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What is the circumference of latitude 0\(^o\)S if R is the radius of the earth?
Four boys and ten girls can cut a field first in 5 hours. If the boys work at \(\frac{5}{4}\) the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?
Reach each number to two significant figures and then evaluate \(\frac{0.02174 \times 1.2047}{0.023789}\)
Find all real number x which satisfy the inequality \(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4)
Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
Factorise (4a + 3) \(^2\) - (3a - 2)\(^2\)
Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
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.