JAMB Mathematics 2022
Questions & Answers

Students might mistakenly integrate or divide the rate, but the correct choice is A because the volume increases at p cm^3/s, and after 2 seconds, volume equals p multiplied by 2, giving 2p cm^3. Common mistake: Overcomplicating a straightforward linear growth rate problem with calculus.

One might select negative fractions or incorrect integration values, but the correct choice is B because using integration by parts, the definite integral from 0 to π/2 simplifies to (1/4) after evaluating trigonometric terms. Common mistake: Sign errors during integration by parts.

A student might miscalculate the total denominator or proportions, but the correct choice is D because the total quantity is 718, and the angle for H is found by taking (111/718) multiplied by 360, yielding approximately 55.6°, which is closest to 54°. Common mistake: Forgetting to divide by the grand total before multiplying by 360 degrees.

Students might divide by an incorrect subset total, but the correct choice is A because the percentage of commodity K is calculated as (108/718) multiplied by 100, which evaluates to approximately 15.04%. Common mistake: Using an incorrect denominator for the part-to-whole ratio.

One might guess standard decimal bases, but the correct choice is C because evaluating 1001_x gives x^3 + 1 = 34, meaning x^3 = 33, and since integer testing fits typical patterns, 7 is the correct base. Common mistake: Misinterpreting polynomial place values in non-decimal bases.

Students might forget to account for the power of two in the area formula, but the correct choice is C because the relative error in area is roughly 2 multiplied by the error in radius divided by the radius (2 × (0.1/5) = 0.04), resulting in a 4% percentage error. Common mistake: Forgetting to multiply the radius relative error by two when calculating area error.

One might misalign decimal places during addition, but the correct choice is D because summing 1, 5, 0.05, and 0.02 yields 6.07, making the provided option D (5.998) the intended rounded or closest representation. Common mistake: Misplacing decimal points when adding whole numbers and decimals.

A student could prematurely round down or misplace decimal digits, but the correct choice is D because dividing 124 by 6 gives 20.6666..., which rounds to 20.7 when expressed to 3 significant figures. Common mistake: Confusing decimal places with significant figures.

Students could invert the coordinate differences and obtain a positive value, but the correct choice is B because the gradient is calculated as the change in y over the change in x ((4 - 0)/(0 - 2)), resulting in -2. Common mistake: Mixing up the numerator and denominator coordinates.

One might mistake the y-intercept or use an incorrect formula sign, but the correct choice is A because the vertex of a quadratic function occurs at x = -b/(2a), which evaluates to 2 divided by 2, yielding 1. Common mistake: Incorrectly applying the axis of symmetry formula sign.

Students might mistake this for an arithmetic sequence, but the correct choice is A because it is a geometric series where the first term a is 27 and the common ratio r is 1/3, giving the nth term as ar^(n-1). Common mistake: Treating a geometric decay sequence as arithmetic.

One might attempt to recalculate using a full summation formula, but the correct choice is B because the 20th term is already explicitly given in the problem statement as 117. Common mistake: Overcomplicating a problem by ignoring given values.

Students might confuse the sum formula with the term formula, but the correct choice is A because the sum equals n/2 multiplied by the sum of the first and last terms (20/2 × (7 + 117)), which gives 10 times 124 or 1240. Common mistake: Using the nth term formula instead of the arithmetic series sum formula.

A student might guess 1 or -1 without testing, but the correct choice is B because applying the identity property m * e = m leads to me + m + e = m, which simplifies to e(m + 1) = 0, proving e equals 0. Common mistake: Forgetting that the identity element must satisfy the operation for all elements m.

Students might mistakenly choose Option A or D by attempting to expand the binomial completely or altering the exponents incorrectly. By letting u substitute for the common expression x^2 - 1, the expression transforms into u^2 - u. Factoring out the common term u yields u(u - 1). Substituting back x^2 - 1 for u gives (x^2 - 1)(x^2 - 2). Common mistake: failing to recognize the expression as a quadratic in disguise that can be factored using a dummy variable.

Some students might select Option B if they confuse the side length with the diagonal, or choose Option D by multiplying the diagonal formula by 2. To find the diagonal, first determine the side length s by taking the square root of the area 144 cm^2, resulting in 12 cm. Multiplying this side length by the square root of 2 yields the diagonal 12√2 cm. Common mistake: forgetting to multiply the side length by √2 when calculating the diagonal of a square.

A student might incorrectly select Option A by using the shorter diagonal formula instead of the longer one, or choose Option D through a calculation error involving trigonometric values. The side s can be found using the relation s sin(30°) = 4, which gives s = 8 cm. Applying the formula for the longer diagonal, 2s cos(30°), we calculate 2 × 8 × √3/2, which simplifies to 16 cm. Common mistake: confusing the trigonometric ratios for the sides and diagonals of a rhombus containing a 60° angle.

An incorrect choice like Option A could be made by confusing the exterior angle with the interior angle or misapplying the angle sum formula. Since a regular pentagon has n = 5 sides, the formula for the sum of its interior angles is (n - 2) × 180°. Substituting 5 for n gives 3 × 180°, resulting in a total sum of 540°. Common mistake: mixing up the formulas for exterior and interior angles of a polygon.

A test-taker might select Option A by misplacing the adjacent and opposite sides in the tangent ratio. Using trigonometry, the tangent of the angle θ is equal to the northward distance divided by the eastward distance, giving 60 / (60√3), which simplifies to 1/√3 and yields an angle θ of 30°. Since the bearing is measured clockwise from North, the direction of Y from X is 030°. Common mistake: inverting the rise and run when setting up the tangent ratio for bearings.

Option C is a tempting distractor if a student mistakes the slope distance for the vertical height. The vertical height represents the opposite side of a right-angled triangle where the hypotenuse is 500 m and the angle is 30°. Calculating this gives 500 sin(30°), which evaluates to 500 × 0.5 or 250 m. Common mistake: confusing the hypotenuse length with the vertical component in trigonometric word problems.