WAEC Mathematics 2019
Questions & Answers

1) Distractor check: Students might mistakenly select 0.359 by dropping leading zeros incorrectly, or 0.00359 by failing to round up based on the fourth digit. 2) Reasoning to the answer: For 0.003597, the significant digits are 3, 5, 9, 7, starting from the first non-zero digit. To round to three significant figures, look at the fourth digit (7), which is 5 or greater, so round up the third digit (9) to 10, carrying over 1 to the second digit (5 becomes 6), resulting in 0.00360 to ensure appropriate precision without unnecessary digits. 3) Common mistake: Treating leading zeros as significant figures when counting precision digits.

1) Distractor check: Students might mistakenly choose negative fractions like -2/5 or -5/2, confusing the inverse operation with a negative sign on the final value. 2) Reasoning to the answer: The expression is the reciprocal of the cube root of 0.064. First, compute the cube root where 0.064 equals 64 over 1000 or (4 over 10)^3, so the cube root is 0.4. Then, the reciprocal of 0.4 is 1 divided by 0.4, which equals 2.5 or 5/2, demonstrating the property of exponents stating a^-n equals 1 over a^n. 3) Common mistake: Applying the negative exponent as a negative numerical value instead of a reciprocal.

1) Distractor check: Students might mistakenly pick y = 19 by forgetting to distribute the final negative sign during the subtraction steps. 2) Reasoning to the answer: Eliminate the fractions by multiplying both sides by the least common multiple of the denominators, which is 6, giving 3(y+1) minus 2(2y-1) equal to 24. Distribute to get 3y plus 3 minus 4y plus 2 equal to 24, combine like terms to find -y plus 5 equal to 24, subtract 5 to get -y equal to 19, and multiply by -1 to arrive at y = -19. 3) Common mistake: Dropping the negative sign when distributing the second numerator term across the subtraction.

1) Distractor check: Students might mistakenly select 611 or 612 by performing standard rounding errors after independent squaring calculations. 2) Reasoning to the answer: Recognize this as a difference of squares where a^2 minus b^2 equals (a minus b)(a plus b), with a equal to 27.63 and b equal to 12.37. Compute a minus b as 15.26 and a plus b as 40.00, yielding a product of 610.4, which rounds to 610 to three significant figures since the fourth digit 4 is less than 5. 3) Common mistake: Manually squaring large decimals directly and introducing computation errors instead of factoring.

1) Distractor check: Students might mistakenly select 11 or 21 by testing the wrong values or failing to find the base congruence sequence. 2) Reasoning to the answer: Modular congruence means 7 + y leaves a remainder of 4 when divided by 8, so y is congruent to 4 minus 7, which is -3 or 5 modulo 8. Thus, y equals 8k plus 5 for integer k, and testing values within 10 <= y <= 30 gives 13 for k=1, 21 for k=2, and 29 for k=3, making 13 the least value. 3) Common mistake: Miscalculating the negative modulo remainder when shifting the constant term.

1) Distractor check: Students might mistakenly choose options containing odd numbers like 1 or 3, forgetting that the prime and odd complements remove them from the intersection. 2) Reasoning to the answer: The universal set is numbers 1 through 10. The primes are {2,3,5,7}, making non-primes {1,4,6,8,9,10}, while odds are {1,3,5,7,9}, making evens {2,4,6,8,10}. The intersection of these two complements contains elements found in both, which are {4,6,8,10}. 3) Common mistake: Including numbers that belong to only one complement set rather than the intersection.

1) Distractor check: Students might mistakenly pick -1/3 or 1/3 by reversing the numerator subtraction order or miscalculating individual log bases. 2) Reasoning to the answer: Evaluate the individual logarithms where log base 3 of 9 equals 2 and log base 2 of 8 equals 3. The numerator becomes 2 minus 3, which is -1, and the denominator is 2, resulting in -1/2 by highlighting base-specific logarithm values and basic arithmetic. 3) Common mistake: Subtracting the denominator value from the numerator incorrectly.

1) Distractor check: Students might mistakenly choose 4 or 5 by miscalculating the binary conversion sum or the base-y polynomial expansion. 2) Reasoning to the answer: Convert binary 1111 to decimal by summing powers of 2 to get 8 plus 4 plus 2 plus 1, which equals 15. Express the base-y number 23 as 2y plus 3, and set them equal to get 2y plus 3 equal to 15, yielding 2y equal to 12 and y equal to 6. 3) Common mistake: Setting up the positional expansion coefficients in reverse order.

1) Distractor check: Students might mistakenly choose 6 or 8 by confusing the middle term with the common difference or endpoints. 2) Reasoning to the answer: In an Arithmetic Progression, the difference between consecutive terms is constant, meaning twice the middle term equals the sum of the outer terms, so 2P equals 6 plus 14, which is 20, making P equal to 10. 3) Common mistake: Subtracting instead of averaging the outer terms to find the middle arithmetic mean.

