1997
A sector with angle 45° is cut from a circle of radius r cm and rolled into a cone, with its straight edges joined. Find the base radius of the cone.
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1997 JAMB UTME Mathematics Past Questions
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1997
An arc of a circle subtends an angle 70o at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.(\(\pi\) = \(\frac{22}{7}\))
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1997
A chord of a circle of a diameter 42cm subtends an angle of 60o at the centre of the circle. Find the length of the minor arc
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1997
Each of the base angles of an isosceles triangle is 59o, and the vertices of the triangle lie on a circle. Determine the angle at which the base of the triangle subtends at the centre of the circle.
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1997
Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & x \\ 0 & 1 & x\end{vmatrix}\) = 0
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1997
Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)
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1997
If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68
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1997
Two binary operations \(\ast\) and \(\oplus\) are defines as m \(\ast\) n = mn - n - 1 and m \(\oplus\) n = mn + n - 2 for all real numbers m, n.Find the value of 3 \(\oplus\) (4 \(\ast\) 50)
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1997
The nth term of a sequence is given by \(3^{1-n}\), find the sum of the first three terms of the sequence.
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1997
The sum of the first n terms of a series is given by \(S_n=n^2-1\). For \(n\ge2\), find the nth term.
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1997
Find the range of values of x which satisfies the inequality 12x2
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1997
Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1.
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1997
Find the value of k if \(\frac{5 + 2r}{(r + 1)(r - 2)}\) expressed in partial fraction is \(\frac{k}{r - 2}\) + \(\frac{L}{r + 1}\) where K and L are constants
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1997
What value of g will make the expression 4x2 - 18xy + g a perfect square?
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1997
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
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1997
Find the minimum value of X2 - 3x + 2 for all real values of x
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1997
Solve the simultaneous equations \(\frac{2}{x} - {\frac{2}{x}}\) = 2, \(\frac{4}{x} + {\frac{3}{y}}\) = 10
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1997
If the function f(x) = x3 + 2x2 + qx - 6 is divisible by x + 1, find q
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1997
A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both languages. How many students speak neither Hausa nor Igbo?
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1997
If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find (X ∩ Y) ∪ Z
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