WAEC Mathematics 2021
Questions & Answers

A student might mistakenly count leading zeros as significant figures or misapply rounding rules by cutting the number off prematurely at 0.0005. Counting begins at the initial non-zero digit (5), meaning the first two significant digits are 5 and 6; because the subsequent digit is 7 (which is 5 or greater), the 6 rounds up to 7, giving 0.00057. Common mistake: Including leading zeros when counting significant digits.

One might mistakenly add the positional values incorrectly or treat the binary digits as a simple base-10 integer. By applying powers of 2 from right to left starting at 2^0, we calculate the bits as 1(8) + 0(4) + 1(2) + 1(1), which yields a sum of 11. Common mistake: Forgetting that binary positional values increase as powers of 2 from right to left.

A student might forget to change the sign when forming the conjugate or fail to square the individual terms in the denominator. Multiplying both parts of the fraction by the conjugate (√5 - √2) produces a numerator of √5 - √2 and a denominator calculated as (√5)^2 - (√2)^2, which simplifies to 5 - 2 = 3. Common mistake: Forgetting to subtract the squared terms in the denominator's difference of squares.

A student might mistakenly multiply the given logarithm by 5 instead of applying the exponent rule correctly. Recognizing that 25 is 5 squared allows us to use the power property of logarithms, bringing the exponent 2 to the front to multiply 0.6990, resulting in 1.3980. Common mistake: Multiplying the log value by the base number instead of doubling it for a squared exponent.

A student might reverse the inequality sign or fail to divide properly after isolating the variable term. Adding 2 to both sides gives 3x > 9, and dividing by 3 results in x > 3 while preserving the strict inequality direction. Common mistake: Dropping or reversing inequality directions during division by a positive number.

A student might forget to distribute the 3 across the parentheses, leading to an incorrect algebraic expansion. Expanding the left side yields 3x - 3 = 2x + 5, and subtracting 2x and adding 3 on both sides isolates x to equal 8. Common mistake: Forgetting to distribute the outer coefficient to all terms inside parentheses.

A student might mistakenly compute the answer using a standard arithmetic progression formula with an assumed common difference instead of utilizing the given formula directly. Substituting n = 10 straight into the provided expression 3n - 2 gives 3(10) - 2, which equals 30 - 2 = 28. Common mistake: Overcomplicating the problem by deriving an AP formula when the nth term rule is already given.

A student might pick positive factors if they overlook the negative sign on the middle coefficient. Factoring requires finding two integers that multiply to +6 and sum to -5, which are -2 and -3, yielding the binomial factors (x - 2)(x - 3). Common mistake: Selecting positive signs for binomial factors when the middle term is negative and the constant is positive.

A student might mix up the signs when solving each linear factor or fail to set both factors to zero. Applying the zero product property, setting 2x - 1 = 0 yields x = 1/2, and setting 3x + 4 = 0 yields x = -4/3. Common mistake: Incorrectly carrying over negative signs when solving linear factors for zero.

A student might mistakenly add the outer exponent to the inner powers instead of multiplying them. Applying the power of a power rule gives a^6 b^3 in the numerator, and dividing by a^5 subtracts the exponents to leave a^1 b^3, or a b^3. Common mistake: Adding exponents during power-of-a-power expansion instead of multiplying them.

A student might confuse the interior angle sum with that of a triangle or a pentagon. Splitting a four-sided polygon into two triangles via a diagonal yields 2 times 180°, resulting in a total interior angle sum of 360°. Common mistake: Using the triangle angle sum of 180° for four-sided polygons.

Distractor check: A student might mistakenly select B (100°) by accidentally summing the two given angles and treating that as the third angle, or choose D (90°) assuming all interior angles must form a right angle. Reasoning to the answer: The total sum of interior angles in any triangle equals 180°. By applying the angle sum property of triangles, we subtract the two known angles from this total: angle C = 180° - 40° - 60° = 80°. Common mistake: Forgetting that all three internal triangle angles add up to 180° rather than 90° or 360°.