1) Distractor check: Students might mistakenly choose 4√7 minus 21√2 by incorrectly adding the radical coefficients instead of combining like surds. 2) Reasoning to the answer: Simplify each radical by extracting square factors so that 2√28 becomes 4√7, 3√50 becomes 15√2, and √72 becomes 6√2. Combining these gives 4√7 minus 15√2 plus 6√2, which simplifies to 4√7 minus 9√2 in simplest radical form. 3) Common mistake: Combining surds with different radicands directly without factoring.

1) Distractor check: Students might mistakenly pick 4/3 or 3/4 by inverting the numerator and denominator polynomial terms. 2) Reasoning to the answer: Substitute the ratio parameters by letting m equal 2k and n equal k. The numerator evaluates to 3(4k^2) minus 2k^2, giving 10k^2, while the denominator evaluates to 4k^2 plus 2k^2, giving 6k^2, resulting in a simplified ratio of 10 over 6, which reduces to 5/3. 3) Common mistake: Failing to square the ratio terms correctly during algebraic substitution.

1) Distractor check: Students might mistakenly select options with positive multipliers or incorrect denominators like 4y^2 by misapplying the square of y. 2) Reasoning to the answer: Direct variation with p and inverse variation with the square of y establishes the relation H equals kp over y^2. Substituting the given values 1 equals k times 8 over 2^2 solves for k as 1/2, giving the final formula H equals p over 2y^2. 3) Common mistake: Forgetting to square the variable y when setting up the inverse proportionality.

1) Distractor check: Students might mistakenly pick negative root combinations like x = 3/2 or x = -5/2 by mishandling signs during quadratic factor grouping. 2) Reasoning to the answer: Use the quadratic formula with a equal to 4, b equal to -16, and c equal to 15 to compute the discriminant as 256 minus 240 equal to 16. This yields x equal to 16 plus or minus 4 over 8, resulting in roots 20/8 which is 5/2, and 12/8 which is 3/2. 3) Common mistake: Dropping the sign of the middle coefficient when applying the quadratic formula.

1) Distractor check: Students might mistakenly select 0.00045 by truncating instead of rounding up based on the third significant digit. 2) Reasoning to the answer: Identify the significant digits starting from the first non-zero entry as 4 and 5. Since the third digit is 6, which is greater than or equal to 5, round up the second digit to 6, giving 4.6 times 10^-4 or 0.00046 while ignoring leading zeros. 3) Common mistake: Counting leading placeholder zeros as significant figures.

1) Distractor check: Students might mistakenly choose 3 log base 10 of 2 by miscalculating the coefficient fractions of log 27. 2) Reasoning to the answer: Apply logarithm properties where log 6 splits into log 2 plus log 3, 3 log 3 becomes log 27, and 2/3 log 27 simplifies to 2 log 3. Combining all terms leaves log 2 plus log 3 minus 3 log 3 plus 2 log 3, which neatly reduces to log 2. 3) Common mistake: Incorrectly distributing the fractional coefficient over the logarithmic power.

1) Distractor check: Students might mistakenly pick 5% or 12% by calculating percentage changes against the wrong selling price base. 2) Reasoning to the answer: Determine the cost price by equating the initial selling price to 1.15 times the cost price, yielding 6900 over 1.15, which is 6000. For the new selling price of ₦6,600, the profit is 600, giving a percentage profit of 600 over 6000 multiplied by 100%, which equals 10%. 3) Common mistake: Calculating the new profit percentage using the original selling price instead of the cost price.

1) Distractor check: Students might mistakenly choose -12 or 7 by misinterpreting the simultaneous equation substitution signs. 2) Reasoning to the answer: Express p in terms of q from the first equation as 4q over 3 and substitute it into the linear relationship form of the second equation to solve for q equal to -3. Back-substituting yields p equal to -4, making their product pq equal to 12. 3) Common mistake: Multiplying variables without verifying consistency across both simultaneous equations.

1) Distractor check: Students might mistakenly pick 3/2 or 5/2 by ignoring the negative sign associated with the decimal base reciprocal power. 2) Reasoning to the answer: Express 0.25 as 1/4 or 2^-2 and 32 as 2^5, transforming the equation into (2^-2)^y equals 2^5. Equating the exponents gives -2y equal to 5, which solves for y as -5/2. 3) Common mistake: Forgetting to convert the decimal base into a matching exponent of 2.

1) Distractor check: Students might mistakenly select 3/4 or 1/3 by placing the number of girls over the total instead of boys. 2) Reasoning to the answer: Determine the total number of people in the lift as 8 boys plus 4 girls, giving 12 individuals in a uniform sample space. The probability of selecting a boy first is the number of favorable outcomes, 8, divided by the total, 12, which simplifies to 2/3. 3) Common mistake: Using the wrong gender count in the numerator of the probability ratio.

1) Distractor check: Students might mistakenly choose (x-7)/(x-7) or (x+7)/(x-7) by factorising one of the quadratic expressions incorrectly. 2) Reasoning to the answer: Factor the numerator into (x-7)(x+2) and the denominator into (x-7)(x-2). Canceling the common factor of (x-7), valid for x not equal to 7, leaves the simplified rational expression as (x+2)/(x-2). 3) Common mistake: Failing to recognize both quadratics share a common binomial factor.