Class 8 Full Year 8th Grade Review

Transcription

1 ID : in-8-full-year-8th-grade-review [1] Class 8 Full Year 8th Grade Review For more such worksheets visit Answer the questions (1) The given figure shows some fruits in a basket. Gauri is getting late for school and just picks up a fruit from the basket without looking at it. Which fruit is most likely to be picked? (2) There are two numbers such that their product is 28 and the sum of their squares is 65. Find square of sum of the numbers. (3) Which is the smallest fraction that must be add to the square root of so that the resulting number is a positive whole number? (4) If a cube has surface area S and volume V, then find the volume of the cube of surface area 2S. (5) Find factors of polynomial (9x xy + 9y 2 - z 2 ). (6) A tyre manufacturer keeps the record of how much distance the tyres manufactured by the company travel before failing. They find the following data Distance traveled in kilometers Number of failing tyres Less than to to to More than If Balvinder buys a tyre from them, what is the probability that it will last more than kilometers? (7) Alisha reaches her office 15 minutes early by traveling at a speed of 30 km/h and reaches 1 minute early by traveling at a speed of 25 km/h. By how much time will she be early or late if she travels at 20 km/h? (8) What is the radius of a circle if the area of the circle is (assume that the value of π is 3.14)? (9) Given the following equations: 5 (a+b) = 3125, and 3125 (a-b) = 5, what is the value of b? (10) Ankur is brother of Ashish. Sita is sister of Ankur. Sunil is brother of Sara. Sara is daughter of Ashish. Aditya is father of Sita. Who is the uncle of Sunil?

2 ID : in-8-full-year-8th-grade-review [2] (11) In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 1279 students in the school. If we know that less than 22 chairs were empty, how many chairs were empty after all the students sat down? (12) What is the probability that an integer in the set 1, 2, 3,...92 is divisible by 2 and not divisible by 3? Choose correct answer(s) from the given choices (13) What will be the shape at the 15 th position? a. b. c. d. (14) If you plot following set of points on a graph, which set of points will form a straight line? a. (0,2) (1,3) (2,5) (4,6) b. (0,0) (2,5) (4,8) (5,10) c. (2,5) (4,9) (5,11) (8,15) (8,17) d. (1,3) (3,5) (5,7) (7,9) (15) Regarding rational numbers: A. The quotient of two integers is always a rational number and B. 4 0 is not a rational number. Which of the following statements is correct? a. A is correct and B is correct explanation of A. b. A is correct but B is incorrect. c. Both A and B are false. d. A is false but B is a correct explanation of A Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : in-8-full-year-8th-grade-review [3] (1) Pear Total number of fruits in the basket = 15 Number of pears in the basket = 6 Number of pomegranates in the basket = 5 Number of mangoes in the basket = 4 As, the number of pears is the maximum. Hence, pear is most likely to be picked from the basket. (2) 121 Let us assume the two numbers to be x and y. It is given that their product is 28. Therefore, xy = 28...(1) Also the sum of their squares is 65. Therefore, x 2 + y 2 = 65...(2) Now, square of sum of the numbers = (x + y) 2 = x 2 + y 2 + 2xy [Since, (x + y) 2 = x 2 + y 2 + 2xy] = (28) [From eqution (1) and (2)] = = 121 Step 5 Thus, square of sum of the numbers is 121.

4 ID : in-8-full-year-8th-grade-review [4] (3) 2 3 Let's first convert mixed fraction to improper fraction = 49 9 Now, = 49 9 = ±7 ±3 = [ Use only positive number since question is about positive whole number] = Now for above number to be a whole number, we just need to find a fraction that must me added to 1/3, such that sum if 1. Therefore required fraction to be added, = = 2 3

5 (4) 2 2 V ID : in-8-full-year-8th-grade-review [5] Let the edge of the cube be a. Then, Surface area, S = 6a 2, and Volume, V = a 3. We can say that a =. Now let us put this value of a in the expression for volume. V then becomes:. Thus, for another cube with surface area 2S, the volume will be: = = Hence the volume of the other cube is 2 2 V. (5) (3x + 3y + z) (3x + 3y - z) We know that, (a + b) 2 = a 2 + 2ab + b 2, a 2 - b 2 = (a + b)(a - b) The factors of the polynomial (9x xy + 9y 2 - z 2 ) can be found using above identities as following, 9x xy + 9y 2 - z 2 = {(3x) xy + (3y) 2 } - (z) 2 = (3x + 3y) 2 - (z) 2 = (3x + 3y + z) (3x + 3y - z)

6 ID : in-8-full-year-8th-grade-review [6] (6) First we need to find the total number of tyres that are given here. We add the number of tyres = To find the probability that the tyre Balvinder purchased would last more than kilometers, we need to add the number of tyres that lasted more than kilometers. This is = The probability that the tyre lasts more than km =

