ID : ww-8-full-year-8th-grade-review [1] Grade 8 Full Year 8th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the 6 rational numbers between -3 10 and -7 10. (2) What is the unit's digit in (14) 102 + (14) 107? (3) Which of the f ollowing numbers is a perf ect square? 220, 122, 17, 980 Choose correct answer(s) f rom given choice (4) Nancy introduces Edward as the son of the brother of her mother. How is Edward related to Nancy? a. Uncle b. Cousin c. Nephew d. Son () If 3 6 = 81 and 4 9 = 169, f ind the value of 1 8. a. 9 b. 8 c. 81 d. 72 (6) Which of the statements below is f alse? a. There is no f raction that cannot be represented as a rational number c. There is no integer that cannot be represented as a rational number b. A negative decimal number cannot be a rational number d. All negative numbers can be represented as rational numbers (7) William is the brother of the son of Edward's son. How is William related to Edward? a. Uncle b. Cousin c. Grandson d. Son (8) Simplif y (a -4 + b -4 ) -1 a. a4 + b 4 a 4 b 4 b. c. a 4 + b 4 d. a 4 b 4 a 4 + b 4 ab a 4 + b 4
ID : ww-8-full-year-8th-grade-review [2] (9) If Donald drives at three f ourth of his usual speed, he covers a certain distance in 2 hours more than the time he takes while driving at his usual speed. Find the time taken by him to cover this distance with his usual speed. a. 6 hours b. 7 hours c. hours d. 8 hours Fill in the blanks (10) Richard bought a plot at $100000. If its value appreciates at the rate of 20% per annum, the value of plot af ter 3 years = $. (11) Mark and Helen run a hundred metres race. Mark wins by 18 metres. For the next race, Mark starts f rom 18 metres behind the original starting line, and Helen starts f rom the original starting line. If they both run at the same speed in which they ran the original race, then will win this race by metres. (12) The largest perf ect square number that is smaller than the largest 4 digit number is (13) Solve the f ollowing using standard identities A) 28 2 = B) 28 2 = C) 898 2 = D) 901 2 = (14) + 2 + 1 + 1 = 1 = (1) If the sum of two consecutive multiple of 3 is 21, then the numbers are and. 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ww-8-full-year-8th-grade-review [3] (1) -1 2, -1 3, -1 4, -1, -1 6, -1 7, (Answers can vary). (2) 0 (3) 122 Perf ect square is a number made by squaring a whole number. Steps to f ind the perf ect square are as f ollows. i. Resolve the given number into prime f actors. ii. Make pairs of prime f actors such that both the f actors in each pair are equal. iii. If there is nothing lef t without the pair of prime numbers so the number is perf ect square otherwise not. Let's check all given numbers Prime f actors of 220, 220 = 7 7 3 3 Now create pairs, 220 = (7 7) (3 3) Since all f actors are not paired, this is not a perf ect square. Prime f actors of 122, 122 = 7 7 Now create pairs, 122 = (7 7) ( ) Since all f actors are paired, this is a perf ect square. Step 4 Prime f actors of 17, 17 = 3 3 7 Now create pairs, 17 = (3 3) ( ) 7 Since all f actors are not paired, this is not a perf ect square. Step Prime f actors of 980, 980 = 7 7 2 2 Now create pairs, 980 = (7 7) (2 2) Since all f actors are not paired, this is not a perf ect square. Step 6 Theref ore correct answer is 122.
(4) b. Cousin ID : ww-8-full-year-8th-grade-review [4] Nancy introduces Edward as the son of the brother of her mother. or we can say that Nancy's mother is the sister of Edward's f ather. or we can say that Nancy is the cousin of Edward. Step 4 Theref ore the relation of Edward to Nancy is: Cousin. () c. 81 If you look at the numbers you will notice that the result is the square of the sum of the numbers. 3 6 = (3 + 6) 2 = 81 4 9 = (4 + 9) 2 = 169 Theref ore, 1 8 = (1 + 8) 2 = 9 2 = 81
(6) b. A negative decimal number cannot be a rational number ID : ww-8-full-year-8th-grade-review [] A rational number is a number which can be written in the f orm p q where p and q both are integers and q is not equal to zero. All integers can be written in the f orm of p/1 (where p is any integer). Hence, all integers are rational numbers. Theref ore, the statement "There is no integer that cannot be represented as a rational number" is true. All f ractions are rational numbers as they are represented in p q f orm where p and q are integers. T heref ore, the statement "T here is no fraction that cannot be represented as a rational number" is true. Step 4 All integers (-ve or +ve) can be written in the f orm p/1 where p is the integer. Theref ore, the statement "All negative numbers can be represented as rational numbers" is true. Step A negative decimal number can be written in p/q f orm, if digits af ter decimal are either terminating or repeating. T heref ore, the statement "A negative decimal number cannot be a rational number" is false. Step 6 The f alse statement is "A negative decimal number cannot be a rational number" and hence, the correct answer is b. (7) c. Grandson It is given that, William is the brother of the son of Edward's son. From above chart we can see that William is grandson of Edward.