Distractor check: A student might mistakenly pick B (108°) by confusing the exterior angle rule with the interior angle formula for a regular polygon, or pick D (90°) guessing a standard perpendicular orientation. Reasoning to the answer: A regular pentagon consists of 5 equal sides and equal angles, and the exterior angles of any regular polygon always sum to 360°. Dividing this total sum of 360° by the number of sides (5) yields 360° / 5 = 72°. Common mistake: Confusing the formula for a polygon's interior angle with the formula for its exterior angle.

Distractor check: A student might select C (90°) by confusing supplementary angles with complementary angles, which add up to 90°. Reasoning to the answer: Supplementary angles are defined as angles that add up to 180°, a property frequently applied in geometry when dealing with a straight line. By subtracting the given angle from this total, we find the remaining angle = 180° - 120° = 60°. Common mistake: Mixing up supplementary angles (180°) with complementary angles (90°).

Distractor check: A student might choose B (False) assuming the relationship between center and circumference angles varies unpredictably or only applies to specific shapes. Reasoning to the answer: This principle stems from a fundamental theorem in circle geometry stating that the angle subtended by an arc at the center is twice the angle subtended at any point on the remaining circumference. This arises because inscribed angles are always half the central angle. Common mistake: Forgetting the 2:1 ratio between the central angle and the inscribed circumferential angle.

Distractor check: A student might mistakenly choose D (49°) by calculating only the squared radius without multiplying by pi, or pick B (44°) by calculating circumference instead of area. Reasoning to the answer: The area of a circle formula is π r². Substituting the given values r = 7 cm and π = 22/7 yields: Area = (22/7) × (7)² = (22/7) × 49 = 22 × 7 = 154 cm². The resulting units are squared because it measures a two-dimensional area. Common mistake: Using the circumference formula (2πr) instead of the area formula (πr²).

Distractor check: A student might pick D (94.2°) through a miscalculation of the radius square or multiplication steps, or choose C (15 cm³) by multiplying dimensions together without accounting for pi and the squared radius. Reasoning to the answer: The volume of a cylinder is calculated as π r² h. With r = 3 cm, h = 5 cm, and π ≈ 3.14, we first square the radius to get 9, multiply by 3.14 to get 28.26, and finally multiply by the height of 5 to obtain 141.3 cm³. This formula is derived from taking the area of the circular base and multiplying it by the height. Common mistake: Squaring both the radius and the height instead of just the radius.

Distractor check: A student might mistakenly pick B (113.14°) by omitting the factor of 4 from the surface area formula, calculating only the area of a single cross-sectional circle. Reasoning to the answer: The surface area of a sphere is given by 4 π r². Using r = 6 cm and π = 22/7, we square the radius to get 36, multiply by 4 to get 144, and then multiply by 22/7, which equals (144/7) × 22 or approximately 452.57 cm². Common mistake: Forgetting the leading coefficient of 4 in the surface area formula for a sphere.

Distractor check: A student might mistakenly choose C (40 cm²) by multiplying the base and height without halving the result, or select B (14 cm²) by adding them instead. Reasoning to the answer: The area of a triangle is calculated using (1/2) × base × height. Substituting base = 10 cm and height = 4 cm gives (1/2) × 10 × 4 = 5 × 4 = 20 cm². This formula holds true for any triangle type because the height represents the perpendicular distance. Common mistake: Forgetting to multiply by one-half at the end of the base times height calculation.

Distractor check: A student might select B (40 cm°) by multiplying length and width to find the area rather than the perimeter, or pick C (13 cm) by adding length and width without doubling the sum. Reasoning to the answer: The perimeter of a rectangle is determined by 2 × (length + width). With a length of 8 cm and a width of 5 cm, we compute 2 × (8 + 5) = 2 × 13 = 26 cm. This accounts for all four boundary sides comprising two lengths and two widths. Common mistake: Calculating the area instead of the perimeter by multiplying length and width.