B

1003029104

Level: 
B
Find the domain of the expression on the left side of the inequality. \[ \frac{x^3-x^2+1}{\left(x^2+9\right)\left(x^3-1\right)}>0 \]
\( \mathbb{R}\setminus\left\{1\right\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus\left\{\pm1\right\} \)
\( \mathbb{R}\setminus\left\{\pm3;\pm1\right\} \)

1003029103

Level: 
B
Find the domain of the expression on the left side of the inequality. \[\frac{x^4}{x^2\left(x^5-1\right)\left(2x^2-4\right)}\leq0 \]
\( \mathbb{R}\setminus\left\{0;1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{\pm1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{0;\pm1;\pm\sqrt2\right\}\)

1003024604

Level: 
B
Without using a calculator, identify which of the following values is the greatest one.
the number of ordered arrangements of \( 5 \) objects taking \( 3 \) at a time
the number of unordered selections of \( 3 \) objects out of \( 5 \) different kinds with repetition allowed
the number of ordered arrangements of \( 5 \) objects in which \( 3 \) are identical
the number of unordered selections of \( 3 \) objects out of \( 5 \) objects

1103021413

Level: 
B
The area of a rectangular trapezium is \( 35\,\mathrm{cm}^2 \). The bases have lengths of \( 6\,\mathrm{cm} \) and \( 8\,\mathrm{cm} \). Express the measure of the angle between the longer base and the longer arm of the trapezium. Round the result to one decimal place.
\( 68.2^{\circ} \)
\( 23.6^{\circ} \)
\( 66.4^{\circ} \)
\( 39.3^{\circ} \)

1103021412

Level: 
B
The figure shows a rectangular trapezium whose bases have lengths of \( 21\,\mathrm{cm} \) and \( 15\,\mathrm{cm} \), and the longer arm is \( 10\,\mathrm{cm} \) long. Calculate the sine of the smallest interior angle of the trapezium.
\( 0.8 \)
\( 0.6 \)
\( 53.13^{\circ} \)
\( 36.87^{\circ} \)