Class 9 Full Year 9th Grade Review

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ID : in-9-full-year-9th-grade-review [1] Class 9 Full Year 9th Grade Review For more such worksheets visit www.edugain.

1 ID : in-9-full-year-9th-grade-review [1] Class 9 Full Year 9th Grade Review For more such worksheets visit Answer the questions (1) In the graph of the linear equation 5x + 2y = 110, there is a point such that its ordinate is one fourth of abscissa. Find coordinates of the point. (2) The average of 7 numbers is 50. If the average of first 3 numbers is 48 and that of last 3 is 45, then find the 4 th number. (3) If there are 44 diagonals in a convex polygon, find the number of sides of the polygon. (4) Alisha and Sneha deposit some amount in a joint bank account such that total balance remains 700. If amount deposited by Alisha and Sneha are plotted as a linear graph on xy plane, find the area between this graph and the coordinate axis. (5) In a square ABCD, E, F, G and H are the mid points of the four sides, what kind of shape is represented by EFGH. (6) If f(a) = -5a 2 + a - 1, the value of f(a) + f(-a) =? (7) Point (-10, 2) lies in which quadrant? (8) If lines AB and CD intersect as shown below, find the value of angle x. (9) The diameter of circumcircle of a rectangle is 13 cm and rectangle's width is 5 cm. Find length of the rectangle. (10) Sita's age is twice that of Tina, Tina's age is twice that of Shweta and Shweta's age is twice that of Joel. If the average of the ages of Sita, Tina, Shweta and Joel is 37.5 years, then what is the present age of Shweta? (11) If x + y - 8t = 0 then find the value of. Choose correct answer(s) from the given choices (12) ABCD is a quadrilateral and A = B = C = D = 90. Then ABCD can be called as a. Parallelogram b. Square c. Rectangle d. Both rectangle and parallelogram

2 (13) Equation 6x + 6y = 9 has: a. Infinitely many solutions b. No solution ID : in-9-full-year-9th-grade-review [2] c. Two solutions d. A unique solution (14) Find the conclusion by assuming following statements to be true (Statements may be contrary to the universal opinion). Statements : (i) All toys are laptops (ii) All tables are toys. Conclusion? a. No table is a laptop b. All tables are laptops c. Some toys are tables d. Some laptops are tables Check True/False (15) The sum of all the angles around a point is 360. True False 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : in-9-full-year-9th-grade-review [3] (1) (20, 5) We are given the following: a. The equation is 5x + 2y = 110 b. The line has a point where the value of the ordinate is one fourth the value of the abscissa. The second fact implies that the point is of the form (x, x ). 4 Substituting y = x 4, in the equation 5x + 2y = 110 we get: 5x + 2x 4 or, x = 20 = 110 We have x = 20, which means the coordinates of the point will be (20, 5). (2) 71 The average of 7 numbers is 50, which means the sum of numbers is equal to 50 7 = 350. The average of first 3 numbers is 48, which means the sum of first 3 numbers is 48 3 = 144. The average of last 3 numbers is 45, which means the sum of last 3 numbers is 45 3 = 135. The sum of first and last 3 numbers is = 279. Step 5 This means the 4 th number is = 71.

4 (3) 11 ID : in-9-full-year-9th-grade-review [4] The diagonal of a polygon is the line segment that connects non-adjacent vertices of a polygon. Let us consider a polygon with n sides. We know, the total number of diagonals of a polygon with n sides = n(n - 3) 2 According to the question, the number of diagonals in the convex polygon are 44. Therefore, 44 = n(n - 3) 2 88 = n 2-3n n 2-3n - 88 = 0 (n - 11)(n + 8) = 0 Either, (n - 11) = 0 or (n + 8) = 0 Since, a polygon never have 0 or less than zero sides, and hence, (n + 8) 0. Therefore, (n - 11) = 0 n = 11 Thus, the given polygon has 11 sides.

5 (4) ID : in-9-full-year-9th-grade-review [5] Let the amount deposited by Alisha be x and by Sneha be y. Since the balance remains 700, the relation between x and y will be given by x + y = 700. We know that the area of a triangle is equal to half the product of base and the height. The area of the given triangle will be equal to: = sq units. (5) Square Following figure shows the square ABCD, Let's assume the side of the square be a. In ΔGDH, DG = DH = a/2 [Since, G and H are the midpoints of the sides CD and DA respectively.] D = 90 [Since, ABCD is a square] GH 2 = DG 2 + DH 2 [By the pythagorean theorem]

