2025 - JAMB Mathematics Past Questions and Answers - page 6

First convert the mixed number slope into an improper fraction:\[3 \frac{1}{5} = \frac{16}{5}\]Use the point-slope formula:\[y - y_1 = m(x - x_1)\]Substitute m = \(\frac{16}{5}\), x₁ = 3, y₁ = 15:\[y - 15 = \frac{16}{5}(x - 3)\]Multiply both sides by 5 to remove fraction:\[5y - 75 = 16x - 48\]Rearrange into standard form:\[5y - 16x - 75 + 48 = 0\]Simplify constants:\[5y - 16x - 27 = 0\]Therefore, the equation of the line is:\[5y - 16x - 27 = 0\]

Two sets are equivalent if they contain the same number of elements.The given set is:\[\{1,2,3,4,5\}\]Count the number of elements:\[5 \text{ elements}\]Now examine each option.The set:\[\{4,3,1,5,2\}\]Also contains exactly 5 elements.The order of elements does not matter in sets.Therefore, the sets are equivalent because they have the same number of elements.Thus, the equivalent set is:\[\{4,3,1,5,2\}\]

The sequence is an arithmetic progression because the difference between consecutive terms is constant.First term:\[a = 3\]Common difference:\[d = 5 - 3 = 2\]The formula for the nth term of an arithmetic progression is:\[T_n = a + (n - 1)d\]Substitute values:\[T_n = 3 + (n - 1)(2)\]Simplify:\[T_n = 3 + 2n - 2\]\[T_n = 2n + 1\]Now find the (n − 2)th term by replacing n with (n − 2):\[T_{n-2} = 2(n - 2) + 1\]Simplify:\[= 2n - 4 + 1\]\[= 2n - 3\]Therefore, the expression is:\[2n - 3\]

First multiply matrix Q by 2:\[2Q = 2 \begin{pmatrix} 3 & -7 \\ 1 & 2 \end{pmatrix}\]Multiply each element:\[\begin{pmatrix} 6 & -14 \\ 2 & 4 \end{pmatrix}\]Now add matrix P:\[\begin{pmatrix} 1 & 3 \\ 2 & -5 \end{pmatrix} + \begin{pmatrix} 6 & -14 \\ 2 & 4 \end{pmatrix}\]Add corresponding elements:\[\begin{pmatrix} 1+6 & 3+(-14) \\ 2+2 & -5+4 \end{pmatrix}\]Simplify:\[\begin{pmatrix} 7 & -11 \\ 4 & -1 \end{pmatrix}\]Therefore:\[\begin{pmatrix} 7 & -11 \\ 4 & -1 \end{pmatrix}\]

Since Y varies partly as x and partly as a constant, the relationship is:\[y = a + bx\]Substitute first condition:\[7 = a + 3b\]Substitute second condition:\[11 = a + 5b\]Subtract the first equation from the second:\[11 - 7 = (a + 5b) - (a + 3b)\]Simplify:\[4 = 2b\]Divide by 2:\[b = 2\]Substitute into first equation:\[7 = a + 6\]Solve for a:\[a = 1\]Therefore, the constants are:\[a = 1, \quad b = 2\]