WAEC Mathematics 2023
Questions & Answers

Distribute the negative sign across the second parenthesis: (2x + 3y) - x + 2y simplifies to 2x - x + 3y + 2y. Combine like terms: x + 5y.

First, expand the right side: 3x - 7 = 2x + 2. Subtract 2x from both sides: x - 7 = 2. Add 7 to both sides: x = 9.

By definition, log10(1000) is the exponent to which 10 must be raised to get 1000. Since 10^3 = 1000, log10(1000) = 3.

To factor the quadratic, find two numbers that multiply to 6 (c) and add to -5 (b): -2 and -3. Thus, x^2 - 5x + 6 = (x - 2)(x - 3).

The formula for the area of a triangle is (1/2) × base × height. Substituting the values: (1/2) × 10 × 5 = 25 cm².

Recognize the perfect square trinomial: x^2 - 4x + 4 = (x - 2)^2 = 0, which gives a double root at x = 2.

In the unit circle, sin(90°) corresponds to the y-coordinate at the top of the circle, which is 1.

Add the two equations to eliminate y: (2x + y) + (x - y) = 5 + 1, resulting in 3x = 6, so x = 2.

The mean is the sum of the numbers divided by the count: (2 + 4 + 6 + 8) / 4 = 20 / 4 = 5.

Using the binomial theorem or FOIL method: (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2.

Subtract 2 from both sides: y/3 = 3. Multiply both sides by 3: y = 9.

This is a perfect square: (x - 3)^2 = 0, so the discriminant is zero, giving a repeated root at x = 3.

In the unit circle, cos(0°) is the x-coordinate at the rightmost point, which is 1.

The volume of a cube is side cubed: 3 × 3 × 3 = 27 cm³.

Assuming common log base 10, log10 x = 2 means x = 10^2 = 100.

Simplify inside the radical first: 16/4 = 4, then √4 = 2.

In the slope-intercept form y = mx + c, the gradient (slope) m is the coefficient of x, which is 2.

tan θ = sin θ / cos θ; at 45°, sin(45°) = cos(45°) = √2/2, so tan(45°) = 1.

For an odd number of observations, the median is the middle value when ordered: the 3rd in 1,3,5,7,9 is 5.

Express both sides with base 2: 4 = 2^2, so (2^2)^x = 2^{2x} = 2^4 = 16, thus 2x = 4, x = 2.

Circumference = 2πr; substitute π = 22/7 and r = 7: 2 × (22/7) × 7 = 2 × 22 = 44 cm.

The ratio a:b = 2:3 directly means a/b = 2/3.

This is the fundamental Pythagorean identity in trigonometry, derived from the unit circle where sin θ and cos θ are coordinates satisfying x^2 + y^2 = 1.

Using the power rule for differentiation: d/dx (x^n) = n x^{n-1}, so for n=2, d/dx (x^2) = 2x.

A fair coin has two equally likely outcomes (heads or tails), so P(heads) = number of favorable outcomes / total outcomes = 1/2.

Follow BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction): First, 8 ÷ 2 = 4 and 4 × 3 = 12, then 4 + 12 = 16.

This is a fundamental property of Euclidean geometry: the interior angles of any triangle sum to 180°.

5% = 0.05, so 0.05x = 10. Divide both sides by 0.05: x = 10 / 0.05 = 200.

The indefinite integral of a constant k is kx + C; here, ∫3 dx = 3x + C, where C is the constant of integration.

The mode is the value that appears most frequently: 3 appears three times, more than any other.

Using the distance formula: √[(3-0)^2 + (4-0)^2] = √[9 + 16] = √25 = 5.

Find the least common denominator (12): 3/4 = 9/12, 5/6 = 10/12, so 9/12 + 10/12 = 19/12.

By definition, sec θ = 1 / cos θ; if cos θ = 1/2, then sec θ = 1 / (1/2) = 2.

Variance quantifies the average squared deviation from the mean, measuring the spread or dispersion of data points.

The absolute value equation |x - 3| = 2 means x - 3 = 2 or x - 3 = -2, so x = 5 or x = 1.

Area = πr^2; with r = 5 and π ≈ 3.14, 3.14 × 25 = 78.5 cm².

The union A ∪ B includes all unique elements from both sets: {1, 2} and {2, 3} combine to {1, 2, 3}.

This is a standard limit in calculus: lim (x→0) sin x / x = 1, often used in deriving derivatives of trigonometric functions.

In (a + b)^3, the general term is C(3, k) a^{3-k} b^k; for a^2 b^1 (k=1), C(3,1) = 3.

Standard deviation is defined as the positive square root of the variance, providing a measure of dispersion in the original units.