6 GH 2 = DG 2 + DG 2 [Since GH = GD] GH 2 = 2DG 2 GH 2 = (2a/2) 2 GH 2 = a 2 GH = a Similarly, HE = EF = FG = a and hence, HE = EF = FG = GH ID : in-9-full-year-9th-grade-review [6] The ΔGDH is an isosceles triangle. [Since, DG = DH] In ΔGDH, D = 90, Therefore, DHG = DGH = 45 [Since, the sum of all the angles of a triangle is equals to 180 ], Similarly, AHE = 45 Now, DHG + AHE + GHE = 180 [Since, the angles on one side of a straight line will always add to 180 degrees.] GHE = GHE = 180 GHE = GHE = 90, Similarly, HEF = EFG = FGH = 90 and hence, HEF = EFG = FGH = GHE = 90 Step 5 Thus, EF = FG = GH = HE and HEF = EFG = FGH = GHE = 90. We know that quadrilateral with four equal sides and four right angles is a square. Therefore, EFGH is a Square. (6) -10a 2-2 It is given that, f(a) = -5a 2 + a - 1 Therefore, and f(-a) = -5(-a) 2 + (-a) - 1 = -5a 2 - a - 1 Now, f(a) + f(-a) = -5a 2 + a - 1-5a 2 - a - 1 = -10a 2-2

(7) Second quadrant ID : in-9-full-year-9th-grade-review [7] For plotting a point (x, y) on the graph, we have to keep in mind the following points: If both the numbers are positive i.e. (x,y), then the point lies in the first quadrant.

7 (7) Second quadrant ID : in-9-full-year-9th-grade-review [7] For plotting a point (x, y) on the graph, we have to keep in mind the following points: If both the numbers are positive i.e. (x,y), then the point lies in the first quadrant. If the first number is negative, and the second number is positive i.e. (-x,y), it lies in the second quadrant. If both the numbers are negative (-x,-y), it lies in the third quadrant. If the first number is positive and the second number is negative (x,-y), it lies in the fourth quadrant. We can see that for the given point, x is less than zero and y is greater than zero. Hence, the point will lie in the Second quadrant.

8 (8) 30 ID : in-9-full-year-9th-grade-review [8] In triangle ADE, DAE + ADE + AED = (Since, the sum of all the angles of a triangle is 180 ) AED = AED = 180 AED = AED = 25 Since, BEC and AED are the opposite angles of the triangle BCE and ADE and we know that the opposite angles of a triangle are equal. Therefore, BEC = AED = (1) Now, in triangle BCE, CBE + BCE + BEC = (Since, the sum of all the angles of a triangle is 180 ) x = Using (1) x = 180 x = x = 30 Hence, the value of x is 30.

9 (9) 12 cm ID : in-9-full-year-9th-grade-review [9] Following figure shows the rectangle ABCD with it's circumcircle, AB, BC and AC are the length, breadth and diameter of circumcircle of the rectangle ABCD. According to the question, AC = 13 cm, BC = AD = 5 cm. Now, in right angled triangle ABC, AB 2 = AC 2 - BC 2 AB = [ AC 2 - BC 2 ] = [ ] = 12 cm Hence, the length of the rectangle is 12 cm.

10 (10) 20 years ID : in-9-full-year-9th-grade-review [10] Let Joel's age be x. According to the question, Shweta's age is twice of Joel's age, which means Shweta's age is 2x. Also, Tina's age is given to be twice of Shweta's age, which means Tina's is 4x. And since Sita's age is given to be twice of Tina's age, her age will be 8x. The average of ages of all of them is 37.5 years. Therefore the sum of their ages will be = 150. But the sum of their ages is also equal to x + 2x + 4x + 8x = 15x. Step 5 From step 4 we have 15x = 150, or x = 10. Step 6 This means the present age of Shweta is 2x, or 20 years. (11) 1 We are given x + y - 8t = 0 It can also be written as: (x - 4t) + (y - 4t) = 0 or (x - 4t) = -(y - 4t) The above step tells us that we may replace (x - 4t) with -(y - 4t) wherever needed. We need to find the value of which is equal to: x -(y - 4t) + 4t y - 4t = = -x + 4t y - 4t -(x - 4t) (y - 4t) As we know that (x - 4t) = -(y - 4t), the answer to the above question becomes 1.

11 (12) d. Both rectangle and parallelogram ID : in-9-full-year-9th-grade-review [11] Following figure shows the quadrilateral ABCD where all four angles are 90 A quadrilateral with all four angles of 90 is a rectangle. We also know that all rectangles are parallelogram since opposite sides of rectangles are parallel and equal to each other. Therefore, the correct answer is 'Both rectangle and parallelogram'. (13) a. Infinitely many solutions For linear equations in two variables, we need at least two equations to find a unique solution for the pair. A single linear equation can assume infinitely many values of the variables, which is the case with the question. The equation will have infinitely many solutions. (14) b. All tables are laptops Since all tables are toys, and all toys are laptops, this means all tables are laptops. Thus the option b is correct. (15) True Since, we know that the sum of all the angles around a point must be 360. Therefore, we can say that the statement " The sum of all the angles at a point is 360 " is True.

Grade 9 Quadrilaterals

ID : pk-9-quadrilaterals [1] Grade 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) In a quadrilateral ABCD, O is a point inside the quadrilateral such that AO