Grade 9 Full Year 9th Grade Review

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1 ID : ww-9-full-year-9th-grade-review [1] Grade 9 Full Year 9th Grade Review For more such worksheets visit Answer t he quest ions (1) A carpenter has cut a board in the shape of trapezium. if the parallel sides of the trapezium are 16 cm and 12 cm and non parallel sides are 13 cm and 15 cm, f ind the area of the board. (2) Jason selects 3 numbers randomly f rom the f ollowing set of 5 numbers 8, 2, 9, 4 and 3. He puts them in the f orm of a proper f raction of the type a b c. What is the probability that you will get a f raction greater than ? (3) Brian and Mark are standing together on a sunny day. Brian's shadow is 10 f eet long and Mark's shadow is 9 f eet long. How tall is Mark? Which of f ollowing statements are suf f icient to answer the question. I. Brian is 5 f eet tall. II. Brian is standing 6 f eet away f rom Mark. (4) You are given a number N with the property that every next digit of N is greater than the previous digit (so second digit f rom the lef t is greater than the f irst digit, and third digit is greater than the second and so on). Now multiply N by 9. What is the sum of the digits of the resulting number? (5) Lines AB and CD intersect at O. If AOC + BOE = 120 and BOD = 60, f ind BOE. (6) If N = , f ind the 5 th digit in the expansion of N.

2 ID : ww-9-full-year-9th-grade-review [2] Choose correct answer(s) f rom given choice (7) The perimeter of a triangular f ield is 540 m and the ratio of the sides is 26:25:3. Which of the f ollowing is the area of the f ield in sq m : a b c d (8) If ADB is a right angle, f ind the value of angle x. a. 81 b. 79 c. 91 d. 73 (9) If a and b are rational numbers such that, than the possible values of a and b are : a. a=0, b=0 OR a =, b = b. a =, b = c. a=0, b=0 d. a =, b =

(10) Find the coordinates of the point shown in the picture. ID : ww-9-full-year-9th-grade-review [3] a. (1.5, -3.5) b. (1.5, 3.5) c. (-1.5, 3.5) d. (-1.5, -3.5) (11) A sphere and a cone have the same radii.

3 (10) Find the coordinates of the point shown in the picture. ID : ww-9-full-year-9th-grade-review [3] a. (1.5, -3.5) b. (1.5, 3.5) c. (-1.5, 3.5) d. (-1.5, -3.5) (11) A sphere and a cone have the same radii. If the volume of the sphere is triple of the volume of the cone, f ind the ratio of the cone's height and radius. a. 3:1 b. 1:2 c. 4:3 d. 2:1 (12) What is the relation of to described as? a. Multiplicative Identity b. Reciprocal c. Additive Inverse d. Multiplicative Inverse (13) If x + y - 8t = 0 then f ind the value of. a. -4 b. 1 c. 4 d. 0 (14) The three angles of a quadrilateral are 85, 83 and 98 respectively. Find the f ourth angle. a. 94 b. 266 c. 4 d. 86

4 ID : ww-9-full-year-9th-grade-review [4] Fill in the blanks (15) If AD and BD are bisectors of CAB and CBA respectively, sum of angle x and y = Edugain ( All Rights Reserved Many more such worksheets can be generated at

5 Answers ID : ww-9-full-year-9th-grade-review [5] (1) 168 cm 2 Following picture shows the trapezium ABCD, Let's draw the line DE parallel to the line BC. We know that the distance between the two parallel lines at every point must be equal. Theref ore, EB = DC = 12 cm AE = AB - EB = = 4 cm Now, we can see that, this trapezium consists of a triangle ΔADE and a parallelogram BCDE. The area of the triangle ΔADE can be calculated using Heron's f ormula, since all sides of the triangles are known. S = (AE + DE + AD)/2 = ( )/2 = 16 cm. The area of the ΔADE = [ S (S - AE) (S - DE) (S - AD) ] = [ 16(16-4) (16-13) (16-15) ] = 24 cm 2 Step 4 T he height of the triangle ΔADE and the parallelogram BCDE is equal. Let's assume, the height of the triangle ΔADE be 'h', as shown in the f ollowing f igure.

6 ID : ww-9-full-year-9th-grade-review [6] We know that the area of a triangle = 1/2(Base Height), 2 (The area of the ΔADE) Theref ore, the height of the ΔADE = Base or h = 2 24 = 48 cm 4 4 The area of the parallelogram BCDE = EB h = = 144 cm 2 Step 5 The area of the board = Area(ADE) + Area(BCDE) = = 168 cm 2

7 (2) 24 ID : ww-9-full-year-9th-grade-review [7] 30 We need to select 3 numbers out of the 5 given in order to get a f raction of the f orm a b c We are also told it is a proper f raction, so b should be greater than c Let's put the integers in a sorted manner. We get 2, 3, 4, 8 and 9 Now we need to see how many proper f ractions can be f ormed f rom them b A proper f raction of the type a has three integers, a whole number a, a numerator b, c and a denominator c Let's assume we use one of the integers in the list above as the whole number a We now can select b and c f rom the remaining 4 integers We can select 2 integers f rom 4 in 4C2 = 4x3 = 6 ways 2x1 For any pair we select, one will be greater than the other, and the smaller integer will f orm the numerator and the larger one the denominator - Note: that the other way won't work - if the numerator is larger than the denominator it is not a proper f raction So f or each of the 5 integers, if we select one as the whole number, we get 6 possible combinations of numerator and denominator that can f orm a proper f raction This means there are 5x6 = 30 possible proper f ractions of the f orm a b c that can be f ormed f rom these 5 integers Step 4 Now we need to f igure out how many of these 30 f ractions are greater than In gt, we see that the whole number is 2, the numerator is 16 and the denominator is 17 We see that the numerator 16 is larger than the largest number in the set of numbers given to us, and the denominator 17 is one larger than 16 The implication of this is that 2 16 will be larger than any f raction that can be f ormed 17 f rom the set of numbers 2, 3, 4, 8 and 9 where the whole number of the f raction is 2 So we only need to count the f ractions that have the whole number greater than 2 These are the f ractions that will have the whole numbers as 3, 4, 8 and 9 Step 5 Now, remember there are 30 proper f ractions you can f orm f rom this list of number From our analysis above, we also saw that f or each number selected as the whole number,

