SSC CHSL Topic Wise Study Material - Quantitative Aptitude - Elementary Algebra

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Elementary Algebra

Contents

SSC CHSL Study Material SSC CHSL Previous Papers SSC CHSL Practice Workbook

A combination of one or more terms including letters in addition to numbers and symbols along with the signs of mathematical operations is termed as an algebraic expression.
It consists of two types of symbols and variables with fundamental arithmetic operations (+,-,÷,x).
Constants Constants are fixed, i.e., 0,1, 2, 3, 4, 5, 6, 7, 8, 9
Variables Variables are the symbols representing any numeral.
e.g., 3x² + 4xy – 10x, 2x + 5y etc. are algebraic expression.

Fundamental Operations on Algebraic Expressions
I. Method of Addition
Step I Collect different groups of like term.
Step II Find the sum of the numerical coefficients of like terms in each group.
Step III Write the final terms after addition.
e.g., (x² + 2y) + (3x² – y) =x² + 3x² + 2y-y = 4x² + y

II. Method of Subtraction
Step I Reverse the sign (from + to – and from – to +) of all the terms of the expression which is to be subtracted.
Step II Now, follow the method used in addition.
e.g., (a² + 2b² -ab) – (4a² -b² + 2ab)
= 4a² – a² -b² -2b² + 2ab + ab
=3a² -3b² + 3ab = 3(a² – b² + ab)

III. Method of Multiplication
Step I Find the product by using the rule that product of two factors with like sign is positive and the product of two factors with unlike sign is negative i.e., (+) x (+) = +, (+) x (-) = -, (-) x (+) = -, (-) x (-) = +
Step II Now, from the surds rule, if x is a variable and m, n are positive integer then x^m x xⁿ=x.^m+n
e.g., Multiply, (x + 2) x (x – 4) =x(x – 4) + 2 (x – 4) = x² – 4x + 2x-8 = x²-2x-8

IV. Method of Division
Step I Arrange the terms of both the polynomials in descending order of their highest power.
Step II Divide the first term of the dividend by the first term of the divisor to obtain the first term of the quotient.
Step III Multiply all terms of the divisor by the first of the quotient and subtract the result from the dividend.
Step IV Consider the remainder (if any) as a new dividend and proceed as before.
Step V Repeat this process till we obtain a remainder which is either ‘zero’ or polynomial of degree less than, that of
the divisor.
e.g.,

Some Useful Facts/Formulae

Reference Corner

1. What are the roots of the quadratic equation 21x² – 37x -28 = 0 ? SSC(10 + 2)2017
(a)-7/3, 4/7
(b) 3/7, -7/4
(c) 7/3,-4/7
(d)-3/7, 7/4
Answer:

2. If x + y = 2a, then the value of a/x-a+a/y-a is SSC(10+ 2)2015
(a) 2
(b)0
(c) -1
(d) 1
Answer:

4. If t² – 4t + 1 = 0, then the value of t³ + 1/t³ is SSC(10 + 2) 2014
(a) 52
(b) 64
(c) 44
(d) 48
Answer:

5. If x + 1/x = 3, then the value of 3x² – 4x + 3/x² – x + 1 is SSC(10 + 2) 2014
(a)4/3
(b)3/2
(c)5/2
(d)5/3
Answer:

6. If x = 3 + 2√2, then x⁶ + x⁴ + x² + 1/x³ is equal to SSC(10 + 2)2014
(a) 216
(b) 192
(c) 198
(d) 204
Answer:

7.

(a)1/a-b-c
(b)1/a+b-c
(c)1/a-b+c
(d)1/a+b+c
Answer:
(d)

8. If x = p + 1/p and y = p – 1/p then value of x⁴– 2x²y²+ y⁴ SSC (10 + 2) 2014
(a) 24
(b) 4
(c) 16
(d) 8
Answer:

9. If xy/x+y=a,xz/x+z=b,yz/y+z=c,where a,b,c are all non-zero numbers, then x equals to SSC (10 + 2) 2013
(a)2abc/ac + bc- ab
(b)abc/ab + bc + ac
(c)2abc/ab + bc- ac
(d)2abc/ab + ac-bc
Answer:

10. If x + y + z = 13 and x² + y² + z² = 69, then the value of xy + z (x + y) is equal to SSC (10 +2) 2013
(a) 50
(b) 60
(c) 70
(d) 40
Answer:

11.

