MATHEMATICS EXAM 2026–2027
250 QUESTIONS AND CORRECT ANSWERS
100% VERIFIED
Introduction
The Mathematics Comprehensive Assessment evaluates advanced quantitative reasoning,
analytical problem-solving, and the execution of mathematical operations across multiple
theoretical and applied domains. This examination covers eight core disciplines: Algebra,
Geometry, Trigonometry, Calculus, Statistics and Probability, Linear Algebra, Discrete
Mathematics, and Number Theory. Each domain assesses the candidate's ability to apply
foundational principles, derive solutions through rigorous methodology, and demonstrate
professional judgment in complex mathematical scenarios. Mastery of these domains is
essential for academic progression, scientific research, engineering applications, and
quantitative decision-making across all analytical professions.
,Q1. Solve for x: 3x² - 12 = 0
A. x = ±6
B. x = ±3
C. x = ±2
D. x = ±4
Rationale: Dividing both sides by 3 gives x² = 4, so x = ±√4 = ±2. Options A, C, and D result from
computational errors in the square root or division steps.
Q2. If f(x) = 2x³ - 5x + 1, what is f(-1)?
A. 8
B. 6
C. -2
D. 4
Rationale: f(-1) = 2(-1)³ - 5(-1) + 1 = -2 + 5 + 1 = 4. Option A incorrectly adds all terms as positive; C and
D result from sign errors in evaluation.
Q3. What is the simplified form of (x² - 9)/(x + 3)?
A. x - 3
B. x + 3
C. x² - 3
D. x - 9
Rationale: x² - 9 factors as (x+3)(x-3). Dividing by (x+3) leaves x - 3, provided x ≠ -3. The other options
fail to apply the difference of squares factorization correctly.
Q4. Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...
A. 810
B. 590
C. 670
, D. 730
Rationale: Using S = n/2(2a + (n-1)d): S = 20/2(2(5) + 19(3)) = 10(10 + 57) = 10(67) = 670. Other
options result from miscounting terms or misidentifying the common difference.
Q5. If log₂(x) = 5, what is x?
A. 32
B. 64
C. 25
D. 10
Rationale: By definition of logarithm, x = 2⁵ = 32. Option A confuses log base 2 with log base 10; B
incorrectly squares the base; D represents 2⁶.
Q6. What is the degree of the polynomial 4x⁵ - 3x³ + 7x - 2?
A. 5
B. 4
C. 3
D. 7
Rationale: The degree is the highest power of x, which is 5. Options A, B, and D confuse the degree with
other coefficients or exponents in the polynomial.
Q7. Solve the inequality: 2x - 7 > 3x + 1
A. x < 8
B. x < -8
C. x > 8
D. x > -8
Rationale: Subtracting 2x and 1 from both sides: -8 > x, or x < -8. The inequality sign direction is critical;
options A and C incorrectly flip or retain the wrong direction.
, Q8. What is the value of the expression 3^(2+1) × 3⁴?
A. 3⁷
B. 3⁸
C. 3¹⁰
D. 3⁹
Rationale: 3^(2+1) = 3³ = 27. Using exponent rules: 3³ × 3⁴ = 3^(3+4) = 3⁷. Other options incorrectly
multiply exponents or miscount the base exponent.
Q9. If f(x) = x² + 3x and g(x) = 2x - 1, what is f(g(2))?
A. 24
B. 18
C. 15
D. 12
Rationale: g(2) = 2(2) - 1 = 3. Then f(3) = 3² + 3(3) = 9 + 9 = 18. The composition evaluates the inner
function first, then applies the outer function to that result.
Q10. What is the vertex form of y = x² - 6x + 11?
A. y = (x - 6)² + 11
B. y = (x + 3)² + 2
C. y = (x - 3)² + 2
D. y = (x - 3)² - 2
Rationale: Completing the square: y = (x² - 6x + 9) + 2 = (x - 3)² + 2. The vertex is at (3, 2). Other options
misapply the completing-the-square technique.
