∠D = ∠D + ∠A = 180◦). vi. A parallelogram in which adjacent sides are equal is called a rhombus. In quadrilateral ABCD, AB = BC = CD = DA and hence, ABCD is a rhombus. vii. In a rhombus, the diagonals bisect each other at right angles, i.e., AC ⊥ BD and AO = OC, BO = OD. viii. If one of the angles in a parallelogram is a right angle then it is a rectangle. In the quadrilateral ABCD, AB = DC and AD = BC, ∠A = ∠B = ∠C = ∠D = 90◦. So, ABCD isa rectangle. ix. In a rectangle, the diagonals are equal and bisect each other (AC = BD; AO = OC and BO = OD). x. A square is a rectangle with equal adjacent sides. In the quadrilateral ABCD, AB = BC = CD = DA, ∠A = ∠B = ∠C = ∠D = 90◦. So, ABCD is a square. xi. In a square, the diagonals are equal and bisect each other at right angles. EXERCISE 12.2. TYPES OF QUADRILATERALS 34
xii. Flow chart of family of quadrilaterals 12.2.2 Additional Questions Objective Questions . 1. [AS1] One of the adjacent angles of a parallelogram is 135◦. Then the other angle is . (A) 135◦ (B) 45◦ (C) 55◦ (D)None of these 2. [AS3] The quadrilateral among the following in which the diagonals are equal is a (A) Parallelogram (B) Rhombus (C) Rectangle (D) Kite 3. [AS1] If the lengths of two diagonals of a rhombus are 6 cm and 8 cm, the length of its side is . (A) 10 cm (B) 12 cm (C) 5 cm (D) 6 cm EXERCISE 12.2. TYPES OF QUADRILATERALS 35
4. [AS1] In a parallelogram PQRS, if PQ = 7 cm and QR = 9 cm then its perimeter is . (A) 32 cm (B) 16 cm (C)34 cm (D)18 cm 5. [AS3] In a rhombus if one of the angles is 90◦ then it becomes a . (A) Parallelogram (B) Rectangle (C) Trapezium (D) Square Very Short Answer Type Questions 6 [AS3] State true or false. [ ] (i) A kite has exactly two consecutive pairs of sides of equal length. . [AS4] Fill in the blanks. (ii) Diagonals necessarily bisect opposite angles in a . (iii) We get a rhombus by joining the mid points of the sides of a [AS3] Choose the correct answer. (iv) A quadrilateral with one pair of opposite sides parallel is called a _______. (A) Parallelogram (B) Rhombus (C) Rectangle (D) Trapezium (v) The figure formed by joining the mid points of the adjacent sides of square is a ______. (A) Square (B) Rhombus (C) Rectangle (D) Parallelogram EXERCISE 12.2. TYPES OF QUADRILATERALS 36
Short Answer Type Questions 7(i) [AS1] HELP is a parallelogram. Given that OE = 4 cm, where O is the point of intersection of the diagonals and HL is 5 cm more than PE, find OH. (ii) [AS1] SHUB is a parallelogram. Given that OS = 7 cm, where O is the point of intersection of the diagonals and HB is 4 cm more than SU. Find BH + SU. 8(i) [AS1] In a rectangle PQRS, if PQ = 6 cm and PR = 10 cm then find the perimeter of the rectangle. (ii) [AS1] Two adjacent angles of a parallelogram ABCD are in the ratio 2 : 3. Find all the angles of the parallelogram. 9(i) [AS1] The perimeter of a parallelogram is 80 m. If the longer side is 10 m greater than the shorter side, find the lengths of the sides of the parallelogram. (ii) [AS1] The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the angles. Long Answer Type Questions 10 [AS1] Find the perimeter of the parallelogram ABCD. EXERCISE 12.2. TYPES OF QUADRILATERALS 37
