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Express \(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).
If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).
Forces of magnitude 8N and 5N act on a body as shown above. Calculate, correct to 2 dp, the angle that the resultant makes with the horizontal.
Forces of magnitude 8N and 5N act on a body as shown above. Calculate, correct to 2 d.p., the resultant force acting at O.
Forces \(F_{1} = (8N, 030°)\) and \(F_{2} = (10N, 150°)\) act on a particle. Find the horizontal component of the resultant force.
The sum, \(S_{n}\), of a sequence is given by \(S_{n} = 2n^{2} - 5\). Find the 6th term.
A 24N force acts on a body such that it changes its velocity from 5m/s to 9m/s in 2 secs.If the body is travelling in a straight line, calculate the distance covered in the period.
If \(2\sin^{2} \theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find the value of \(\theta\).
Simplify: \(^{n}C_{r} ÷ ^{n}C_{r-1}\)
In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.
Four fair coins are tossed once. Calculate the probability of having equal heads and tails.
Given that \(y = 4 - 9x\) and \(\Delta x = 0.1\), calculate \(\Delta y\).
A particle starts from rest and moves in a straight line such that its acceleration after t secs is given by \(a = (3t - 2) ms^{-2}\). Find the distance covered after 3 secs.
A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t - 2) ms^{-2}\). Find the other time when the velocity would be zero.
Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.
Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)
If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.
Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.
A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with constant velocity. \([g = 9.8ms^{-2}]\)
| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| Number of candidates | 6 | 4 | 8 | 10 | 9 |
3 |
The table above shows the distribution of marks scored by students in a test. Find the interquartile range of the distribution.