(8) b. a 4 b 4 a 4 + b 4 We have been asked to simplif y (a -4 + b -4 ) -1. ID : ww-8-full-year-8th-grade-review [6] Now, (a -4 + b -4 ) -1 = 1 a -4 + b -4 = = = 1 1 + a 4 1 b 4 + a 4 a 4 b 4 a 4 b 4 a 4 + b 4 1 b 4 Theref ore, the result is a 4 b 4 a 4 + b 4. (9) a. 6 hours
(10) 172800 ID : ww-8-full-year-8th-grade-review [7] We have been asked to f ind the value of the plot af ter 3 years. Principal, P = $100000 Rate, R = 20% Time, n = 3 years R Amount = P(1 + ) n 100 20 = 100000(1 + 100 = 100000 1.728 = 172800 ) 3 Theref ore, the value of plot af ter the 3 years is $172800. (11) (12) Mark 3.24 9801 The largest 4 digit number is 9999. We need to f ind the largest perf ect square number that is smaller than 9999. Let us f irst look at the square root of 9999. The square root of 9999 = 99.99 The largest perf ect square number smaller than 9999 must be the square of the integer just smaller than 99.99. The integer just smaller than 99.99 is 99 and the square of 99 = (99) 2 = 9801 Step 4 Theref ore, the largest perf ect square number that is smaller than the largest 4 digit number is 9801.
(13) A) 784 ID : ww-8-full-year-8th-grade-review [8] Use the standard identities here For example (a+b) 2 = a 2 + b 2 +2ab Similarly,(a-b) 2 = a 2 + b 2-2ab Take the last question here, which is 28 2 Now, 28 = 30-2 Theref ore, 28 2 = (30-2) 2 28 2 = 30 2 + 2 2 - (2 x 30 x 2) 28 2 = 900 + 4-120 28 2 = 784 B) 784 Use the standard identities here For example (a+b) 2 = a 2 + b 2 +2ab Similarly,(a-b) 2 = a 2 + b 2-2ab Take the last question here, which is 28 2 Now, 28 = 30-2 Theref ore, 28 2 = (30-2) 2 28 2 = 30 2 + 2 2 - (2 x 30 x 2) 28 2 = 900 + 4-120 28 2 = 784 C) 806404 Use the standard identities here For example (a+b) 2 = a 2 + b 2 +2ab Similarly,(a-b) 2 = a 2 + b 2-2ab Take the last question here, which is 898 2 Now, 898 = 900-2 Theref ore, 898 2 = (900-2) 2 898 2 = 900 2 + 2 2 - (2 x 900 x 2) 898 2 = 810000 + 4-3600 898 2 = 806404
D) 811801 ID : ww-8-full-year-8th-grade-review [9] Use the standard identities here For example (a+b) 2 = a 2 + b 2 +2ab Similarly,(a-b) 2 = a 2 + b 2-2ab Take the last question here, which is 901 2 Now, 901 = 900 + 1 Theref ore, 901 2 = (900 + 1) 2 901 2 = 900 2 + 1 2 + (2 x 900 x 1) 901 2 = 810000 + 1 + 1800 901 2 = 811801 (14) 1 According to question + 2 + 1 + 1 = 1 + 4 = 1 = 1-4 = - 4 = 1 = 1 Now the value of is 1.
(1) 9 12 ID : ww-8-full-year-8th-grade-review [10] Let's assume two consecutive multiples of 3 are x and x + 3. According to the question the sum of two consecutive multiples of 3 is 21. Theref ore, x + x + 3 = 21 2x = 21-3 2x = 18 x = 18 2 x = 9 Theref ore, the numbers are 9 and 12.