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. What is the solution to the equation 4x - 2 = 2x + 6?

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

Solution

Subtract 2x from both sides: 2x - 2 = 6. Then add 2: 2x = 8. Finally, divide by 2: x = 4.

Correct Answer: A — x = 2

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Q. What is the solution to the equation 4x - 5 = 3x + 2?

A. x = -7
B. x = -5
C. x = 5
D. x = 7

Solution

Step 1: Subtract 3x from both sides: x - 5 = 2. Step 2: Add 5 to both sides: x = 7.

Correct Answer: D — x = 7

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Q. What is the solution to the equation 4x - 7 = 5?

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

Solution

Step 1: Add 7 to both sides: 4x = 12. Step 2: Divide both sides by 4: x = 3.

Correct Answer: B — x = 2

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Q. What is the solution to the equation 4x - 7 = 5x + 2?

A. x = -9
B. x = 9
C. x = -1
D. x = 1

Solution

Step 1: Subtract 4x from both sides: -7 = x + 2. Step 2: Subtract 2 from both sides: -9 = x. Step 3: x = -9.

Correct Answer: C — x = -1

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Q. What is the solution to the equation 4x^2 + 8x + 4 = 0?

A. x = -1
B. x = -2
C. x = 1
D. x = 0

Solution

This can be factored as 4(x^2 + 2x + 1) = 0, which simplifies to 4(x + 1)(x + 1) = 0. Thus, x = -1.

Correct Answer: B — x = -2

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Q. What is the solution to the equation 4x^2 - 12x + 9 = 0?

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

Solution

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

Correct Answer: C — x = 3

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Q. What is the solution to the equation 4x^2 - 16 = 0?

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

Solution

Step 1: Factor the equation: 4(x^2 - 4) = 0. Step 2: Set x^2 - 4 = 0: (x - 2)(x + 2) = 0. Step 3: Solutions are x = 2 or x = -2.

Correct Answer: C — 2

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Q. What is the solution to the equation 5(x - 1) = 3(x + 2)?

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

Solution

Distributing gives 5x - 5 = 3x + 6. Rearranging gives 2x = 11, so x = 5.5.

Correct Answer: C — x = 3

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Q. What is the solution to the equation 5(x - 2) = 3x + 4?

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

Solution

Distribute: 5x - 10 = 3x + 4. Rearranging gives 2x = 14, so x = 7.

Correct Answer: B — x = 5

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Q. What is the solution to the equation 5x + 2 = 17?

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

Solution

Step 1: Subtract 2 from both sides: 5x = 15. Step 2: Divide by 5: x = 3.

Correct Answer: B — x = 4

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Q. What is the solution to the equation 5x + 2 = 3x + 10?

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

Solution

Step 1: Subtract 3x from both sides: 2x + 2 = 10. Step 2: Subtract 2 from both sides: 2x = 8. Step 3: Divide by 2: x = 4.

Correct Answer: A — x = 4

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Q. What is the solution to the equation 5x + 3 = 2x + 12?

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

Solution

Subtract 2x from both sides: 3x + 3 = 12. Subtract 3: 3x = 9. Divide by 3: x = 3.

Correct Answer: B — 3

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Q. What is the solution to the equation 5x - 2 = 3x + 6?

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

Solution

Step 1: Subtract 3x 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 = 3

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Q. What is the solution to the equation 5x^2 - 20 = 0?

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

Solution

First, add 20 to both sides: 5x^2 = 20. Then divide by 5: x^2 = 4. Taking the square root gives x = 4 and x = -4.

Correct Answer: C — x = 4

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Q. What is the solution to the equation 6x + 2 = 20?

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

Solution

Step 1: Subtract 2 from both sides: 6x = 18. Step 2: Divide by 6: x = 3.

Correct Answer: B — x = 3

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Q. What is the solution to the equation 6x + 4 = 10?

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

Solution

Step 1: Subtract 4 from both sides: 6x = 6. Step 2: Divide both sides by 6: x = 1.

Correct Answer: A — x = 1

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Q. What is the solution to the equation 6x + 4 = 34?

A. x = 5
B. x = 6
C. x = 7
D. x = 8

Solution

Step 1: Subtract 4 from both sides: 6x = 30. Step 2: Divide both sides by 6: x = 5.

Correct Answer: A — x = 5

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Q. What is the solution to the equation 6x - 4 = 2x + 8?

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

Solution

Step 1: Subtract 2x from both sides: 4x - 4 = 8. Step 2: Add 4 to both sides: 4x = 12. Step 3: Divide by 4: x = 3.

Correct Answer: B — x = 3

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Q. What is the solution to the equation 6x - 5 = 19?

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

Solution

Step 1: Add 5 to both sides: 6x = 24. Step 2: Divide both sides by 6: x = 4.

Correct Answer: C — x = 4

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Q. What is the solution to the equation 7x + 1 = 22?

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

Solution

Step 1: Subtract 1 from both sides: 7x = 21. Step 2: Divide both sides by 7: x = 3.

Correct Answer: C — x = 4

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Q. What is the solution to the equation 7x + 2 = 23?

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

Solution

Subtract 2 from both sides: 7x = 21. Divide by 7: x = 3.

Correct Answer: C — x = 4

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Q. What is the solution to the equation 7x + 2 = 3x + 18?

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

Solution

Step 1: Subtract 3x from both sides: 4x + 2 = 18. Step 2: Subtract 2: 4x = 16. Step 3: Divide by 4: x = 4.

Correct Answer: A — x = 4

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Q. What is the solution to the equation 7x - 2 = 5x + 6?

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

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: A — x = 4

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Q. What is the solution to the equation 8 - 2x = 0?

A. x = 2
B. x = 4
C. x = 6
D. x = 8

Solution

Step 1: Subtract 8 from both sides: -2x = -8. Step 2: Divide both sides by -2: x = 4.

Correct Answer: A — x = 2

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Q. What is the solution to the equation 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: A — x = 1

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Q. What is the solution to the equation 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: C — x = 4

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Q. What is the solution to the equation 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, x = -4 or x = 2.

Correct Answer: C — x = 4, -2

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Q. What is the solution to the equation x^2 + 4x + 4 = 0?

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

Solution

Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Step 3: Solution is x = -2.

Correct Answer: A — x = -2

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Q. What is the solution to the equation x^2 + 5x + 6 = 0?

A. x = -2, -3
B. x = 2, 3
C. x = -1, -6
D. x = 1, 6

Solution

Step 1: Factor the equation: (x + 2)(x + 3) = 0. Step 2: Set each factor to zero: x + 2 = 0 or x + 3 = 0. Solutions are x = -2, -3.

Correct Answer: A — x = -2, -3

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Q. What is the solution to the equation x^2 + 6x + 9 = 0?

A. x = -3
B. x = 3
C. x = 0
D. x = -6

Solution

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

Correct Answer: A — x = -3

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Algebra (Secondary)

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