If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).
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2008
The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.
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2008
Find the value of the constant k for which \(a = 4 i - k j\) and \(b = 3 i + 8 j\) are perpendicular.
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
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2008
A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?
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2008
A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?
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2008
Express \(r = (12, 210°)\) in the form \(a i + b j\).
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2008
Marks2345678No of students5796364The table above shows the distribution of marks by some candidates in a test. If a student is selected at random, what is the probability that she scored at least 6 marks?
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2008
Marks2345678No of students5796364The table above shows the distribution of marks by some candidates in a test. Find, correct to one decimal place, the mean of the distribution.
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2008
Marks2345678No of students5796364The table above shows the distribution of marks by some candidates in a test. What is the median score?
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2008
Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the resultant force.
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2008
The probability of Jide, Atu and Obu solving a given problem are \(\frac{1}{12}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) respectively. Calculate the probability that only one solves the problem.
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2008
Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
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2008
If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).
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2008
If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.
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2008
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
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2008
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
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2008
The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
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2008
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)