OAU Post UTME Mathematics Past Questions

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A father leaves a legacy of ₦45 million for his children - Peter, David and Paul to be shared in the ratio 7:5:3. What amount in million Naira would each receive respectively?

Find x if \(x^2 - 2x - 15 = 0\)

A square has a perimeter of 40cm. What is its area in cm square?

Express in partial fraction \(\frac{3x}{x^2-1}{\equiv}\frac A{x-1}+\frac B{x+1}\). Then A and B respectively is

Find \(x\) if \(2^{x^2}=4^{(x+4)}\)

The line perpendicular to the straight line \(y+\frac 3 2x - 1=0\) has the gradient

The circle \(2x^2+2(y-\frac 3 2)^2=2\) has centre and radius respectively as

Find the value of \(\int_0^{\frac{\pi}{2}}\left(2\pi +2\cos 2x\right)\mathit{dx}\)

Find the value of \(\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt 6}}}}\)

If the binary operation * is defined as x * y = 2, find 2 * (4 * 5)

Given that \(a=\frac 1{2-\sqrt 3}, b=\frac 1{2+\sqrt 3},\) find the value of \(a^2+b^2\)

Evaluate \(x\) if \(\log_4(x+3)(x-3)=2\)

The speed of 30 kilometres per minute, expressed centimeters per second is

The reciprocal of \(\frac{\frac 3 4}{\frac 1 4+\frac 1 3}\) is

Convert \(69_{10}\) to a number in base two

Let \(\alpha\) and \(\beta\) be roots of quadratic equation \(x^2 + 2x\text{-} 3 = 0\), then \(\alpha \beta\) is

Factorize: \(a^2 - b^2+(a+b)^2\)

If the mean of the numbers \(a\), \(b\), \(c\), \(d\), \(e\) is \(x\), find the mean of numbers \(a+k\), \(b+2k\), \(c-k\), \(d-2k\), e.

A die is tossed twice. What is the probability of obtaining a total of 6 if both numbers are odd?

Integrate \(\frac 1{2x}\)

4 5 6 7 8

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