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.

A student could choose 243 by miscalculating the sixth power instead of the seventh power of the common ratio. Identifying the first term a = 1 and common ratio r = 3/1 = 3, we substitute into the geometric term formula ar^(7-1) to get 1 × 3^6, which evaluates to 1 × 729, giving 729. Common mistake: using n instead of n-1 in the exponent for the nth term of a geometric sequence.

A student might incorrectly select options like B, C, or D by miscalculating the fraction multiplication or ignoring replacement rules. To determine the correct probability, first establish the aggregate number of balls as 10, which makes the individual draw probability for blue equal to 4/10. Because the selection is performed with replacement, the draw events remain independent and retain identical probabilities. Multiplying the single probability by itself yields (4/10) × (4/10), resulting in 16/100, which simplifies to 4/25. Common mistake: Forgetting to multiply the independent probabilities or incorrectly reducing the fraction.

Students might mistakenly select options like A, C, or D by missing a number in the sum or dividing by the wrong count. To find the correct value, sum the given numbers 1, 3, 5, 7, 9, and 11 to obtain 36, and then divide that total by the quantity of numbers, which is 6. This calculation yields 36 divided by 6, resulting in 6. Common mistake: Dividing by the wrong number of terms or adding the values incorrectly.

A test-taker might select option A, B, or D by confusing the mode with the median, mean, or range of the data set. By examining the frequency of each number in the sequence 2, 3, 3, 4, 4, 4, 5, it becomes clear which value appears most often. The number 4 appears three times, which is more frequent than any other entry, making it the mode. Common mistake: Confusing the mode with the median or calculating the mean instead of counting frequencies.

Someone might choose option B, C, or D by assuming a simple linear probability or miscounting the total outcomes. Tossing a coin twice produces a sample space of 4 total outcomes, which are HH, HT, TH, and TT. Out of these, only one outcome represents getting two heads, leading to a probability of 1/4. Common mistake: Miscounting the sample space outcomes or listing duplicate combinations.

A student could choose option B, C, or D by omitting the division by two or misapplying the formula dimensions. The area of a trapezium is calculated using the formula (1/2) multiplied by the sum of the parallel sides and the height. Substituting the given values gives (1/2) multiplied by (6 + 10) and then by 5, which simplifies to (1/2) multiplied by 16 multiplied by 5, resulting in 40 cm^2. Common mistake: Forgetting to multiply by one-half at the beginning of the trapezium area formula.

A test-taker might mistakenly select option B, C, or D by adding the dimensions instead of multiplying them together. The volume of a cuboid is found by multiplying its length, width, and height together. Multiplying the given dimensions of 4 cm, 5 cm, and 6 cm yields 4 times 5 times 6, which equals 120 cm^3. Common mistake: Adding the dimensions together instead of finding their product.

An unprepared student might pick option B, C, or D by confusing cosine with sine or other trigonometric ratios. Knowing standard trigonometric values for special angles reveals that the cosine of 30° is equal to the square root of 3 divided by 2, which is approximately 0.866. Common mistake: Confusing the trigonometric values for sine 30° and cosine 30°.

A student might mistakenly choose option A, B, or D by incorrectly evaluating exponents or misjudging the power of 5. To solve the equation 5^x = 125, express 125 as a power of 5, which is 5 cubed. Equating the exponents on both sides of 5^x = 5^3 shows that x equals 3. Common mistake: Guessing the exponent or confusing base and power values.

Someone might select option A, C, or D by inverting the coordinate differences or subtracting in the wrong order. The gradient of a line is determined by finding the change in y divided by the change in x between two points. Using the coordinates (2, 4) and (4, 8), calculate (8 minus 4) divided by (4 minus 2), which gives 4 divided by 2, resulting in a gradient of 2. Common mistake: Placing the change in x over the change in y instead of y over x.

A student could pick option B, C, or D by making a sign error during the algebraic expansion or transposition. Using the point-slope formula y minus y1 equals gradient times (x minus x1), substitute the gradient of 4 and point (1, 3) to get y minus 3 equals 4(x minus 1). Expanding and rearranging this yields y minus 3 equals 4x minus 4, which simplifies to y equals 4x minus 1. Common mistake: Distributing the gradient incorrectly or mishandling negative signs during transposition.

