Mathematics 2022 Jamb Examination

A perpendicular line from the center of a circle to a chord bisects that chord. Therefore, XZ = \(\frac{1}{2}\)XY = \(\frac{1}{2}(8)\) = 4cm.
OX is the radius, given as 5cm. OX, XZ, and OZ form a right-angled triangle (\(\Delta OZX\)).
Using Pythagoras' theorem: \(OZ^2 + XZ^2 = OX^2\)\[OZ^2 + 4^2 = 5^2\]\[OZ^2 + 16 = 25 \implies OZ^2 = 9\]\[OZ = \sqrt{9} = 3\text{ cm}\]

Substitute a = 3 and b = 5 into the given operation definition:\[3 \ast 5 = 3 - 5 + (3 \times 5)^2\]\[= -2 + (15)^2\]\[= -2 + 225 = 223\]

Inverse variation is defined by the relationship \(y = \frac{k}{x}\) or \(xy = k\).
Find the constant k: \(3 \times 4 = 12\), so \(k = 12\).
Now find x when y = 12:\[12x = 12\]\[x = \frac{12}{12} = 1\]

In an Arithmetic Progression, the difference between consecutive terms is constant (d).
Term 1 (a) = 8. Term 4 = 26.
Using \(U_n = a + (n-1)d\):\[26 = 8 + (4-1)d\]\[26 - 8 = 3d \implies 18 = 3d \implies d = 6\]Now calculate p and q:
p = \(a + d = 8 + 6 = 14\)
q = \(p + d = 14 + 6 = 20\)

The mean is the sum of the values divided by the count:\[\frac{2x + 4x + (2x - 13) + 6x}{4} = 4\]Combine like terms in the numerator:\[\frac{14x - 13}{4} = 4\]\[14x - 13 = 16\]\[14x = 29 \implies x = \frac{29}{14} \approx 2.07\]Looking at the options and the prompt, let's re-verify the terms. If the sum was intended to be \(14x - 2 = 16\), then \(x\) would be clean. However, based on the specific text provided, 2.0 is the closest approximation.

This expression follows the difference of two squares pattern: \(x^2 - y^2 = (x - y)(x + y)\).
Rewrite the terms as squares:\[(2a)^2 - (3b)^2\]Factorize using the formula:\[(2a - 3b)(2a + 3b)\]

Use the formula for the union of two sets:\[n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)\]Substitute the given values:\[40 = 20 + 30 - n(P \cap Q)\]\[40 = 50 - n(P \cap Q)\]\[n(P \cap Q) = 50 - 40 = 10\]

Translate the sentence into a mathematical inequality:\[3x - 2 < x - 6\]Subtract x from both sides:\[2x - 2 < -6\]Add 2 to both sides:\[2x < -4\]Divide by 2:\[x < -2\]

When representing inequalities on a number line, a solid (closed) circle indicates that the number itself is included (equal to), and the direction of the arrow indicates if the values are greater than or less than. A solid circle at 2 with the line shaded to the right indicates all values greater than or equal to 2.

A 20% discount means the selling price is 80% of the original price (100% - 20% = 80%).
Let the original price be x:\[0.80x = 3800\]\[x = \frac{3800}{0.80}\]\[x = \frac{38000}{8} = 4750\]The original price was ₦4,750.00.