Free Printable OGUN STATE JUNIOR OLYMPIAD FINALS MATHEMATICS

1.

Simplify $\sqrt{\left(-\frac{1}{64}\right)^{-\frac{2}{3}}}$

a)

−4

b)

$−\frac{1}{4}$

c)

$−\frac{1}{8}$

d)

4

e)

$\frac{1}{8}$

2.

Given that $\log_{9}\,y^{\frac{1}{2}}=\log_{5}\,125$ , find the value of y.

a)

16

b)

25

c)

36

d)

64

e)

81

3.

If $\log_{9}3+2x=1$ find $x$ .

a)

$-\frac{1}{2}$

b)

$-\frac{1}{4}$

c)

3/4

d)

$\frac{1}{2}$

e)

$\frac{1}{3}$

4.

Solve the equation $\sqrt{x+3}-\sqrt{x}=1$ .

a)

−3

b)

−2

c)

−1

d)

1

e)

2

5.

Given that the equation $x^{2}+6x+13-k\,(x^{2}-5)=0$ has equal roots, find the possible values of the constant $k$ .

a)

$\frac{2}{5}$ or $-2$

b)

$\frac{5}{2}$ or $-\frac{1}{2}$

c)

$-\frac{5}{2}$ or $-2$

d)

$-2$ or $10$

e)

$-10$ or $5$

6.

The roots of $x^{2}+5x-7=0$ are $\alpha$ and $\beta$ , find the equation whose roots are $\alpha^{2}$ and $\beta^{2}$ .

a)

$x^{2}+25x+49=0$

b)

$x^{2}+11x+49=0$

c)

$x^{2}-11x-49=0$

d)

$x^{2}-39x+49=0$

e)

$x^{2}-12x-49=0$

7.

A line is perpendicular to $3x-y+11=0$ and passes through the point $(1,-5)$ , find its equation.

a)

$3y-x-14=0$

b)

$3x+y+1=0$

c)

$3y+x+1=0$

d)

$3y+x+14=0$

e)

$3y+x-1=0$

8.

The equation of a circle is $3x^{2}+3y^{2}-6x+16y+23=0$ , find its radius.

a)

1

b)

$\sqrt{3}$

c)

$\sqrt{11}$

d)

6

e)

3

9.

Find the possible values of the constant $m$ for which the curve $|m+5|\,x^{2}+|m^{2}-1|\,y^{2}+2x-5y+5=0$ is a circle.

a)

2 and 3

b)

2 and −3

c)

−2 and −3

d)

−2 ∧ −3

e)

−2 and 3

10.

The end-points of the diameter of a circle are $(-1,-2)$ and $(-3,2)$ , find the equation of the circle.

a)

$x^{2}+y^{2}-2x+4y=0$

b)

$x^{2}+y^{2}-2x-4y=0$

c)

$x^{2}+y^{2}+4x-1=0$

d)

$x^{2}+y^{2}+4x-21=0$

e)

$x^{2}+y^{2}+4x-5=0$

11.

Differentiate $y=\iota$ with respect to $x$ .

a)

$12\,\iota$

b)

$24\,\iota$

c)

$12x\,\iota$

d)

$24x\,\iota$

e)

$16\,\iota$

12.

If $y^{2}+xy-x=0$ , find $\frac{dy}{dx}$ .

a)

$\frac{1-y}{2y}$

b)

$\frac{1-y}{2y}$

c)

$\frac{1-2y}{x}$

d)

$\frac{1-y}{x+2y}$

e)

$\frac{1+y}{x-2y}$

13.

If $f(x)=\iota$ is defined on the set of real number $\mathbb{R}$ , find the gradient of $f(x)$ at $x=\frac{1}{2}$ .

a)

4.0

b)

6.0

c)

6.5

d)

10.6

e)

5.5

14.

In the diagram below, O is the centre of the circle. If AN is a tangent at M and ∠AMQ = 64°, calculate the value of angle P.

a)

128°

b)

64°

c)

52°

d)

32°

e)

26°

15.

Make r the subject of the relation $v=P\left[1+\frac{r}{100}\right]^t$ .

a)

$100\left(\sqrt{\frac{v}{p}}-1\right)$

b)

$\sqrt{\frac{v}{p}}-1$

c)

$\sqrt{\frac{v}{p}}$

d)

$\sqrt{\frac{v}{p}}+2$

e)

$100\sqrt{\frac{v}{p}}-1$

16.

The base of a triangle is 3cm longer than its height. If the area is 44cm², find the length of its base.

a)

8cm

b)

11cm

c)

12cm

d)

15cm

e)

20cm

17.

A sector of a circle of radius 14cm subtends an angle of 135° at the centre of the circle. What is the perimeter of the sector? (Take $\pi=\frac{22}{7}$ )

a)

47cm

b)

51cm

c)

56cm

d)

88cm

e)

231cm

18.

Which of the angle(s) is/are equal to ∠WZX in the diagram below? I. ∠WVX; II. ∠WYX; III. ∠WVZ.

a)

I only

b)

II only

c)

III only

d)

I & II only

e)

II & III only

19.

Find the 7th term of the geometric progression 4, 12, 36, ….

a)

365

b)

729

c)

1458

d)

2916

e)

4374

20.

The sum of the first three terms of an A.P. is 12. If its 4th term is 8, find its common difference.

a)

2

b)

4

c)

6

d)

8

e)

12

OGUN STATE JUNIOR OLYMPIAD FINALS MATHEMATICS

Total questions: 20

Worksheet time: 15mins

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