Algebra for SSC CGL, Download PDF of Questions & Formulas

Algebra for SSC CGL Exam: Algebra is an important topic of the Quantitative Aptitude section for the SSC CGL exam. You can expect at least 2-3 questions from Algebra in the SSC CGL Exam. Questions from this topic can be a bit challenging in the exam but you can easily attempt it if you have followed the good approach. The best way to cover this topic is to first understand the basic concept of algebra, then formulas related to algebra, and at last easy to advanced level questions for practice. This blog provides you the all the way discussed above along with the topic-wise and complete mock test.

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)

Algebra Previous Year’s Questions for SSC CGL, Download Free PDF

Below we have provided the free PDF to download for the algebra previous year’s questions for SSC CGL exam.

1. If x² – 8x – 1= 0, what is the value of x² + 1/x²

(a) 66
(b) 68
(c) 62
(d) 64

2. If (x – 1/x=10), what is the value of (x⁴ + 1/x⁴) ?

(a) 10404
(b) 10400
(c) 10402
(d) 10406

3. If (x + 1/x=9), what is the value of (x⁴ + 1/x⁴) ?

(a) 5431
(b) 6561
(c) 6239
(d) 6156

4. If (y – 1/y=4), find the value of (y⁶ + 1/y⁶).

(a) 4096
(b) 5774
(c) 5776
(d) 5778

5. If (y + 1/y =4), find the value of (y⁶ + 1/y⁶).

(a) 2702
(b) 4096
(c) 2704
(d) 2706

6. If x² – 15x + 1 = 0, what is the value of x⁴ −223x² + 6?

(a) 6
(b) 9
(c) 5
(d) 0

7. Simplify the given expression. (a – 2b) (b – 3a) + (a + b) (a – 3b) – (b – 3a) (4a – 5b)

(a) 10a² – 14ab
(b) 10a² – 4ab
(c) 8a² + 10ab
(d) 8a² – 10ab

8. Simplify the following expression. (4x + 1)² – (4x + 3)(4x – 1)

(a) (4x – 3)
(b) (4x + 1)
(c) 4
(d) 4x

9. If x and y are positive numbers such that x – y = 5 and xy = 150, then the value of (x + y) is:

(a) 35
(b) 25
(c) 15
(d) 45

10. If x + y = 7 and xy = 19, then calculate the value of x² + y².

(a) 11
(b) 12
(c) 17
(d) 19

Algebra Test for SSC CGL

Below we have provided the direct link to the algebra test for SSC CGL. The questions provided in the test are the most asked questions and mimics the real exam environment. Practicing questions under time constraint is very important. So, click on the link and get your free topic-wise test reward.

Sample Questions of Algebra for SSC CGL

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

Tips to Master the Algebra

Below we have provided some useful tips that will help you to become master on algebra questions.

• Understand Basic Terms: Make sure that you aware of variable (such as: x, y, z), constants (numbers), coefficients (numbers multiplying variables), and expressions (like 3x + 5).
• Break Complex Problem into Small Problems: It happens most of the time that the question asked very complex or big. Try to break that questions into small tasks and solve each task individually to get the accurate answers.
• Solve Equations Step-by Step: Make sure that you solve the questions step-by-step process. Look for question first carefully and think which operation can apply first. Solving questions without strategy may lead to wrong answer.
• Practice Mock Tests and More Questions: Speed and accuracy is must for this topic. As this topic can take time and SSC CGL exam is time constraint exam. Practice is the only way to maintain speed as well as accuracy. Solving mock test will be the best way to master this topic.

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