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 x^2 - 7x + 10 = 0?

A. x = 5, 2
B. x = 3, 4
C. x = 1, 10
D. x = 0, 7

Solution

Factoring gives (x - 5)(x - 2) = 0. Thus, x = 5 and x = 2.

Correct Answer: A — x = 5, 2

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

A. x = 3
B. x = -3
C. x = 0
D. x = 9

Solution

Factor: (x - 3)(x + 3) = 0. Solutions are x = 3 and x = -3.

Correct Answer: A — x = 3

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Q. What is the solution to the inequality 2x + 1 > 3?

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

Solution

Subtract 1 from both sides: 2x > 2. Then divide by 2: x > 1.

Correct Answer: B — x > 1

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Q. What is the solution to the inequality 2x + 1 > 5?

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

Solution

Subtract 1 from both sides: 2x > 4. Then divide by 2: x > 2.

Correct Answer: B — x > 2

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Q. What is the solution to the inequality 2x + 1 > 7?

A. x < 3
B. x > 3
C. x < 4
D. x > 4

Solution

Subtract 1 from both sides: 2x > 6. Then divide by 2: x > 3.

Correct Answer: B — x > 3

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Q. What is the solution to the inequality 2x + 1 ≥ 3?

A. x ≤ 1
B. x ≥ 1
C. x < 1
D. x > 1

Solution

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

Correct Answer: B — x ≥ 1

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Q. What is the solution to the inequality 2x + 3 ≥ 7?

A. x ≤ 2
B. x ≥ 2
C. x < 2
D. x > 2

Solution

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

Correct Answer: B — x ≥ 2

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Q. What is the solution to the inequality 2x + 5 > 15?

A. x < 5
B. x > 5
C. x < 10
D. x > 10

Solution

2x + 5 > 15. Subtract 5 from both sides: 2x > 10. Divide by 2: x > 5.

Correct Answer: B — x > 5

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Q. What is the solution to the inequality 2x + 5 ≥ 3?

A. x ≥ -1
B. x ≤ -1
C. x ≥ 1
D. x ≤ 1

Solution

Subtract 5 from both sides: 2x ≥ -2. Then divide by 2: x ≥ -1.

Correct Answer: A — x ≥ -1

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Q. What is the solution to the inequality 2x - 3 < 5?

A. x < 4
B. x > 4
C. x < 1
D. x > 1

Solution

Add 3 to both sides: 2x < 8. Divide by 2: x < 4.

Correct Answer: A — x < 4

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Q. What is the solution to the inequality 3x + 2 < 11?

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

Solution

Subtract 2 from both sides: 3x < 9. Divide by 3: x < 3.

Correct Answer: B — x < 4

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Q. What is the solution to 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. What is the solution to the inequality 3x - 5 < 4?

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

Solution

Add 5 to both sides: 3x < 9. Then divide by 3: x < 3.

Correct Answer: A — x < 3

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Q. What is the solution to the inequality 3x - 7 < 2?

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

Solution

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

Correct Answer: B — x < 1

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Q. What is the solution to the inequality 4x - 8 < 0?

A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2

Solution

4x - 8 < 0. Add 8 to both sides: 4x < 8. Divide by 4: x < 2.

Correct Answer: A — x < 2

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Q. What is the solution to the inequality 5x + 2 ≥ 12?

A. x ≥ 2
B. x ≤ 2
C. x ≥ 3
D. x ≤ 3

Solution

Subtract 2 from both sides: 5x ≥ 10. Then divide by 5: x ≥ 2.

Correct Answer: C — x ≥ 3

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Q. What is the solution to the inequality 5x + 3 > 2x + 12?

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

Solution

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

Correct Answer: B — x > 3

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Q. What is the solution to the inequality 5x - 2 < 3?

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

Solution

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

Correct Answer: A — x < 1

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Q. What is the solution to the inequality 5x - 3 < 12?

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

Solution

5x - 3 < 12. Add 3 to both sides: 5x < 15. Divide by 5: x < 3.

Correct Answer: A — x < 3

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Q. What is the solution to the inequality x + 5 > 2?

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

Solution

Subtract 5 from both sides: x > -3.

Correct Answer: A — x > -3

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Q. What is the solution to the inequality x^2 - 4 > 0?

A. x < -2 or x > 2
B. x > -2 and x < 2
C. x < 2
D. x > 4

Solution

Factoring gives (x - 2)(x + 2) > 0. The critical points are x = -2 and x = 2. The solution set is x < -2 or x > 2.

Correct Answer: A — x < -2 or x > 2

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Q. What is the solution to the inequality x^2 - 4 < 0?

A. -2 < x < 2
B. x < -2 or x > 2
C. x > -2 and x < 2
D. x = 0

Solution

Step 1: Factor the inequality: (x - 2)(x + 2) < 0. Step 2: The solution is between the roots: -2 < x < 2.

Correct Answer: A — -2 < x < 2

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Q. What is the solution to the inequality x^2 - 5x + 6 > 0?

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

Solution

Factoring gives (x - 2)(x - 3) > 0. The roots are x = 2 and x = 3. The solution set is x < 2 or x > 3.

Correct Answer: A — x < 2 or x > 3

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Q. What is the solution to the inequality: -3x + 4 > 1?

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

Solution

Step 1: Subtract 4 from both sides: -3x > -3. Step 2: Divide by -3 (reverse the inequality): x < 1.

Correct Answer: D — x > 3

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Q. What is the solution to the inequality: -3x + 6 ≤ 0?

A. x ≥ 2
B. x ≤ 2
C. x > 2
D. x < 2

Solution

Step 1: Subtract 6 from both sides: -3x ≤ -6. Step 2: Divide by -3 (reverse the inequality): x ≥ 2.

Correct Answer: A — x ≥ 2

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Q. What is the solution to the inequality: 2(x - 1) > 3(x + 2)?

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

Solution

Step 1: Distribute: 2x - 2 > 3x + 6. Step 2: Rearrange: -x > 8. Step 3: Divide by -1 (reverse inequality): x < -8.

Correct Answer: A — x < -1

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Q. What is the solution to the inequality: 2(x - 1) < 3(x + 2)?

A. x < 7
B. x > 7
C. x < 5
D. x > 5

Solution

Step 1: Distribute: 2x - 2 < 3x + 6. Step 2: Subtract 2x: -2 < x + 6. Step 3: Subtract 6: -8 < x, or x > -8.

Correct Answer: C — x < 5

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Q. What is the solution to the inequality: 2(x - 1) ≥ 3x + 4?

A. x ≤ -2
B. x ≥ -2
C. x < -2
D. x > -2

Solution

Step 1: Distribute: 2x - 2 ≥ 3x + 4. Step 2: Subtract 2x from both sides: -2 ≥ x + 4. Step 3: Subtract 4: -6 ≥ x. Solution: x ≤ -6.

Correct Answer: A — x ≤ -2

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Q. What is the solution to the inequality: 2(x - 3) > 4?

A. x > 5
B. x < 5
C. x > 1
D. x < 1

Solution

Step 1: Distribute: 2x - 6 > 4. Step 2: Add 6 to both sides: 2x > 10. Step 3: Divide by 2: x > 5.

Correct Answer: A — x > 5

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Q. What is the solution to the inequality: 2(x - 3) ≥ 4?

A. x ≥ 5
B. x ≤ 5
C. x > 5
D. x < 5

Solution

Step 1: Distribute: 2x - 6 ≥ 4. Step 2: Add 6: 2x ≥ 10. Step 3: Divide by 2: x ≥ 5.

Correct Answer: A — x ≥ 5

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Algebra (Secondary)

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