12. If 4x – 5z = 16 and xz = 12, the value of 64x³ – 125z³ is equal to SSC (10 + 2) 2013
(a) 15610
(b) 15616
(c) 15618
(d) 15620
Answer:

13. If x + y + z = 15, xy + yz+ zx= 75, then x+4y+z/3z is equal to SSC (10 + 2) 2013
(a) 1
(b) 0
(c) 2
(d) -1
Answer:

Practice Exercise

1.The Solution of the equations p/x+q/y=m and q/x+p/y=n is

2.If (x + 1/x) = 4, then (x⁴ + 1/x⁴) is equal to
(a) 190
(b) 180
(c) 193
(d) 194

3.If x² + 5x – 2k is exactly divisible by (x – 1), then the value of k is
(a)1
(b) 2
(c) 3
(d) 4

4.If x + 1/x = 4, then the value of x³ + 1/x³ is
(a) 52
(b) 64
(c) 68
(d) 76

5. If x + y = 8 and xy = 7, then the value of x³ + y³ is
(a) 344
(b) 342
(c) 345
(d) 340

6. If x¹⁰⁰ + 2x⁹⁹ + k, is divisible by (x + 1), then the value of k is
(a)1
(b) 4
(c) 3
(d)0

7. The value of k for which x -1 is a factor of 4x³ + 3x² – 4x + k is
(a) 3
(b) 1
(c) -2
(d) -3

8. One factor of x⁴ + x² – 20 is x² + 5. The other factor is
(a)x²-4
(b)x-4
(c)x²-5
(d)x+2

9. If a + b + c = 0, then a³ + b³ + c³ is
(a) 2abc
(b) 3abc
(c) abc
(d) 4abc

10.The factors of x⁸ + x⁴ + 1 are
(a)(x⁴+ 1 – x²),(x² + 1 + x),(x² + 1 – x)
(b)(x⁴+ 1 – x²),(x² -1 + x),(x² + 1 + x)
(c)(x⁴+ 1 + x²),(x² -1 + x),(x² + 1 + x)
(d)(x⁴– 1 + x²),(x² + 1 – x),(x² + 1+ x)

11.The expression 10xy⁴ -10x⁴y can be expressed in factors as
(a)10xy (x- y) (x² + xy + y²)
(b)10xy (y – x) (x² + xy + y²)
(c)10xy (y-x) (x² -xy + y²)
(d) None of these

12. GCD of (a+b- c)⁶ and (a+b- c)⁴ is
(a)(a+b-c)⁶
(b)(a+b-c)²
(c)(a+b-c)¹⁰
(d)(a+b-c)⁴

13. (4x + 3y)² + (4x – 3y)² is equal to
(a) 16x² – 9y²
(b) 32x² + 18y²
(c) 16x² + 9y²
(d) 32x² + 9y²

14. If a/b=4/5 and b/c=15/16,then(c²-a²)/(c²+a²) is equal to
(a)1/7
(b)7/25
(c)3/4
(d)None of these

15. If a/x + y/b = 1 and b/y + z/c = 1, then (x/a+c/z) is equal to
(a)0
(b)b/y
(c)1
(d)y/b

16. If x = (1 – a), y = (2a + 1) and x = y, then a is equal to
(a) 2
(b) 1/2
(c) 0
(d) -1

17.

(a) 0
(b) 1/9
(c) 1/3
(d) 1

18. If x + y + z = 0, then (x² + xy + y²) is equal to
(a)(y² + yz + z²)
(b)(y² -yz + z²)
(c)(z² -zx+ x²)
(d)(z² +zx+ x²)

19.

(a )[(x+y)(y+z)(z+x)]^-1
(b )x+y+z
(c)x-y+z
(d) None of these

20. If a + b + c = 2s, then [(s – a)² + (s – b)² + (s – c)² + s²] is equal to
(a) (s² – a² – b² – c²)
(b) (s² + a² + b² + c²)
(c) (a² + b² + c²)
(d) (4s² – a² – b² – c²)

21. If a/3 = b/2, then value of 2a + 3b/3a – 2b is SSC (10 + 2) 2011
(a)12/5
(b)5/12
(c)1
(d)12/7

22.

(a) a
(b) b
(c) 2ab
(d) 2

23. If x = b + c – 2a, y = c + a – 2b, z = a + b – 2c, then the value of x² + y² – z² + 2xy is SSC (10 + 2) 2011
(a) 0
(b) a + b + c
(c) a – b + c
(d) a + b – c