Q11. Simplify: (2x³y²)³ × (xy)²
A. 4x¹¹y⁶
B. 8x¹¹y⁸
C. 8x⁹y⁶
250 QUESTIONS AND CORRECT ANSWERS
100% VERIFIED
Introduction
The Mathematics Comprehensive Assessment evaluates advanced quantitative reasoning,
analytical problem-solving, and the execution of mathematical operations across multiple
theoretical and applied domains. This examination covers eight core disciplines: Algebra,
Geometry, Trigonometry, Calculus, Statistics and Probability, Linear Algebra, Discrete
Mathematics, and Number Theory. Each domain assesses the candidate's ability to apply
foundational principles, derive solutions through rigorous methodology, and demonstrate
professional judgment in complex mathematical scenarios. Mastery of these domains is
essential for academic progression, scientific research, engineering applications, and
quantitative decision-making across all analytical professions.
,Q1. Solve for x: 3x² - 12 = 0
A. x = ±6
B. x = ±3
C. x = ±2
D. x = ±4
Rationale: Dividing both sides by 3 gives x² = 4, so x = ±√4 = ±2. Options A, C, and D result from
computational errors in the square root or division steps.
Q2. If f(x) = 2x³ - 5x + 1, what is f(-1)?
A. 8
B. 6
C. -2
D. 4
Rationale: f(-1) = 2(-1)³ - 5(-1) + 1 = -2 + 5 + 1 = 4. Option A incorrectly adds all terms as positive; C and
D result from sign errors in evaluation.
Q3. What is the simplified form of (x² - 9)/(x + 3)?
A. x - 3
B. x + 3
C. x² - 3
D. x - 9
Rationale: x² - 9 factors as (x+3)(x-3). Dividing by (x+3) leaves x - 3, provided x ≠ -3. The other options
fail to apply the difference of squares factorization correctly.
Q4. Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...
A. 810
B. 590
C. 670
, D. 730
Rationale: Using S = n/2(2a + (n-1)d): S = 20/2(2(5) + 19(3)) = 10(10 + 57) = 10(67) = 670. Other
options result from miscounting terms or misidentifying the common difference.
Q5. If log₂(x) = 5, what is x?
A. 32
B. 64
C. 25
D. 10
Rationale: By definition of logarithm, x = 2⁵ = 32. Option A confuses log base 2 with log base 10; B
incorrectly squares the base; D represents 2⁶.
Q6. What is the degree of the polynomial 4x⁵ - 3x³ + 7x - 2?
A. 5
B. 4
C. 3
D. 7
Rationale: The degree is the highest power of x, which is 5. Options A, B, and D confuse the degree with
other coefficients or exponents in the polynomial.
Q7. Solve the inequality: 2x - 7 > 3x + 1
A. x < 8
B. x < -8
C. x > 8
D. x > -8
Rationale: Subtracting 2x and 1 from both sides: -8 > x, or x < -8. The inequality sign direction is critical;
options A and C incorrectly flip or retain the wrong direction.
, Q8. What is the value of the expression 3^(2+1) × 3⁴?
A. 3⁷
B. 3⁸
C. 3¹⁰
D. 3⁹
Rationale: 3^(2+1) = 3³ = 27. Using exponent rules: 3³ × 3⁴ = 3^(3+4) = 3⁷. Other options incorrectly
multiply exponents or miscount the base exponent.
Q9. If f(x) = x² + 3x and g(x) = 2x - 1, what is f(g(2))?
A. 24
B. 18
C. 15
D. 12
Rationale: g(2) = 2(2) - 1 = 3. Then f(3) = 3² + 3(3) = 9 + 9 = 18. The composition evaluates the inner
function first, then applies the outer function to that result.
Q10. What is the vertex form of y = x² - 6x + 11?
A. y = (x - 6)² + 11
B. y = (x + 3)² + 2
C. y = (x - 3)² + 2
D. y = (x - 3)² - 2
Rationale: Completing the square: y = (x² - 6x + 9) + 2 = (x - 3)² + 2. The vertex is at (3, 2). Other options
misapply the completing-the-square technique.
Q11. Simplify: (2x³y²)³ × (xy)²
A. 4x¹¹y⁶
B. 8x¹¹y⁸
C. 8x⁹y⁶
