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If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\)
Simplify, correct to three significant figures, (27.63)\(^2\) - (12.37)\(^2\)
Solve: \(\frac{y + 1}{2} - \frac{2y - 1}{3}\) = 4
Evaluate: (0.064)\(^{-\frac{1}{3}}\)
Express, correct to three significant figures, 0.003597.
Evaluate \(\frac{2\sin 30 + 5\tan 60}{\sin 60}\), leaving your answer in surd form.
If \(\sin x = \frac{4}{5}\), find \(\frac{1 + \cot^2 x}{\csc^2 x - 1}\).
Calculate the volume of the regular three dimensional figure drawn above, where < ABC = 90° (a right- angled triangle).
In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.
The histogram above represents the number of candidates who did Further Mathematics examination in a school. How many candidates scored more than 40?
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2y - 2 | y - 1 | 3y - 4 | 3 - y | 6 - 2y |
The table above is the distribution of data with mean equals to 3. Find the value of y.
Find the equation of a line perpendicular to the line 4y = 7x + 3 which passes through (-3, 1)
Find the distance between the points C(2, 2) and D(5, 6).
Differentiate \(\frac{2x}{\sin x}\) with respect to x.
If y = 8x\(^3\) - 3x\(^2\) + 7x - 1, find \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).
Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.
If \(\begin{vmatrix} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{vmatrix} = 132\), find the value of x.
If 2x\(^2\) + x - 3 divides x - 2, find the remainder.
Find the polynomial if given q(x) = x\(^2\) - x - 5, d(x) = 3x - 1 and r(x) = 7.
Determine the values for which \(x^2 - 7x + 10 \leq 0\)