Algebra (Secondary) for Competitive Exam Success

Algebra (Secondary)

3D Geometry Arithmetic and Geometric Progressions Arithmetic and Geometric Progressions - Applications Arithmetic and Geometric Progressions - Case Studies Arithmetic and Geometric Progressions - Problem Set Binomial Theorem Binomial Theorem (Intro) Binomial Theorem (Intro) - Applications Binomial Theorem (Intro) - Case Studies Binomial Theorem (Intro) - Problem Set Complex Numbers and Quadratic Equations Coordinate Geometry - Circles Coordinate Geometry - Straight Lines Differential Equations Factorization Techniques Factorization Techniques - Applications Factorization Techniques - Case Studies Factorization Techniques - Problem Set Indices and Surds Indices and Surds - Applications Indices and Surds - Case Studies Indices and Surds - Problem Set Inequalities and Their Applications Inequalities and Their Applications - Applications Inequalities and Their Applications - Case Studies Inequalities and Their Applications - Problem Set Integral Calculus Limit, Continuity and Differentiability Linear Equations in One Variable Linear Equations in One Variable - Applications Linear Equations in One Variable - Case Studies Linear Equations in One Variable - Problem Set Linear Programming Basics Linear Programming Basics - Applications Linear Programming Basics - Case Studies Linear Programming Basics - Problem Set Mathematical Induction Matrices and Determinants Pair of Linear Equations - Word Problems Pair of Linear Equations - Word Problems - Applications Pair of Linear Equations - Word Problems - Case Studies Pair of Linear Equations - Word Problems - Problem Set Permutations and Combinations Polynomials - Introduction Polynomials - Introduction - Applications Polynomials - Introduction - Case Studies Polynomials - Introduction - Problem Set Polynomials - Roots and Factor Theorem Polynomials - Roots and Factor Theorem - Applications Polynomials - Roots and Factor Theorem - Case Studies Polynomials - Roots and Factor Theorem - Problem Set Quadratic Equations Quadratic Equations - Applications Quadratic Equations - Case Studies Quadratic Equations - Problem Set Quadratic Formula Applications Quadratic Formula Applications - Applications Quadratic Formula Applications - Case Studies Quadratic Formula Applications - Problem Set Sequences and Series Sets, Relations and Functions Simultaneous Linear Equations Simultaneous Linear Equations - Applications Simultaneous Linear Equations - Case Studies Simultaneous Linear Equations - Problem Set Trigonometry - Advanced Problems Vector Algebra

Q. Solve for x: 7x - 2 = 5x + 6

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Step 1: Subtract 5x from both sides: 2x - 2 = 6. Step 2: Add 2 to both sides: 2x = 8. Step 3: Divide by 2: x = 4.

Correct Answer: B — x = 2

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Q. Solve for x: 7x - 4 = 24

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Add 4 to both sides: 7x = 28. Step 2: Divide by 7: x = 4.

Correct Answer: D — x = 5

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Q. Solve for x: 8 - 3x = 2.

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Step 1: Subtract 8 from both sides: -3x = -6. Step 2: Divide both sides by -3: x = 2.

Correct Answer: B — x = 2

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Q. Solve for x: 9x + 1 = 28.

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 1 from both sides: 9x = 27. Step 2: Divide both sides by 9: x = 3.

Correct Answer: B — x = 3

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Q. Solve for x: x/4 + 5 = 8

A. x = 12
B. x = 16
C. x = 20
D. x = 24

Solution

Step 1: Subtract 5 from both sides: x/4 = 3. Step 2: Multiply both sides by 4: x = 12.

Correct Answer: B — x = 16

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Q. Solve for x: x/4 + 5 = 9

A. x = 12
B. x = 16
C. x = 20
D. x = 24

Solution

Subtract 5 from both sides: x/4 = 4. Multiply by 4: x = 16.

Correct Answer: B — x = 16

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Q. Solve for x: x/4 - 2 = 1

A. x = 8
B. x = 12
C. x = 16
D. x = 20

Solution

Add 2 to both sides: x/4 = 3. Multiply by 4: x = 12.

Correct Answer: A — x = 8

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Q. Solve for x: x^2 + 2x - 8 = 0.

A. x = 2, -4
B. x = -2, 4
C. x = 4, -2
D. x = -4, 2

Solution

Factoring gives (x + 4)(x - 2) = 0. Thus, the solutions are x = -4 and x = 2.

Correct Answer: C — x = 4, -2

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Q. Solve for x: x^2 + 4x + 4 = 0

A. x = -2
B. x = 2
C. x = 0
D. x = -4

Solution

Factor: (x + 2)(x + 2) = 0. So, x = -2.

Correct Answer: A — x = -2

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Q. Solve for x: x^2 - 5x + 6 = 0.

A. 1
B. 2
C. 3
D. 4

Solution

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Correct Answer: B — 2

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Q. Solve for y in the equation 2y - 3 = 7.

A. 3
B. 4
C. 5
D. 6

Solution

Add 3 to both sides: 2y = 10. Divide by 2: y = 5.

Correct Answer: C — 5

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Q. Solve for y in the equation 4y - 2 = 10.

A. 2
B. 3
C. 4
D. 5

Solution

Add 2 to both sides: 4y = 12. Divide by 4: y = 3.

