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Find the length of the chord |AB| in the diagram shown above.
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?
| Age in years | 7 | 8 | 9 | 10 | 11 |
| No of pupils | 4 | 13 | 30 | 44 | 9 |
The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.
Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)
If \(N = \begin{pmatrix} 3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1 \end{pmatrix}\), find \(|N|\).
If X, Y can take values from the set (1, 2, 3 ,4), find the probability that the product of X and Y is not greater than 6
Add 54 \(_{eight}\) and 67\(_{eight}\) giving your answers in base eight
From a point R, 300m north of P, a man walks eastwards to a place; Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree
Simplify 25\(^{(\frac{1}{2}}\) × 8\(^{(\frac{-2}{3}}\)
Approximate 0.9875 to 1 decimal place.
Calculate the area of an equilateral triangle of side 8cm
Which one of the following gives the members of the set A1 n B n C?
A box contains two red balls and four blue balls. A ball is drawn at random from the box and then replaced before a second ball is drawn. Find the probability of drawing two red balls.
if y = 23\(_{five}\) + 101\(_{three}\) find y leaving your answer in base two
From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P and R.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Tossing a coin and rolling a die are two separate events. What is the probability of obtaining a tail on the coin and an even number on the die?