Algebra Most Expected Questions for SSC CGL Tier 2 Exam

Algebra for SSC CGL Tier 2 Exam

Algebra for SSC CGL Exam: Algebra is a very important topic of the Quantitative Aptitude section for the SSC CGL Tier 2 exam. Candidates can expect at least 3-6 questions from this topic in the Tier 2 exam. Questions from this topic can be a bit challenging as these questions appear in the SSC CGL Tier 2 exam. This is the main reason that candidates must practice a lot on different types of questions based on different patterns. In this blog, we have provided the algebra most expected questions for SSC CGL Tier 2 exam with their answers and solutions. Along with the questions we have also provided the basic concept which candidates must read and understand before solving the questions.

Concept of Algebra

Algebra is a mathematical topic that uses symbols, letters, and numbers to represent and solve equations. The primary goal is to find unknown values, usually represented by variables such as x, y, z, etc. In algebra, we work with expressions, equations, and functions, among other concepts.

Common Algebraic Formulas

1. Linear Equations:

A linear equation has the form ax+b=0, where a and b are constants. The solution is x =−b/a.

2. Quadratic Equations:

A quadratic equation is in the form ax²+bx+c=0. The solutions can be found using:

a. Factoring: (x−p)(x−q)=0⇒x=p or x = q.

b. Quadratic Formula:

c. Completing the square: A method of solving by manipulating the equation into a perfect square trinomial.

3. Exponent Rules:

a. Product of Powers: x^m⋅xⁿ=x^m+n

b. Quotient of Powers: x^m/xⁿ=x^m−n

c. Power of a Power: (x^m)ⁿ=x^m⋅n

d. Zero Exponent: x⁰=1

e. Negative Exponent: x⁻ⁿ=1/xⁿ​

4. Polynomials:

A polynomial is an expression involving sums and differences of terms that are products of variables raised to non-negative integer powers.

a. General form: P(x)=a_nxⁿ+a_n−1xⁿ⁻¹+⋯+a₁​x+a₀​

b. Degree: The highest power of the variable x in the polynomial.

5. Factoring:

a. Common Factor: ax+ay=a(x+y)

b. Difference of Squares: a²−b²=(a−b)(a+b)

c. Perfect Square Trinomial: a²+2ab+b²=(a+b)²

d. Trinomial Factoring: ax²+bx+c=(px+q)(rx+s), if factors exist.

6. Exponential Growth and Decay:

a. Growth formula: A=P(1+r)^t (where P is the initial amount, r is the growth rate, and t is time).

b. Decay formula: A=P(1−r)^t (for decay).

7. Systems of Equations:

a. A system of two equations can be solved by substitution, elimination, or graphing.

Example: 2x+y=7 and x−y=3

b. Substitution: Solve one equation for one variable and substitute into the other equation.

c. Elimination: Add or subtract the equations to eliminate one variable.

8. Slope of a Line:

The slope of a line passing through points (x1, y1) and (x2, y2) is given by:

9. Slope-Intercept Form of a Line:

Equation of a line: y=mx+b, where m is the slope, and b is the y-intercept.

10. Distance Formula:

To find the distance between two points (x1, y1) and (x2, y2):

11. Midpoint Formula:

To find the midpoint between two points (x1, y1) and (x2, y2):

12. Logarithms:

a. log⁡_b(x)=y means b^y=x.

b. Logarithmic Properties:

• log⁡_b(xy)=log_⁡b(x)+log⁡_b(y)
• log⁡_b(x/y) = log⁡_b(x) − log⁡_b(y)
• log⁡_b(xⁿ)=nlog⁡_b(x)

Most Expected Important Questions PDF for Algebra

Question 1: If a² + b² + 64c² + 16c + 3 = 2(a + b), then find the value of 4a⁷ + b⁷ + 8c².

A) (43/4)

B) (36/5)

C) (41/8)

D) (37/2)

Question 2: If (ab + bc + ca) = 8, (a² + b² + c²) = 20, then which of the following can be the value of {(a + b + c)/2}{(a – b)² + (b – c)² + (c – a)²}

A) 108

B) 56

C) 64

D) 72

Question 3: If 2x² + y² + 6x – 2xy + 9 = 0, then find the value of (4x² – y³ + x²y²).

A) 144

B) 152

C) 138

D) 124

Question 4: If a + b + c = 0, then the value of a³ + b³ + c³ is:

A) 0

B) abc

C) 3abc

D) None of these

Question 5: Find the value of {x² + (1/x²)} if:

A) 47

B) 55

C) 28

D) 71

SSC CGL 2024 Tier 2 Free Preparation Resources

Below we are providing the SSC CGL 2024 Tier 2 Free Preparation Resources that contains multiple tests, including section-wise mock tests covering all the sections like English, General Awareness, Quantitative Aptitude, and Reasoning. Practicing these tests will help you revise all these sections in a time-bound manner and also test your skills and knowledge acquired in the last stretch of revision.

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