11 [AS1] In a parallelogram BEST, if ∠B = 60 ◦ Find the other angles. . 12 [AS1] ABCD is a parallelogram, given OA = 6 cm where O is the point of intersection of the diagonals and DB is 3 cm shorter than AC, find OB. 13 [AS1] BASE is a rectangle. Its diagonals intersect at O. Find x, if OB = 5x + 1 and OE = 2x + 4. 14 [AS1] (i) Two adjacent sides of a parallelogram are in the ratio 4 : 5. The perimeter of the parallelogram is 54 cm. Find the length of each of its sides. (ii) In a trapezium RENT, RE is parallel to NT, ∠R = 110◦ and ∠E = 60◦. Find the remaining angles. 15 [AS2] The angles A, B, C and D of a quadrilateral ABCD are in the ratio 1 : 3 : 7 : 9. a) Find the measure of each angle. b) Is ABCD a trapezium? Why? c) Is ABCD a parallelogram? Why? EXERCISE 12.2. TYPES OF QUADRILATERALS 38
16 [AS1] In the given figure, HOPE is parallelogram. Find the values of x, y and z. 17 [AS1] In the given figure, RUNS is a parallelogram. Find x and y if their lengths are in cm. 18 [AS2] The diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Draw a rough figure to justify your answer. 19 [AS2] ABCD is a square with AC and BD as diagonals. Prove that AC and BD are equal. EXERCISE 12.2. TYPES OF QUADRILATERALS 39
CHAPTER 14 UNDERSTANDING 3D AND 2D SHAPES EXERCISE 14.1 INTRODUCTION 14.1.1 Key Concepts i. We see different two–dimensional and three–dimensional shapes around us. ii. We can identify geometric shapes in 2 and 3 dimensional shapes. iii. The 2 and 3 dimensional shapes are a combination of geometric shapes. iv. We can identify the faces, edges and vertices of 3 dimensional shapes. 14.1.2 Additional Questions Objective Questions . 1. [AS3] The number of edges of a cube is (A) 10 (B) 12 (C) 13 (D) 14 2. [AS3] The number of faces of a cuboid is . (A) 10 (B) 12 (C) 6 (D) 8 3. [AS3] The number of vertices of a cube is . (A) 4 (B) 5 (C) 7 (D) 8 EXERCISE 14.1. INTRODUCTION 40
4. [AS3] The number of faces of a square pyramid is . (A) 3 (B) 4 (C) 5 (D) 6 5. [AS3] The number of dimensions of a solid is . (A) 1 (B) 2 (C) 3 (D) 4 Very Short Answer Type Questions 6. [AS4] Match the real life objects with their basic 3D shapes. Column A Column B i. Cube a. Battery cell ii. Cylinder b. Dice iii. Sphere c. Brick iv. Cuboid d. Ice cream v. Cone e. Ball EXERCISE 14.1. INTRODUCTION 41
Long Answer Type Questions 7 [AS5] Identify and state the number of faces, edges and vertices of the figures given. S.No 3 –D figures No. of No. of No. of i. vertices edges faces ii. iii. iv. EXERCISE 14.1. INTRODUCTION 42
8 [AS5] Identify and state the number of faces, edges and vertices of the figures given. S.No 3 –D figures No. of No. of No. of i. Sphere vertices edges faces ii. Triangular prism iii. Rectangular pyramid iv. Square pyramid EXERCISE 14.1. INTRODUCTION 43
EXERCISE 14.2 NETS OF 3-D SHAPES 14.2.1 Key Concepts i. A net is a sort of skeleton – outline in 2–D, which, when folded, results in a 3–D shape. ii. A 3-D shape can have more than one net based on the way we cut it. Example: iii. 3–D shapes can be visualized by drawing their nets on 2–D surfaces. EXERCISE 14.2. NETS OF 3–D SHAPES 44
14.2.2 Additional Questions 45 Objective Questions 1. [AS5] Identify the net of a cone. (A) (B) (C) (D) EXERCISE 14.2. NETS OF 3–D SHAPES
2. [AS5] Identify the net of a cube. (A) (B) (C) (D) EXERCISE 14.2. NETS OF 3–D SHAPES 46
3. [AS5] Identify the net of a cylinder. (A) (B) (C) (D) EXERCISE 14.2. NETS OF 3–D SHAPES 47
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