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.

A student might mistakenly square the sum and product directly without algebraic expansion, or miscalculate the subtraction. By applying the binomial identity where the target expression equals the square of the sum minus twice the product, you substitute the known values to compute forty-nine minus twenty-four, resulting in twenty-five. Common mistake: forgetting to multiply the product term by two when expanding the binomial.

One might incorrectly sum only the initial terms or misidentify the common ratio as something other than a half. Identifying the first term as one-half and the common ratio likewise as one-half, you apply the infinite sum formula for geometric sequences by dividing the first term by one minus the common ratio, which yields one-half divided by one-half, simplifying to one. Common mistake: failing to correctly subtract the common ratio from one in the denominator.

A test-taker could mistakenly choose the identity matrix or an incorrect entry sum by confusing row-column multiplication rules. Multiplying the given matrices row by column yields the resulting entries: two times one plus one times zero, two times zero plus one times one, one times one plus three times zero, and one times zero plus three times one, which simplifies back to the original matrix. Common mistake: adding corresponding elements directly like addition instead of performing matrix multiplication.

A student might incorrectly subtract only one base angle from the total sum of angles, or confuse the base angles with the vertex. Subtracting the combined sum of the two seventy-degree base angles from the total interior angle sum of one hundred eighty degrees leaves forty degrees for the remaining vertex angle. Common mistake: forgetting that an isosceles triangle has two equal base angles that both need to be subtracted.

One might mistakenly add the given angles and equate that sum to the answer, or subtract from ninety degrees instead of a straight angle. By taking the total sum of angles in a triangle as one hundred eighty degrees and subtracting the sum of fifty and sixty degrees, you find that the remaining angle measures seventy degrees. Common mistake: using ninety degrees as the sum of angles instead of one hundred eighty degrees.

A test-taker could mistakenly multiply the area directly by pi or confuse the radius with the diameter. Using the area formula where pi times radius squared equals one-fourty-four, rearranging to solve for radius squared by multiplying by seven and dividing by twenty-two yields forty-nine, meaning the radius is seven centimeters. Common mistake: confusing area and circumference formulas during the rearrangement.

A student might mistakenly square the radius as if calculating an area instead of finding linear distance. Multiplying two by the fraction twenty-two over seven and the radius of seven centimeters cancels out the denominator, leaving a total circumference of forty-four centimeters. Common mistake: using the area formula instead of the circumference formula.

One might mistakenly compute the full circle area instead of taking the fractional sector proportion. Calculating the sector area involves multiplying the angle ratio of ninety over three-sixty by twenty-two over seven and fourteen squared, which simplifies to one-quarter multiplied by twenty-two over seven and one-ninety-six, giving one hundred fifty-four square centimeters. Common mistake: omitting the fractional angle multiplier when finding sector areas.

A test-taker could mistakenly use the circumference directly as the radius without dividing by two pi. Finding the radius first from the base circumference gives seven centimeters, and substituting this into the cone volume formula of one-third pi r squared h yields six hundred sixteen cubic centimeters. Common mistake: forgetting the one-third factor unique to the volume of a cone.

A student might mistakenly add the coordinate differences instead of squaring them, or miscalculate the signs. Applying the coordinate distance formula by taking the square root of the sum of squared differences in x and y coordinates gives the square root of nine plus sixteen, which evaluates to five. Common mistake: forgetting to take the square root at the final step of the distance calculation.

One might mistakenly drop the coefficient of x or incorrectly reduce the exponent of the linear term. Differentiating the polynomial term by term using the power rule brings down the exponent for the quadratic term to get six x and leaves five for the linear term, yielding six x plus five. Common mistake: failing to eliminate the constant term during differentiation.

A test-taker could mistakenly differentiate instead of integrating, or forget to include the constant of integration. Integrating two x increases its power to two and divides by two, leaving x squared, while integrating the constant three adds an x term, resulting in x squared plus three x plus c. Common mistake: omitting the constant of integration c at the end of an indefinite integral.

A student might mistakenly choose a negative trigonometric function by confusing differentiation with integration rules. Applying standard calculus derivative formulas to the sine function directly yields the cosine function. Common mistake: confusing the derivative of sine with the derivative of cosine which yields a negative sign.

One might mistakenly set the function itself to zero instead of its derivative. Finding the first derivative as two x minus six and setting it equal to zero because a parallel tangent has a zero slope allows you to solve for x, yielding three. Common mistake: setting the original equation to zero rather than the derivative.

A test-taker could mistakenly evaluate the integral at the lower bound or integrate the terms incorrectly. Integrating x squared plus one yields x cubed over three plus x, and evaluating this definite integral from zero to two gives eight thirds plus two, which combines to fourteen thirds. Common mistake: arithmetic errors when combining fractions with whole numbers.

A student might mistakenly count the wrong number of items or miscalculate the total sum. Finding the mean requires adding all given values together to get thirty and dividing by the total count of five numbers, which results in six. Common mistake: dividing by the wrong number of terms in the dataset.

One might mistakenly select the highest age value instead of the one with the maximum frequency. Inspecting the frequency distribution table reveals that the age of seventeen has the highest student count of fifteen, making it the modal age. Common mistake: confusing the mode with the maximum value in the data category rather than the highest frequency.

A test-taker could mistakenly divide by the number of categories instead of the total frequency sum. Multiplying each age by its corresponding student count, summing those products to get seven hundred seventy-two, and dividing by the total fifty students gives fifteen point four four, which rounds to fifteen point five. Common mistake: using the wrong denominator by dividing by the number of age groups instead of total frequency.

A student might mistakenly invert the ratio or use the blue face count instead of red. Dividing the number of favorable red faces by the total number of faces gives four over six, which simplifies to two-thirds. Common mistake: failing to reduce the fraction to its simplest form.

One might mistakenly use only the red count as the denominator or confuse the red and blue quantities. Calculating the probability involves placing the number of red balls over the total sum of red and blue balls, yielding five over eight. Common mistake: putting only one color in the denominator instead of the total number of items.