A test-taker might select option A, C, or D by using the wrong formula or miscounting the number of sides in a hexagon. The sum of the interior angles of any polygon is found using the formula (n minus 2) multiplied by 180°, where n represents the number of sides. For a hexagon, n is 6, giving (6 minus 2) multiplied by 180°, which equals 4 multiplied by 180°, resulting in 720°. Common mistake: Using an incorrect polygon angle sum formula or misidentifying the number of sides.

Someone might choose option B, C, or D by forgetting to account for the fraction of the circle or misusing the radius squared. The area of a circular sector is calculated as the angle divided by 360° multiplied by pi and the radius squared. Substituting 180° for the angle, 3.14 for pi, and 6 cm for the radius gives (180/360) multiplied by 3.14 multiplied by 36, which equals 0.5 multiplied by 3.14 multiplied by 36, yielding 56.52 cm^2. Common mistake: Omitting the fraction of the circle or failing to square the radius.

A student might pick option B, C, or D by making an arithmetic error during substitution or elimination. From the second equation 2x minus y equals 3, express y as 2x minus 3, and substitute this into the first equation 5x + 3(2x minus 3) = 24. Expanding this gives 5x + 6x minus 9 = 24, which simplifies to 11x minus 9 = 24, leading to 11x = 33 and x = 3. Common mistake: Incorrectly distributing the coefficient during substitution.

A test-taker might select option B, C, or D by incorrectly guessing factors that do not multiply to the constant term while summing to the coefficient. To find the roots of x^2 minus 10x + 21 = 0, look for two numbers that multiply to 21 and add up to negative 10. These numbers are negative 3 and negative 7, allowing the equation to be factored as (x minus 3)(x minus 7) = 0, yielding roots x = 3 and x = 7. Common mistake: Mixing up the signs of the factors when determining the roots.

Someone could choose option B, C, or D by misapplying the arithmetic progression sum formula or making an error in algebra. The sum formula for an arithmetic progression is n/2 times [2a + (n minus 1)d]. Substituting n = 8, a = 6, and sum = 96 produces 96 = (8/2)[2(6) + (8 minus 1)d], which simplifies to 96 = 4[12 + 7d], leading to 24 = 12 + 7d, 7d = 12, and d = 2. Common mistake: Miscalculating the brackets or dividing incorrectly when isolating the common difference.

A student might mistakenly select option A, C, or D by adding the common difference instead of multiplying by the common ratio. In the geometric progression 5, 10, 20, ..., the first term a is 5 and the common ratio r is 10 divided by 5, which is 2. The fourth term is calculated using ar^(n minus 1) as 5 multiplied by 2 cubed, which equals 5 multiplied by 8, resulting in 80. Common mistake: Treating the sequence as an arithmetic progression instead of geometric.

A test-taker might pick option A, B, or D by failing to adjust the denominator for selections made without replacement. With a total of 10 balls in the bag, the probability of picking a green ball first is 5/10. Because the ball is not replaced, the remaining pool has 9 balls with 4 green ones, making the second probability 4/9. Multiplying these probabilities gives (5/10) multiplied by (4/9), which equals 20/90, simplifying to 5/18. Common mistake: Forgetting to decrease both the numerator and denominator for the second draw.

Someone might choose option A, C, or D by miscalculating the sum of the sequence or dividing by an incorrect quantity. To find the mean of the numbers 4, 6, 8, 10, 12, and 14, add them together to get 54, and then divide that sum by the total count of 6 numbers. This gives 54 divided by 6, resulting in a mean of 9. Common mistake: Adding an extra term or dividing by the wrong denominator.

A student could select option B, C, or D by missing some favorable pairs or miscalculating the sample space for two dice. Rolling a die twice yields a total sample space of 6 multiplied by 6, which is 36 outcomes. The specific pairs that sum to 8 are (2,6), (3,5), (4,4), (5,3), and (6,2), totaling 5 favorable outcomes, giving a probability of 5/36. Common mistake: Forgetting the repeated pair like (4,4) or miscounting the total successful outcomes.