JAMB Mathematics 2004
Questions & Answers

An incorrect subtraction of fractions by directly subtracting numerators and denominators without finding a common denominator leads many to wrong choices like 3/10 or 6/5. First, convert 2/5 into 4/10 so it can be subtracted by 1/10 to give 3/10, and then multiply that result by 3 to arrive at 9/10. Common mistake: Failing to find a common denominator before subtracting fractional quantities.

A careless sign error when factoring can easily cause a student to select options with positive values instead of negative roots. By factoring the quadratic expression into (x + 4)(x - 2) = 0, setting each factor to zero reveals the exact solutions are x = -4 and x = 2. Common mistake: Dropping or reversing negative signs during the factorization of quadratic roots.

Students might mistakenly pick √2/2 by forgetting that multiplying two identical radical fractions squares both the numerator and denominator. Since both cos 45° and sin 45° equal √2/2, multiplying them together gives (√2/2) × (√2/2) = 2/4, which simplifies to 1/2. Common mistake: Multiplying fractions with square roots by only multiplying the numerators and leaving the denominators unchanged.

A student might hastily subtract the two given mean values directly to find the difference, arriving at an incorrect number. Multiplying the original seven numbers by their mean of 12 gives a total sum of 84, while the remaining six numbers multiplied by their new mean of 11 yields 66, leaving 18 as the removed value upon subtraction. Common mistake: Subtracting averages directly instead of finding the difference between total sums.

Choosing 1/52 is a common error made by students who confuse the probability of drawing one specific card with drawing any card from the entire suit. Since a standard deck contains 4 kings out of 52 total cards, the correct probability fraction reduces from 4/52 to 1/13. Common mistake: Forgetting to account for the total number of matching target items in a collection when calculating probabilities.

Students might mistakenly select 5 by looking at the y-intercept constant instead of examining the coefficient attached to the variable x. In the slope-intercept form equation y = -3x + 5, the gradient m is explicitly represented by the coefficient of x, which is -3. Common mistake: Confusing the y-intercept value with the slope coefficient in linear equations.

Evaluating an integral incorrectly by forgetting to raise the power of x can lead students to mismatched answers like 7 or 8. Integrating the expression (3x + 2) yields (3/2)x² + 2x, and substituting the upper limit of 2 gives (6 + 4) - 0 = 10. Common mistake: Incorrectly applying power rules during definite integration calculations.

Multiplying the base and exponent together to get 6 is a frequent error made by learners who confuse logarithms with basic multiplication. The logarithmic statement log₃(x) = 2 translates into exponential form as x = 3², which evaluates directly to 9. Common mistake: Treating logarithmic equations as linear multiplication problems instead of exponential inverses.

An incorrect addition or failure to multiply properly can lead students to select alternative sequence values like 24. Substituting n = 6 into the given nth term formula 4n + 1 means multiplying 4 by 6 to get 24, and then adding 1 results in 25. Common mistake: Performing addition before multiplication when evaluating sequence formulas.

Options like 40 cm² might be picked by mistakenly subtracting or using incorrect arithmetic. To find the correct area, multiply the given dimensions together, yielding 10 multiplied by 5, which results in 50 cm². Common mistake: Multiplying or adding dimensions incorrectly instead of taking length times width.

A student might incorrectly choose √9 or √6 by mishandling the radical division. Combining the radicals under a single division yields 72 divided by 8, which simplifies to √9, and evaluating this gives 3. Common mistake: Stopping at the intermediate square root step instead of fully evaluating it.

Options like x = 2, y = 3 look plausible if substitution errors are made. Expressing x in terms of y from the second equation as x equals 2y plus 1 allows substitution into the first expression to produce 2 times the quantity 2y plus 1 plus y equaling 7, which simplifies to 5y plus 2 equaling 7, ultimately determining y is 1 and x is 3. Common mistake: Distributing incorrectly when substituting the rearranged expression.

Options such as 1/2 or √2/2 are easy to confuse with other standard angle ratios. Evaluating the trigonometric ratio for this specific angle relies on standard triangle values, directly giving √3/2 for the sine of 60 degrees. Common mistake: Mixing up the sine and cosine values for 30 and 60 degree angles.

A distractor like 2 or 3 might be guessed if variance is miscalculated. Computing the mean gives 5, and squaring the deviations from this mean produces 16, 4, 0, 4, and 16, which sum to 40; dividing by 5 yields a variance of 8, and taking the square root gives approximately 2.83. Common mistake: Forgetting to take the square root of the variance to find the standard deviation.

A student might mistakenly select 5π cm by confusing the radius with the diameter. Multiplying the given diameter of 10 cm by pi yields a circumference of 10π cm. Common mistake: Using the radius instead of the diameter when calculating the circumference.

Distractors like x < 3 arise from reversing the inequality sign during transposition. Subtracting 2 from both sides leaves 3x greater than 9, and dividing by 3 results in x being greater than 3. Common mistake: Flipping the inequality sign when dividing by a positive number.

Options such as 4x³ + 3x can tempt students who forget to apply the power rule correctly to every term. Differentiating x to the fourth power gives 4x³, and differentiating 3x squared gives 6x, combining to form 4x³ + 6x. Common mistake: Forgetting to multiply by the original exponent when applying the power rule.

A student might mistakenly choose the union {2, 4, 5, 6} instead of the intersection. Finding the elements that appear in both sets identifies the common values 4 and 6, resulting in {4, 6}. Common mistake: Confusing set intersection with set union.

An option like 54 might be chosen if exponents are multiplied by the base rather than evaluated as powers. Calculating 3 cubed gives 27, and 2 squared gives 4, which multiplied together equal 108. Common mistake: Multiplying the base by the exponent instead of raising it to that power.

Options like 2 might be selected by confusing the mode with the median or mean. Examining the frequency of each number shows that 3 appears most frequently, making it the mode. Common mistake: Selecting the middle number instead of the most frequently occurring one.