Algebra Questions for SSC GD: Download Free PDF & Practice Now

Do you dream of wearing the uniform of the BSF, CRPF, or CISF? The SSC GD Constable exam is your first step toward that dream. But it looks difficult for some students due to the math section. When you see x and y in a question, do you feel like skipping it? Here is the truth: Algebra in SSC GD is not rocket science. It is not the complex math you see in engineering. It is basic, formula-based math. If you remember just 3 or 4 simple formulas like (a+b)², you can solve these questions in seconds. To make it easy for you, we have analyzed the exam papers from many past years. We have compiled the most repeated Algebra questions into a free PDF. You don’t need to hunt for them. Just download it below and start practicing today.

Why is Algebra Important for SSC GD?

In the Elementary Mathematics section, Algebra might seem small, but it is a “Hidden Gem.”

• Easy Marks: You can expect 2 to 3 questions in the exam. These are often the quickest to solve if you know the formula.
• No Calculation Errors: Unlike huge multiplication in Mensuration, Algebra relies on short tricks.
• Formula-based: The questions are standard. They don’t change much. If you learn the pattern once, you are set for life.

Important Algebra Formulas You Must Know

You don’t need the whole book. Just focus on these three pillars:

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

Download Free PDF of Algebra Questions for SSC GD

We have prepared a comprehensive PDF containing exam-level questions. These are the exact types of questions you will face in the exam hall—simple, logical, and scoring. Download it, save it, and practice it to remove your fear of x and y.

Q1. If x + 1/x = 4, find the value of x^2 + 1/x^2.

(a) 14
(b) 16
(c) 12
(d) 18

Answer: (a) 14
Logic: Short trick: k^2 − 2. Here k = 4. So, 4^2 − 2 = 16 − 2 = 14.

Q2. Evaluate: 98 × 102 using algebraic identity.

(a) 9996
(b) 9984
(c) 9994
(d) 10004

Answer: (a) 9996
Logic: Write it as (100 − 2)(100 + 2). Using (a − b)(a + b) = a^2 − b^2.
So, 100^2 − 2^2 = 10000 − 4 = 9996.

Q3. If a + b = 5 and ab = 6, find the value of a^2 + b^2.

(a) 12
(b) 13
(c) 25
(d) 19

Answer: (b) 13
Logic: (a + b)^2 = a^2 + b^2 + 2ab
25 = a^2 + b^2 + 12
a^2 + b^2 = 13

Q4. If 2x + 3 = 9, find the value of 3x + 2.

(a) 11
(b) 12
(c) 10
(d) 13

Answer: (a) 11
Logic: 2x = 6, so x = 3
3x + 2 = 9 + 2 = 11

Q5. Solve for x: x/3 + x/4 = 7.

(a) 10
(b) 11
(c) 12
(d) 14

Answer: (c) 12
Logic: LCM of 3 and 4 is 12
(4x + 3x)/12 = 7
7x = 84
x = 12

Q6. If a − b = 3 and a^2 − b^2 = 27, find the value of a + b.

(a) 6
(b) 9
(c) 12
(d) 8

Answer: (b) 9
Logic: a^2 − b^2 = (a − b)(a + b)
27 = 3(a + b)
a + b = 9

Q7. If x + 1/x = 2, find x^100 + 1/x^100.

(a) 0
(b) 1
(c) 2
(d) 100

Answer: (c) 2
Logic: x + 1/x = 2 implies x = 1
1^100 + 1/1^100 = 2

Q8. The roots of the equation x^2 − 5x + 6 = 0 are:

(a) 2, 3
(b) −2, −3
(c) 1, 6
(d) 2, −3

Answer: (a) 2, 3
Logic: Numbers that multiply to 6 and add to −5 are −2 and −3
Roots are x = 2 and x = 3

Q9. Simplify: (205)^2 − (195)^2

(a) 4000
(b) 2000
(c) 3000
(d) 400

Answer: (a) 4000
Logic: a^2 − b^2 = (a + b)(a − b)
(205 + 195)(205 − 195) = 400 × 10 = 4000

Q10. If 3x − y = 5 and x = 2, find y.

(a) 2
(b) 3
(c) 1
(d) 0

Answer: (c) 1
Logic: 3(2) − y = 5
6 − y = 5
y = 1

How to Prepare for Algebra Easily?

Don’t treat Algebra like a monster. It’s just a puzzle.

• Memorize the Identities: Write (a+b)^2, (a-b)^2, and a^2-b^2 on your study table. These 3 formulas cover 80% of SSC GD algebra.
• Value Putting Method: This is a magician’s trick. If a question has variables (a, b, c) in the options, try setting a = 1, b = 1, and c = 1 and see which option matches. It works wonders!
• Don’t Fear the “x”: Basic linear equations (like 2x+5=15) are just like calculating money at a shop. Treat ‘x’ as the price of an item.
• Practice with Topic Tests: Reading is not enough. You must calculate. Attempt our Free Topic Tests to increase your speed.

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