Question Library

(a) Solve the equation : \(\frac{2}{3}(3x - 5) - \frac{3}{5}(2x - 3) = 3\) (b) In the diagram, < STQ = m, < TUQ = 80^\circ, < UPQ = r, < PQU = n and < RQT = 88^\circ. Find the value of (m + n).

If the sixth term of an Arithmetic Progression (A.P) is 37 and the sum of the first six terms is 147, find the (a) first term; (b) sum of the first fifteen terms.

(a) Copy and complete the table of values for the equation \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\). x -3 -2 -1 0 1 2 3 4 5 6 y 13 -9 -14 -12 6 (b) Using scales of 2cm to 1 unit on the x- axis and 2cm to 4 units on the y- axis, draw the graphs of \(y = 2x^{2} - 7x - 9\) for \(-3 \leq x \leq 6\). (c) Use the graph to estimate the : (i) roots of the equation \(2x^{2} - 7x = 26\); (ii) coordinates of the minimum point of y; (iii) range of values for which \(2x^{2} - 7x < 9\).

(a) Using completing the square method, solve, correct to 2 decimal places, the equation \(3y^{2} - 5y + 2 = 0\). (b) Given that \(M = \begin{pmatrix} 1 & 2 \\ 4 & 3 \end{pmatrix}, N = \begin{pmatrix} m & x \\ n & y \end{pmatrix}\) and \(MN = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}\), find the matrix N.

The nth term of the sequence 3, 9, 27, 81.....is

The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?

The roots of a quadratic equation are \(\frac{4}{3}\) and -\(\frac{3}{7}\). Find the equation

Find the next three terms of the sequence; 0, 1, 1, 2, 3, 5, 8...

(a) Copy and complete the table of values, correct to one decimal place, for the relation \(y = 3\sin x + 2\cos x\) for \(0^\circ \leq x \leq 360^\circ\). x 0^\circ 30^\circ 60^\circ 90^\circ 120^\circ 150^\circ 180^\circ 210^\circ 240^\circ 270^\circ 300^\circ 330^\circ 360^\circ y 3.0 1.6 -2.0 -3.6 -3.0 2.0 (b) Using scales of 2cm to 30^\circmon the x- axis and 2cm to 1 unit on the y- axis, draw the graph of the relation \(y = 3\sin x + 2\cos x\) for \(0^\circ\leq x \leq 360^\circ\). (c) Use the graph to solve : (i) \(3\sin x + 2\cos x = 0\) (ii) \(2 + 2\cos x + 3\sin x = 0\).

Find the x and z intercepts of the graph of 3x - z \(\leq\) 9

Solve the equation \( 3x^2 − 4x − 5 = 0 \)

The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms

Find the equation of a line which is form origin and passes through the point (−3, −4)

Make x the subject of the equation s = 2 + \(\frac{t}{5} \)(x + ⅗y)

Determine the third term of a geometrical progression whose first and second term are 2 and 54 respectively