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Mathematics Past Questions

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90 questions JAMB 2359 WAEC 1853 NECO 179 POST_UTME 6 CUSTOM 10

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Past Questions

90 questions

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Question 31

jamb 1997

The angle of elevation of a building from a measuring instrument placed on the ground is 30o. If the building is 40m high, how far is the instrument from the foot of the building?

A\(\frac{20}{√3}\)m

B\(\frac{40}{√3}\)m

C20√3m

D40√3m

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Question 32

jamb 1997

Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

A3√10

B3√5

C√26

D√13

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Question 33

jamb 1997

A point P moves so that its equidistant from point L and M. If LM is16cm, find the distance of P from LM when P is 10cm from L

A12cm

B10cm

C8cm

D6cm

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Question 34

jamb 1997

The angle between the positive horizontal axis and a given line is 135^o. Find the equation of the line if it passes through the point (2,3)

Ax - y = 1

Bx + y = 1

Cx + y = 5

Dx - y = 5

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Question 35

jamb 1997

A cone with a sector angle of 45° is cut out of a circle of radius r cm. Find the base radius of the cone.

A\(\frac{r}{16}\) cm

B\(\frac{r}{6}\) cm

C\(\frac{r}{8}\) cm

D\(\frac{r}{2}\) cm

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Question 36

jamb 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.(\(\pi\) = \(\frac{22}{7}\))

A22cm²

B44cm²

C66cm²

D88cm²

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Question 37

jamb 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 mirror arc

A22cm

B44cm

C110cm

D220cm

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Question 38

jamb 1997

Each of the base angles of a isosceles triangle is 58° and the verticles of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.

A128^o

B16^o

C64^o

D58^o

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Question 39

jamb 1997

Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x\end{vmatrix}\) = 0

C√3

D√2

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Question 40

jamb 1997

Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)

D12

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Question 41

jamb 1997

If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68

A24

B22

C-12

D-21

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Question 42

jamb 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 \(\ast\) 5)

A60

B57

C54

D42

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Question 43

jamb 1997

The nth term of a sequence is given \(3^{1 - n}\), find the sum of the first three terms of the sequence.

A\(\frac{13}{9}\)

C\(\frac{1}{3}\)

D\(\frac{1}{9}\)

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Question 44

jamb 1997

Sn is the sum of the first n terms of a series given by Sn = n\(^2\) - 1. Find the nth term

A4n + 1

B4n - 1

C2n + 1

D2n - 1

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Question 45

jamb 1997

Find the range of values of x which satisfies the inequality 12x² < x + 1

A-\(\frac{1}{4}\) < x < \(\frac{1}{3}\)

B\(\frac{1}{4}\) < x < -\(\frac{1}{3}\)

C-\(\frac{1}{3}\) < x < \(\frac{1}{4}\)

D-\(\frac{1}{4}\) < x < - \(\frac{1}{3}\)

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Question 46

jamb 1997

Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1

Ax < - \(\frac{3}{4}\)

Bx > - \(\frac{4}{3}\)

Cx > - \(\frac{3}{4}\)

Dx > - 12

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Question 47

jamb 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

D-1

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Question 48

jamb 1997

What value of g will make the expression 4x² - 18xy + g a perfect square?

B\(\frac{9y^2}{4}\)

C81y^2

D\(\frac{18y^2}{4}\)

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Question 49

jamb 1997

Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)

A\(\frac{gv-t^2}{gt^2}\)

B\(\frac{gt^2}{gv-t^2}\)

C\(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)

D\(\frac{gv}{t^2 - g}\)

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Question 50

jamb 1997

Find the minimum value of X² - 3x + 2 for all real values of x

A-\(\frac{1}{4}\)

B-\(\frac{1}{2}\)

C\(\frac{1}{4}\)

D\(\frac{1}{2}\)

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