JAMB Mathematics 2017
Questions & Answers

One might be tempted by options like x + 3 if they misinterpret the factorization of the numerator or forget how algebraic cancellation functions. To resolve this, one must first factorize the quadratic numerator x^2 + 2x - 3 into (x + 3)(x - 1); dividing this expression by (x + 3) leaves x - 1, given that x cannot equal -3 to prevent division by zero. Common mistake: failing to account for the restricted domain value where the denominator equals zero.

A student might mistakenly select solutions like 1 and 3 by incorrectly guessing factors without handling the leading coefficient. By factorizing the expression into (2x - 1)(x - 3) = 0, we can set each individual factor to zero, yielding 2x - 1 = 0 which gives x = 1/2, and x - 3 = 0 which results in x = 3. Common mistake: forgetting to divide by the leading coefficient when solving quadratic equations by grouping or factoring.

A test-taker could pick an incorrect value like 3 if they confuse the coordinates or mistakenly substitute the intercept for the slope. Substituting the given point coordinates (2, 7) into the linear equation y = kx + 3 gives 7 = k(2) + 3, which simplifies to 2k = 4, successfully isolating k as 2. Common mistake: incorrectly plugging in the x and y coordinates by reversing their respective positions.

One might select 3 by misapplying the arithmetic progression formula or incorrectly distributing terms within the brackets. Utilizing the standard sum formula Sum = n/2 [2a + (n-1)d] with n = 6 and a = 3 leads to 48 = 3 [6 + 5d], which simplifies to 16 = 6 + 5d, ultimately yielding 5d = 10 and d = 2. Common mistake: computational errors when simplifying the bracketed expression inside the summation formula.

A student might choose 128 by miscalculating the exponent or doubling the common ratio an incorrect number of times for the sixth term. Identifying the initial term a = 2 and finding the common ratio r = 4/2 = 2 allows us to apply the geometric progression formula ar^(6-1), resulting in 2 multiplied by 2^5, which evaluates to 2 multiplied by 32 to give 64. Common mistake: miscounting the power of the common ratio for the nth term (using r^6 instead of r^5).

A learner could mistakenly choose 1/2 by accidentally comparing the blue balls to a subset instead of the entire collection. Finding the overall sum of the items as 6 + 4 + 2 = 12, we place the number of blue balls over this total to get 4/12, which reduces down to 1/3. Common mistake: using an incorrect denominator that omits one or more categories of items.

A test-taker might select 4 without organizing the numbers first, accidentally picking the middle item of the raw, unsorted sequence. Sorting the values in ascending order yields 1, 2, 3, 4, 6, 7, and 9, and locating the exact middle value of this ordered set reveals the median to be 4. Common mistake: failing to arrange data points in numerical order before attempting to find the median.

One might select 6 by confusing the mean with the middle value or miscounting the quantity of items in the dataset. Adding the numbers together gives 2 + 4 + 6 + 8 + 10 + 12 = 42, and dividing this aggregate sum by the count of 6 items produces a mean value of 7. Common mistake: dividing the sum by an incorrect count of numbers.

A student might mistakenly choose 1/3 by overlooking some of the qualifying outcomes on a standard die. Identifying the even numbers on a die as 2, 4, and 6 gives 3 successful outcomes out of 6 total possibilities, which simplifies to a probability of 1/2. Common mistake: missing one of the even numbers when counting sample space outcomes.

A learner could mistakenly pick 16 by adding the length and width instead of multiplying them together. Computing the area requires multiplying the length of 10cm by the width of 6cm, resulting in an area of 60 cm^2. Common mistake: confusing the formula for the perimeter of a rectangle with the formula for its area.

A test-taker might select 56.52 by forgetting to cube the radius properly or misapplying the fraction in the formula. Applying the sphere volume formula (4/3)πr^3 with a radius of 3cm and π = 3.14 gives (4/3) × 3.14 × 27, which evaluates to (4/3) × 3.14 × 27 equaling 113.04 cm^3. Common mistake: multiplying by the radius instead of cubing it in the volume calculation.

One might mistakenly choose √3/2 by confusing the sine of 45° with standard values for 60°. Evaluating the trigonometric ratio for a 45° angle in a right isosceles triangle gives 1/√2, which is approximately 0.707. Common mistake: mixing up standard trigonometric table values for common angles like 30°, 45°, and 60°.

A student could select 4 by mistakenly thinking the equation asks for the square root of 16 rather than solving for the exponent. Recognizing that 16 can be expressed as a power of 4, namely 4^2, allows us to equate the exponents in 4^x = 4^2, yielding x = 2. Common mistake: confusing exponential equations with basic square root operations.

A learner might choose 1 if they invert the coordinate differences or subtract the x-coordinates in the wrong order. Calculating the gradient via the formula (y2 - y1)/(x2 - x1) using points (1, 2) and (3, 6) gives (6 - 2)/(3 - 1), which simplifies to 4/2 and results in 2. Common mistake: placing the change in x over the change in y instead of rise over run.

A test-taker could mistakenly select y = x - 2 by misapplying the signs during the expansion and rearrangement steps. Utilizing the point-slope form y - y1 = m(x - x1) with gradient 1 and point (2, 4) produces y - 4 = 1(x - 2), which simplifies to y = x - 2 + 4, ultimately yielding the equation y = x + 2. Common mistake: making a sign error when transposing constants to isolate y.

One might mistakenly pick 360° by assuming the shape behaves like a quadrilateral or a circle. Applying the interior angle sum formula (n-2) × 180° for a pentagon where n = 5 gives (5-2) × 180°, which equals 3 × 180° resulting in 540°. Common mistake: using the wrong number of sides (n) for a pentagon in the polygon angle formula.

A student could select 12.56 by forgetting to scale the full circumference by the fraction of the circle's total angle. Computing the arc length via (θ/360) × 2πr with a 90° angle and radius of 4cm gives (90/360) × 2 × 3.14 × 4, which simplifies to (1/4) × 25.12, yielding 6.28 cm. Common mistake: calculating the full circumference instead of fractional arc length.

A learner might choose 2 by incorrectly substituting variables or making an arithmetic error while solving the simultaneous equations. Expressing y as x - 4 from the second equation and substituting it into 3x + y = 12 leads to 3x + (x - 4) = 12, which simplifies to 4x = 16 and yields x = 4. Common mistake: dropping negative signs when substituting linear expressions.

A test-taker could mistakenly pick 2, 3 by incorrectly guessing the factorization or misinterpreting the middle term signs. Factorizing the quadratic expression x^2 - 4x + 3 yields (x - 1)(x - 3) = 0, which directly produces the roots x = 1 and x = 3. Common mistake: incorrectly identifying the signs of the factors for a quadratic equation with a negative middle coefficient and positive constant.

One might select 2 by incorrectly applying the arithmetic progression sum formula or miscalculating the number of terms. Using the formula Sum = n/2 [2a + (n-1)d] with n = 4 and a = 4 results in 28 = 2 [8 + 3d], which simplifies to 14 = 8 + 3d, leading to 3d = 6 and d = 3. Common mistake: algebraic errors when solving for the common difference from the sum formula.