7 (7) 20 minutes late ID : in-8-full-year-8th-grade-review [7] Let us assume, the distance traveled by Alisha to the office at the speed of 'S' km/minute in 'T' minutes is 'D' km. We know that, D = S T It is given that, Alisha reaches her office 15 minutes early by traveling at the speed of 30 km/h, We know that 1 hour = 60 minutes, Therefore, speed = 30/60 km/minute Now, D = 30 (T - 15) (1) 60 It is also given that, Alisha reaches 1 minute early by traveling at a speed of 25 km/h. Therefore, D = 25 (T - 1) (2) 60 From (1) and (2), we get, 30 (T - 15) = 25 (T - 1) (T - 15) = 25(T - 1) 30T = 25T - 25 (30-25)T = 425 T = (425)/(5) T = 85 minutes Step 5 Put T = 85, in (1), we get, D = 35 km Thus, Alisha reaches to office in 85 minutes. Step 6 If Alisha travels at the speed 20 km/h, 35 Then, T = 20/60 = = 105 minutes Step 7 Therefore, she will be late by (105-85) minutes = 20 minutes

8 (8) 36 ID : in-8-full-year-8th-grade-review [8] According to question the area of the circle is The area of a circle = πr = 3.14r r 2 = r 2 = r 2 = 1296 r 2 = 36 2 r = 36 Now the radius of a circle is 36.

9 ID : in-8-full-year-8th-grade-review [9] (9) 12 5 We know that 3125 = 5 5. If we replace 3125 by 5 to the power 5, we get: 5 5(a-b) = 5 5 (a+b) = 5 5 From the above step we have: 5(a - b) = 1 or, 5a - 5b = (1) a + b = (2) or, 5a + 5b = (3) [On multiplying by 5.] Adding equation (1) and (3) we have: 10a = 26 Or, a = 13 5 Putting this value in equation (2) we get: b = 5 - a Or, b = Or, b = 12 5 (10) Ankur Ankur is the brother of Ashish. Sita is the sister of Ankur. So Sita is also the sister of Ashish.

10 Sunil is the brother of Sara. ID : in-8-full-year-8th-grade-review [10] Sara is the daughter of Ashish. So Ashish is also the father of Sunil Step 5 Aditya is the father of Sita. So Aditya is also the father of Ankur and Ashish. Step 6 Since Sita is female, she cannot be uncle of Sunil, therefore only possibility is Ankur. Step 7 Therefore, Ankur is the uncle of Sunil.

11 (11) 17 ID : in-8-full-year-8th-grade-review [11] We have been told that the number of chairs in a row is the same as the number of rows of chairs. It means if there are n chairs in a row, then the number of rows also is n. That is, the total number of chairs makes a perfect square. Total number of students in the school = 1279 Square root of 1279 = Since the number of chairs is a perfect square, the number of chairs in a row is an integer more than The integers more than are 36, 37, 38 and so on. How do we tell how many chairs are there in a row out of 36, 37, 38 and so on? In order to find that, let us make use of the fact that there were less than 22 chairs empty after all students were seated. The number 22 is less than , the square root of This means, the number of chairs in a row should be the integer just greater than This means, the number of chairs in a row is 36 and the total number of chairs is 36 2 = Step 5 Total number of chairs = 1296 Number of students = 1279 Number of chairs left = Total number of chairs - Number of students = = 17 Step 6 Therefore, there were 17 chairs left in the auditorium of the school after all the students sat down.

12 ID : in-8-full-year-8th-grade-review [12] (12) We know that, the integers divisible by 2 and 3 are also divisible by 6. Therefore, the number of integers divisible by 2 and not divisible by 3 = The number of integers divisible by 2 - The number of integers divisible by 6 The number of integers in the set 1, 2, 3,...92, divisible by 2 = quotient of 92/2 = 46 The number of integers in the set 1, 2, 3,...92, divisible by 6 = quotient of 92/6 = 15 Now, the number of integers in the set 1, 2, 3,...92, divisible by 2 and not divisible by 3 = = 31 The probability that an integer in the set 1, 2, 3,...92 is divisible by 2 and not divisible by 3 The integers in the set 1, 2, 3,...92 is divisible by 2 and not divisible by 3 = The total number of integers in the set 1, 2, 3,...92 = (13) c. If we look at the given pattern carefully, we notice that every shape is repeated after 4 positions. For example, is repeated at = 5 th position. is repeated at = 6 th position and so on. Since, every shape is repeated after 4 positions, the remainder of 15 and 4 will give the position of the shape that will be repeated at 15 th position. The remainder of 15 and 4 is 3. Since, the remainder is 3, we can say that the shape at 3 rd position will be repeated at 15 th position. Thus, the image at 15 th position will be. Step 5 Hence, option c is the correct answer. (14) d. (1,3) (3,5) (5,7) (7,9)

13 (15) d. A is false but B is a correct explanation of A. ID : in-8-full-year-8th-grade-review [13] Any number that can be expressed in the form of a fraction is called a Rational number. The quotient of two integers will always be a rational number, only if the denominator is not zero. The second statement says that 4 0 is not a rational number, which is exactly why the quotient of any fraction with denominator equal to zero is not a rational number. Hence we conclude that first statement is false, but second statement is the correct explanation of first state. Step 5 Therefore, A is false but B is a correct explanation of A.