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. Find the value of x in the inequality 3x - 5 < 4.

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

Solution

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

Correct Answer: A — x < 3

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Q. Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.

A. x = -2
B. x = -4
C. x = 0
D. x = -6

Solution

Using the quadratic formula: a = 3, b = 12, c = 12. Discriminant = 12² - 4(3)(12) = 144 - 144 = 0. x = -b / 2a = -12 / 6 = -2.

Correct Answer: B — x = -4

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Q. Find the x-intercepts of the equation y = x^2 - 4.

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

Solution

Set y = 0: 0 = x^2 - 4. This factors to (x - 2)(x + 2) = 0, giving x = 2 and x = -2.

Correct Answer: A — x = 2, -2

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Q. Find x if 2(x + 3) = 14.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 7. Step 2: Subtract 3 from both sides: x = 4.

Correct Answer: A — x = 4

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Q. Find x if 2(x + 3) = 16.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.

Correct Answer: A — x = 4

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Q. Find x if 2(x - 3) = 10.

A. x = 5
B. x = 8
C. x = 10
D. x = 13

Solution

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

Correct Answer: B — x = 8

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Q. Find x if 7x + 2 = 23.

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

Solution

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

Correct Answer: C — x = 4

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Q. Find x in the equation 2(x + 3) = 16.

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.

Correct Answer: C — x = 6

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Q. Find x in the equation 3(x - 2) = 12.

A. x = 4
B. x = 6
C. x = 8
D. x = 10

Solution

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

Correct Answer: B — x = 6

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Q. Find x in the equation 4(x - 2) = 12.

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

Solution

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

Correct Answer: C — x = 6

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Q. If -x + 6 > 2, what is the solution for x?

A. x < 4
B. x > 4
C. x < 6
D. x > 6

Solution

Step 1: Subtract 6 from both sides: -x > -4. Step 2: Multiply by -1 (reverse inequality): x < 4.

Correct Answer: B — x > 4

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Q. If 2(x + 3) = 10, what is x?

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

Solution

Divide by 2: x + 3 = 5. Subtract 3: x = 2.

Correct Answer: B — x = 2

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Q. If 2(x + 3) = 14, what is x?

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Divide both sides by 2: x + 3 = 7. Step 2: Subtract 3 from both sides: x = 4.

Correct Answer: A — x = 4

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Q. If 2(x + 3) = 16, what is x?

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Divide by 2: x + 3 = 8. Subtract 3: x = 5.

Correct Answer: B — x = 5

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Q. If 2x + 3 > 11, what is the solution for x?

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

Solution

Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.

Correct Answer: A — x > 4

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Q. If 2x + 3 > 7, what is the solution for x?

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

Solution

Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.

Correct Answer: A — x > 2

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Q. If 2x + 3 > 7, what is the solution set for x?

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

Solution

Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.

Correct Answer: A — x > 2

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Q. If 2x + 3y = 12 and y = 2, what is the value of x?

A. 0
B. 1
C. 2
D. 3

Solution

Step 1: Substitute y = 2 into the equation: 2x + 6 = 12. Step 2: Subtract 6: 2x = 6. Step 3: Divide by 2: x = 3.

Correct Answer: C — 2

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Q. If 2x + 5 > 3x - 1, what is the solution for x?

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

Solution

Step 1: Subtract 2x from both sides: 5 > x - 1. Step 2: Add 1: 6 > x, or x < 6.

Correct Answer: D — x > -6

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Q. If 2x + 5 = 3x - 1, what is the value of x?

A. -6
B. 6
C. 4
D. 2

Solution

Rearranging gives: 5 + 1 = 3x - 2x, thus x = 6.

Correct Answer: A — -6

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Q. If 2x - 5 = 3x + 1, what is x?

A. x = -6
B. x = -4
C. x = 4
D. x = 6

Solution

Step 1: Subtract 2x from both sides: -5 = x + 1. Step 2: Subtract 1 from both sides: x = -6.

Correct Answer: B — x = -4

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Q. If 2x^2 - 8 = 0, what is the value of x?

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

Solution

Add 8 to both sides: 2x^2 = 8. Divide by 2: x^2 = 4. Taking the square root gives x = ±2.

Correct Answer: C — 2

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Q. If 2x^2 - 8 = 0, what is x?

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

Solution

Add 8: 2x^2 = 8. Divide by 2: x^2 = 4. Take square root: x = 4 or x = -4.

Correct Answer: C — x = 4

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Q. If 3 times a number plus 4 equals 19, what is the number?

A. 3
B. 5
C. 6
D. 7

Solution

Let the number be x. The equation is 3x + 4 = 19. Subtracting 4 from both sides gives 3x = 15. Dividing by 3 gives x = 5.

Correct Answer: B — 5

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Q. If 3(x + 2) < 2(x + 5), what is the value of x?

A. x < 1
B. x > 1
C. x = 1
D. x = 0

Solution

Step 1: Distribute: 3x + 6 < 2x + 10. Step 2: Subtract 2x from both sides: x + 6 < 10. Step 3: Subtract 6: x < 4.

Correct Answer: A — x < 1

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Q. If 3(x - 1) < 2x + 4, what is the solution for x?

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

Solution

Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

Correct Answer: C — x < 5

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Q. If 3(x - 1) < 2x + 4, what is the value of x?

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

Solution

Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

Correct Answer: A — x < 7

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Q. If 3(x - 2) = 12, what is x?

A. x = 4
B. x = 6
C. x = 8
D. x = 10

Solution

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

Correct Answer: B — x = 6

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Q. If 3(x - 4) = 9, what is x?

A. x = 1
B. x = 4
C. x = 7
D. x = 10

Solution

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

Correct Answer: C — x = 7

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Q. If 3x + 2 < 5, what is the value of x?

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

Solution

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

Correct Answer: A — x < 1

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Algebra (Secondary)

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