2003 - WAEC Mathematics Past Questions and Answers - page 4
If \(P = \sqrt{QR\left(1+\frac{3t}{R}\right)}\), make R the subject of the formula.
From the Venn diagram below, how many elements are in P∩Q?
From the Venn Diagram below, find Q' ∩ R.
Q' ∩ R
Q' = U - Q
Q' = {a, b, c, d, g, h, i}
R = {c, e, h, g}
Q' ∩ R = {c, h, g}
The square root of a number is 2k. What is half of the number
Let the number be x.
\(\sqrt{x} = 2k \implies x = (2k)^2\)
= \(4k^2\)
\(\frac{1}{2} \times 4k^2 = 2k^2\)
Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?
\(p \propto q^2\)
\(q \propto \frac{1}{\sqrt{r}\)
\(p = kq^2\)
\(q = \frac{c}{\sqrt{r}}\)
where c and k are constants.
\(q^2 = \frac{c^2}{r}\)
\(p = \frac{kc^2}{r}\)
If k and c are constants, then kc\(^2\) is also a constant, say z.
\(p = \frac{z}{r}\)
p varies inversely as r.
Prob (passing Maths) = Y
Prob (failing English) = 1 - x
Prob (failing Maths) = 1 - y
Prob (failing both test) = Prob(failing English) and Prob(failing Maths) = (1 - x)(1 - y)
=1 - y - x + xy
=1 - (y + x) + xy
Find the equation whose roots are \(-\frac{2}{3}\) and 3
\(x = -\frac{2}{3} \implies x + \frac{2}{3} = 0\)
\(x = 3 \implies x - 3 = 0\)
\(\implies (x - 3)(x + \frac{2}{3}) = 0\)
\(x^2 - 3x + \frac{2}{3}x - 2 = 0\)
\(x^2 - \frac{7}{3}x - 2 = 0\)
\(3x^2 - 7x - 6 = 0\)
\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\
\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}\)
In constructing an angle, Olu draws line OX. With centre O and a convenient radius, he draws an arc intersecting OX at P. With centre P and the same radius, he draws an arc intersecting the first arc at Q and finally joins OQ. What is the size of angle POQ so constructed?