8 we can f orm 6 f ractions f rom this list of numbers ID : ww-9-full-year-9th-grade-review [8] Step 6 So using each of the numbers f rom 3, 4, 8 and 9 as the whole number, we can f orm 6 proper f ractions The total number of f ractions that can be f ormed using 3, 4, 8 and 9 as the whole number = 6 x 4 = 24 Step 7 Out of the 30 f ractions, 24 will be greater than Step 8 The probability is theref ore = (3) Statement I alone is suf f icient to answer the problem.

9 (5) 60 ID : ww-9-full-year-9th-grade-review [9] If you look at the given f igure caref ully, you will notice that AB and CD are straight lines. AOC + BOE = 120 and BOD = 60. The angles of straight line add up to 180. Line AB is a straight line, theref ore we can say that AOC + COE + BOE = 180 AOC + BOE + COE = COE = 180 [Since AOC + BOE = 120 ] COE = COE = 60 CD is also a straight line, theref ore COE + BOE + BOD = BOE + 60 = 180 [Since COE = 60 and BOD = 60 ] BOE = 180 BOE = BOE = 60. Step 4 Now BOE = 60. (6) 5

10 (7) b ID : ww-9-full-year-9th-grade-review [10] Since we know the perimeter, we can use Heron's f ormula to help us compute the area The f ormula states that the area of a triangle with sides a, b and c, and perimeter 2S = Let us assume the 3 sides are of length a=26x, b=25x and c=3x (we know this because the ratio of the sides is given as 26:25:3) We also know that a+b+c = x + 25x + 3x = 540 ( )x = x = 540 x = 540 = Step 4 From this we see that a = 260, b = 250 and c=30. Also S=270 Step 5 Putting these values into Heron's f ormula, Area = = Solving, we f ind the area = 3600

11 (8) a. 81 ID : ww-9-full-year-9th-grade-review [11] According to the question ADB is the right angle, ADB = 90, DAB = 40 In right angled triangle ΔADB, ADB + DAB + ABD = 180 [Since, the sum of all the angles of a triangle is equal to 180 ] ABD = ABD = 180 ABD = 50 In ΔBEC, ABD + BEC + 31 = BEC + 31 = 180 BEC + 81 = 180 BEC = BEC = 99 x + BEC = 180 [Since, the sum of all angles on one side of a straight line is equal to 180.] x = BEC x = x = 81 Step 4 Hence, the value of angle x is 81.

12 (9) c. a=0, b=0 ID : ww-9-full-year-9th-grade-review [12] If a and b are non-zero, than they have to satisf y f ollowing relationship, a/b = We know that number on right hand side of above equation is an irrational number. Theref ore at least one of the number on lef t hand side should also be irrational number. It is given in question that a and b are rational numbers. Theref ore above relationship can never be satisf ied, and a and b have to be 0.

13 (10) b. (1.5, 3.5) ID : ww-9-full-year-9th-grade-review [13] In order to f ind the coordinates of the point shown in the picture, let's draw a horizontal and a vertical line which connect this point to the y and x axis respectively. We can see that the vertical line intersects the x-axis at 1.5. Theref ore, the x-coordinate of the point is 1.5. Similarly, the horizontal line intersects the y-axis at 3.5. T heref ore, the y-coordinate of the point is 3.5. Step 4 Hence the coordinates of the given point are (1.5, 3.5)

14 (11) c. 4:3 ID : ww-9-full-year-9th-grade-review [14] We know that the volume of a cone with radius r and height h = 1/3 π r 2 h. We also know that the volume of a sphere with radius r = 4/3 π r 3. We have been told that the volume of the sphere in question is triple of the volume of the cone in question. Theref ore, 4/3 π r 3 = 3 x (1/3 π r 2 h) h/r = 4:3 Step 4 Thus, the ratio of the cone's height and radius is 4:3. (12) d. Multiplicative Inverse Multiplicative Inverse: When we multiply a number by its "Multiplicative Inverse", we get 1. Mathematically, n 1 n = 1 The multiplicative inverse of is 22 12, since = 1. (13) b. 1 (14) a. 94 According to the question, the three angles of the quadrilateral are 85, 83 and 98 respectively. Let's assume, the f ourth angle of the quadrilateral be x. We know that, the sum of all interior angles of a quadrilateral is 360. Theref ore, x = x = 360 x = x = 94. Hence, the f ourth angle of the quadrilateral is 94.

15 (15) 45 ID : ww-9-full-year-9th-grade-review [15] It is given that AD and BD are bisectors of CAB and CBA respectively. Theref ore, x = CAB/ (1) y = CBA/ (2) In triangle ABC, CAB + CBA + ACB = [The sum of all three angles of a triangle is 180 ] CAB + CBA + 90 = 180 CAB + CBA = CAB + CBA = 90 CAB/2 + CBA/2 = 90/2 x + y = 45...[From equation (1) and (2)] Hence, the sum of the angles x and y is 45.

Class 9 Full Year 9th Grade Review

ID : in-9-full-year-9th-grade-review [1] Class 9 Full Year 9th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a parallelogram with E and F as the mid-points