Correct Answer: B — 3

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Q. Solve for y: 2y - 3 = 7.

A. 2
B. 3
C. 5
D. 10

Solution

2y - 3 = 7. Add 3 to both sides: 2y = 10. Divide by 2: y = 5.

Correct Answer: C — 5

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Q. Solve for y: 2y - 4 = 10.

A. 5
B. 7
C. 8
D. 10

Solution

2y - 4 = 10. Add 4 to both sides: 2y = 14. Divide by 2: y = 7.

Correct Answer: B — 7

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Q. Solve the equation 2x^2 + 4x - 6 = 0.

A. x = 1, -3
B. x = -1, 3
C. x = 3, -1
D. x = -3, 1

Solution

First, divide the equation by 2: x^2 + 2x - 3 = 0. Factor to (x + 3)(x - 1) = 0. Thus, x = -3 and x = 1.

Correct Answer: A — x = 1, -3

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Q. Solve the equation 2x^2 - 8 = 0.

A. x = 2
B. x = -2
C. x = 4
D. x = -4

Solution

First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Finally, take the square root: x = ±2, so the solutions are x = 2 and x = -2.

Correct Answer: C — x = 4

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Q. Solve the equation 3x + 7 = 16.

A. x = 3
B. x = 2
C. x = 1
D. x = 4

Solution

To solve 3x + 7 = 16, subtract 7 from both sides: 3x = 9. Then divide by 3: x = 3.

Correct Answer: A — x = 3

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Q. Solve the equation x^2 + 4x + 4 = 0.

A. x = -2
B. x = 2
C. x = -4
D. x = 0

Solution

This can be factored as (x + 2)(x + 2) = 0. Therefore, x = -2 is a double root.

Correct Answer: A — x = -2

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Q. Solve the equation: 5x + 3 = 2x + 12

A. x = 3
B. x = 4
C. x = 5
D. x = 6

Solution

Subtract 2x from both sides: 3x + 3 = 12. Then subtract 3: 3x = 9. Finally, divide by 3: x = 3.

Correct Answer: B — x = 4

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Q. Solve the inequality 2x + 3 > 7.

A. x < 2
B. x > 2
C. x < 3
D. x > 3

Solution

To solve 2x + 3 > 7, subtract 3 from both sides: 2x > 4. Then divide by 2: x > 2.

Correct Answer: B — x > 2

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Q. Solve the inequality 2x + 3 ≥ 7.

A. x ≥ 2
B. x ≤ 2
C. x ≥ 3
D. x ≤ 3

Solution

Step 1: Subtract 3 from both sides: 2x ≥ 4. Step 2: Divide both sides by 2: x ≥ 2.

Correct Answer: A — x ≥ 2

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Q. Solve the inequality 3x + 5 > 2.

A. x > -1
B. x < -1
C. x > 1
D. x < 1

Solution

Subtract 5 from both sides: 3x > -3. Divide by 3: x > -1.

Correct Answer: A — x > -1

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Q. Solve the inequality 3x - 4 < 5.

A. x < 3
B. x > 3
C. x < 1
D. x > 1

Solution

Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.

Correct Answer: A — x < 3

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Q. Solve the inequality 3x - 5 < 4.

A. x < 3
B. x < 2
C. x > 3
D. x > 2

Solution

Step 1: Add 5 to both sides: 3x < 9. Step 2: Divide by 3: x < 3.

Correct Answer: B — x < 2

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Q. Solve the inequality 3x - 5 < 7.

A. x < 4
B. x > 4
C. x < 2
D. x > 2

Solution

To solve 3x - 5 < 7, add 5 to both sides: 3x < 12. Then divide by 3: x < 4.

Correct Answer: A — x < 4

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Q. Solve the inequality 3x - 7 < 2.

A. x < 3
B. x < 2
C. x > 3
D. x > 2

Solution

To solve 3x - 7 < 2, add 7 to both sides: 3x < 9. Then divide by 3: x < 3.

Correct Answer: A — x < 3

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Q. Solve the inequality 5x - 2 < 3.

A. x < 1
B. x > 1
C. x < 2
D. x > 2

Solution

Step 1: Add 2 to both sides: 5x < 5. Step 2: Divide both sides by 5: x < 1.

Correct Answer: A — x < 1

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Q. Solve the inequality 5x - 7 < 3.

A. x < 2
B. x > 2
C. x < 1
D. x > 1

Solution

Step 1: Add 7 to both sides: 5x < 10. Step 2: Divide by 5: x < 2.

Correct Answer: A — x < 2

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Q. Solve the inequality: -2(x + 3) > 4.

A. x < -1
B. x > -1
C. x < -7
D. x > -7

Solution

Step 1: Distribute -2: -2x - 6 > 4. Step 2: Add 6: -2x > 10. Step 3: Divide by -2 (reverse inequality): x < -5.

Correct Answer: C — x < -7

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Q. Solve the inequality: -2(x + 3) > 6.

A. x < -6
B. x > -6
C. x < 0
D. x > 0

Solution

Step 1: Distribute: -2x - 6 > 6. Step 2: Add 6: -2x > 12. Step 3: Divide by -2 (reverse inequality): x < -6.

Correct Answer: A — x < -6

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Algebra (Secondary)

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