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1003024002

Level:

The equation of an ellipse is given by \( \frac{x^2}{48} +\frac{y^2}{36} = 1\). The point \( [-2,5] \) represents:

a point inside the ellipse

vertex of the ellipse

co-vertex of the ellipse

a point outside the ellipse

the centre of the ellipse

1003030107

Level:

Solve. \[ \sqrt[2x+6]{9^{x+2}}=\sqrt[6]{243}\]

\( x=3 \)

\( x=-8 \)

\( x=\frac{-24}7 \)

\( x=-3 \)

1003030106

Level:

How many solutions does the following equation have? \[ 2^x\cdot5^x=100^{3-x} \]

Exactly one solution

No solutions

Infinitely many solutions

Exactly two solutions

1003030105

Level:

How many solutions does the following equation have? \[ \sqrt{81^{x+1}}=3^{2x}\]

No solutions

Infinitely many solutions

Exactly one solution

Exactly two solutions

1003030104

Level:

Decide which of the following intervals contains \( d \), if \( \left(0.1^{d-1}\right)^3=10^{d-1} \).

\( [-1,3] \)

\( [9,13] \)

\( [4,8] \)

\( [-6,-2] \)

1003030103

Level:

Solve. \[ 8^{2x}=16\sqrt[3]4\]

\( x=\frac79 \)

\( x=\frac{11}{12} \)

\( x=\frac49 \)

\( x=\frac13 \)

1003030102

Level:

Solve. \[ 5^{8-2x}=1\]

\( x=4 \)

\( x=-4 \)

\( x=\frac72 \)

The equation has no solution.

1003030101

Level:

Solve. \[ 2^x=-4\]

The equation has no solution.

\( x=2 \)

\( x=-2 \)

\( x=-\frac12 \)

1003037306

Level:

The ratio of two more than five times \( x \) and five is equal to the sum of \( x \) and \( a \). Determine \( a \).

\( 0.4 \)

It is not possible to determine the number \( a \) uniquely without knowing the number \( x \).

\( 2 \)

\( 10 \)

Suppose we increase the numerator of five-ninth by an integer and we decrease the denominator of five-ninth by the same integer. We get the fraction with numerator six times greater than the denominator. Find the integer.

\( 7 \)

\( 3 \)

There is no such an integer.

\( 1 \)

A

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