2024 - JAMB Mathematics Past Questions and Answers - page 3

For two lines to be parallel, their slopes must be equal. The slope of the first line is 5 (from p = 5x + 3), and the slope of the second line is w (from p = wx + 5). Therefore:

\(5 = w\)

Hence, the value of w is 5.

Total playing football or volleyball:

\(22 + 26 - 3 = 45\)

Therefore, number who play neither:

\(46 - 45 = 1\)

Find intersection:

\(2x + 4 = 7 - x\)

\(3x = 3\)

\(x = 1\)

Substitute:

\(y = 2(1) + 4 = 6\)

Distance between (4, 3) and (1, 6):

Since y varies directly as \(w^2\):

\(y = k w^2\)

Given y = 8, w = 2:

\(8 = k(4)\)

\(k = 2\)

Now substitute w = 3:

\(y = 2(3^2) = 18\)

The sum of the ratio is:

\(5 + 3 + 2 = 10\)

The highest share corresponds to 5 parts:

\(40 = \frac{5}{10}T\)

Solve for T:

\(T = \frac{40 \times 10}{5} = 80\)

The smallest share is 2 parts:

\(\frac{2}{10} \times 80 = 16\) apples

Since:

\(x = k\sqrt{y}\)

Given x = 81, y = 9:

\(81 = k(3)\)

\(k = 27\)

Convert mixed number:

\(1\frac{7}{9} = \frac{16}{9}\)

\(\sqrt{\frac{16}{9}} = \frac{4}{3}\)

Thus:

\(x = 27 \times \frac{4}{3} = 36\)

Formula for curved surface area:

\(CSA = 2\pi r h\)

Given \(CSA = 110\), \(h = 5\):

\(110 = 2 \times \frac{22}{7} \times r \times 5\)

\(110 = \frac{220}{7} r\)

\(r = \frac{110 \times 7}{220} = 3.5\) cm

Rewrite the expression:

\(a^2 - 4a + 4 - b^2 = (a - 2)^2 - b^2\)

Apply difference of squares:

\((a - 2 - b)(a - 2 + b)\)

Multiply each score by the number of students:

• 0 x 4 = 0
• 1 x 3 = 3
• 2 x 7 = 14
• 3 x 8 = 24
• 4 x 6 = 24
• 5 x 2 = 10

Total = 0 + 3 + 14 + 24 + 24 + 10 = 75

Substitute \(x = 2\) into both equations:

\(y = 4p + q\)

\(y = 8 - 1 = 7\)

Equate:

\(4p + q = 7\)

Solve for p:

\(p = \frac{7 - q}{4}\)