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AnswerAnswer: a) 10ExplanationIn the given series20 , 19 , 17 , 14 , ________ , 520 – 1 = 1919 – 2 = 1717 – 3 = 14We have observed that, every number is decreased by 1 , 2 , 3 and so on .Therefore to get the missing number, we need to subtract 4 from the previous numberSo, 14 – 4 = 10Hence the missing number is 10We can also see that subtracting next consecutive number i.e 5 from the missing number we get the next number of the series which is already given10 – 5 = 5 Q.2) Look at the patterns and complete the series.1600 , 1400 , 1200 , 1000 , 800 , __ , __ , __a) 1000 , 800 , 600b) 800 , 600 , 400c) 600 , 400 , 200AnswerAnswer: c) 600 , 400 , 200ExplanationIn the given series1600 , 1400 , 1200 , 1000 , 800 , ___ , ___ , ___1600 – 200 = – 200 = – 200 = – 200 = 800We have observed that, every number is 200 less than the previous number. Therefore to get the next three numbers of the series we need to subtract 200 from the previous numberSo, we can write the next numbers as800 – 200 = 600600 – 200 = 400400 – 200 = 200Therefore the next three numbers of the series are 600 , 400 , 200 Number Patterns Grade 5 WorksheetsQ.3) Find the missing numbers in the following series3 , 5 , 8 , 12 , ___ , 23a) 17b) 15c) 20AnswerAnswer: a) 17ExplanationIn the given series3 , 5 , 8 , 12 , ___ , 233 + 2 = 55 + 3 = 88 + 4 = 12We have observed that, every number is increased by 2 , 3 , 4 and so on .Therefore to get the missing number, we need to add 5 to the previous number 12So, 12 + 5 = 17Hence the missing number is 17We can also see that adding next consecutive number i.e 6 to the missing number we get the next number of the series which is already given17 + 6 = 23 Q.4) Find the missing numbers in the following series5 , 5 , 8 , 8 , 11 , __ , __a) 11, 14b) 13, 16c) 9, 12AnswerAnswer: a) 11, 14ExplanationIn the given series5 , 5 , 8 , 8 , 11 , __ , __5 x 1 = 55 + 3 = 88 x 1 = 88 + 3 = 11In the given series , the second number is 1 times the previous number and the number after the second number is 3 more than the previous number . Again the next number is 1 times the previous number and the number after it is 3 more than the previous number and so on .Therefore to get the first missing number, we need to multiply the previous number by 1So, 11 x 1 = 11Now to get the next missing number, we need to add 3 to the previous number11 + 3 = 14Hence the missing numbers are 11 and 14 Q.5) Find the missing numbers in the following series2 , 6 , 24 , 120 , __a) 960b) 720c) 840AnswerAnswer: b) 720Number Patterns Grade 5 WorksheetsExplanationIn the given series2 , 6 , 24 , 120 , __2 x 3 = 66 x 4 = 2424 x 5 = 120We have observed that, every number is 3 times , 4 times , 5 times and so on to its previous number .Therefore to get the missing number, we need to multiply 6 to the previous number .So, 120 x 6 = 720Hence the missing number is 720 Q.6) Look at the patterns and complete the series.100 , 200 , 400 , 800 , ___ , ___a) 2400 , 7200b) 800 , 1600c) 1600 , 3200AnswerAnswer: c) 1600 , 3200ExplanationIn the given series100 , 200 , 400 , 800 , ____ , ___100 x 2 = 200200 x 2 = 400400 x 2 = 800We have observed that, every number is 2 times the previous number. Therefore to get the next two numbers of the series we need to multiply the previous number by 2So, we can write the next numbers as800 x 2 = x 2 = 3200Therefore the next two numbers of the series are 1600 and 3200 Q.7) Look at the patterns and complete the series.1 , 5 , 9 , 13 , 17 , ___ , ___ , ___a) 25 , 29 , 33b) 21 , 25 , 29c) 20 , 24 , 28AnswerAnswer: b) 21 , 25 , 29ExplanationIn the given series1 , 5 , 9 , 13 , 17 , __ , __ , __1 + 4 = 55 + 4 = 99 + 4 = 1313 + 4 = 17We have observed that, every number is 4 more than the previous number. Therefore to get the next three numbers of the series we need to add 4 to the previous numberSo, we can write the next numbers as17 + 4 = 2121 + 4 = 2525 + 4 = 29Therefore the next three numbers of the series are 21 , 25 , 29 Maths Worksheets for Grade 5 1. The factors of 6x2 + 5x – 6 are:(a) (2x – 3)(3x – 2)(b) (2x – 3)(3x + 2)(c) (2x + 3)(3x – 2)(d) (2x + 3)(3x + 2)2. The factors of 12x2 – 7x + 1 are:(a) (4x – 1)(3x – 1)(b) (4x – 3)(3x + 1)(c) (4x + 1)(3x – 1)(d) (4x + 1)(3x + 1)3. On dividing x3 + 3x2 + 3x + 1 by x we get remainder:(a) 1(b) 0(c) -1(d) 24. Find the correct identity:(a) (a + b)2 = a2 + 2ab + b2(b) (a + b)2 = a2 – 2ab + b2(c) (a – b)2 = a2 + 2ab + b22(d) (a2 – b2) = a2 + 2ab + b25. Find the incorrect mathematical statement.(a) 4(x – 5) = 4x – 20(b) 3x + 2x = 5x2(c) x(3x + 2) = 3x2 + 2x(d) 2x + 3x = 5x6. Factors of a2 + 8a + 16 are:(a) (a + 4)(a – 4)(b) (a + 4)(a + 4)(c) (a + 4)(4 – a)(d) (a – 4)(a – 4)7. Factors of 12a2b + 15ab2 is(a) 3ab(4a + 5b)(b) 3ab(4a + 15b)(c) ab( 12a + 15b)(d) None of these8. Factors of 14pq + 35pqr is(a) pq(14 + 35r)(b) 7pq(2 + 5 r)(c) 7pq(14 + 5r)(d) None of these9. Factors of 2xy + 2y + 3x + 3 is(a) (x + 1)(2y + 1)(b) (x + 1)(2y + 3)(c) (x + 3)(2y + 1)(d) None of these10. Factors of 6xy – 4y + 6 – 9x is(a) (3x – 2)(2y + 3)(b) (3x – 1)(2y – 3)(c) (3x + 2)(2y – 3)(d) None of these11. Factors of 5x2y – 15xy2 is(a) xy(5x – 15y)(b) 5xy(x – 3y)(c) 5xy(x – 5y)(d) None of these12. Factors of 15pq + 15 + 9q + 25p is(a) (5p + 3)(3q + 5)(b) (5p + 3)(q + 5)(c) (p + 3)(3q + 5)(d) None of these13. Factors of z – 7 + 7xy – xyz is(a) (z – 7)( 1 – xy)(b) (z – 7)(xy – 1)(c) (7 – z)(1 – xy)(d) None of these14. Factors of x2 + 8x + 16 is(a) (x + 8)(x + 2)(b) (x + 4)(x + 2)(c) (x + 4)(x + 4)(d) None of these15. Factors of 4y2 – 12y + 9 is(a) (2y – 3)(2y – 6)(b) (2y – 3)(2y – 3)(c) (4y – 3)(y – 3)(d) None of these16. Factors of 49p2 – 36 is(a) (7p – 9)(7p + 4)(b) (4p + 4)(7p – 9)(c) (7p – 6)(7p + 6)(d) None of these17. Factors of a2 – 2ab + b2 – c2 is(a) (a – b – c)(a – b + c)(b) (a + b – c)(a + b + c)(c) (a – b + c)(a – b + c)(d) None of these18. Factors of x2 + 5x + 6 is(a) (x + 3)(x + 2)(b) (x + 4)(x + 2)(c) (x + 6)(x + 1)(d) None of these19. Factors of 36 – 9x2 will be(a) (6 + 3x)(6 – 3x)(b) (3x – 6)(6 – 3x)(c) (3x + 6)(3x -6)(d) (12x – 3x)(3 + 3x)20. Square of will be:(a) x2 – 2 – (b) x2 – 2 + (c) x2 – 4 – (d) x2 – 2 + Class 8 Maths Factorisation Fill In The Blanks1. Division is opposite of …………… .2. If (2x – 5)(x + 3) = 2x2 + x + a, then a is …………….. .3. The product (x + y)(x – y)(x2 + y2) is ………………. .4. All the factors of 4x2 are ……………… .5. The value of 105 × 95 is ……………. .Class 8 Maths Factorisation True(T) Or False(F)1. = -52. 3(y – 2) = 3y – 23. 4x + 3y = 7xy4. (3x)2 + 4(3x) + 5 = 3x2 + 12x + 55. a(5a + 2) = 5a2 + 2aClass 8 Maths Factorisation Very Short Answer Type Questions1. Factorise 12a2b + 15ab22. Factorise x2 – 36 using identity3. Divide (x2 – 16) by (x + 4)4. Find the greatest common factor of -4a3 b2, 12 a3b3c, 16a5bc5. Factorise (a + b)2 – (a – b)26. Divide (x2 – 6x + 9) by (x – 3)Class 8 Maths Factorisation Short Answer Type Questions1. Evaluate (502)2 – (498)2 using suitable identity.2. Evaluate (8.6)2 – (1.4)2 using suitable identity.3. Factors of x2 – 7x + 12 is4. Factors of x2 + x – 56 isClass 8 Maths Factorisation Long Answer Type Questions1. Resolve into factors: 2x2 – 3ax – 2a22. Divide: 44(x4 – 5x3 – 24x2) by 11x(x – 8).3. Divide: z(5z2 – 80) by 5z(z + 4)Worksheets for Class 8 Maths
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