Quadratic equations and inequalities

9000025603

Level:

In the following list identify an equation equivalent to the following quadratic equation. \[ 2(x - 8)\left (x + \frac{1} {2}\right ) = 0 \]

$2x^{2} - 15x - 8 = 0$

$2x^{2} - 8x + \frac{1} {2} = 0$

$8x^{2} - 15x + \frac{1} {2} = 0$

$8x^{2} - 8x - 1 = 0$

9000025604

Level:

In the following list identify an equation which does not have solution in the set of real numbers.

$8x^{2} - x + 1 = 0$

$8x^{2} + 8x - 1 = 0$

$8x^{2} - 8x + 1 = 0$

$8x^{2} - x - 1 = 0$

9000025605

Level:

Find the interval which contains all the solutions of the following quadratic equation. \[ \text{$5x^{2} - 3x - 2 = 0$} \]

$(-0.5;2)$

$[ - 1;0] $

$[ 0;4)$

$[ - 3;1)$

9000025606

Level:

In the following list identify a quadratic equation which has a unique solution.

$x^{2} + 2x + 1 = 0$

$x^{2} - 3x - 1 = 0$

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

$x^{2} - 3x + 1 = 0$

9000025607

Level:

In the following list identify a quadratic equation which cannot be factorized in $\mathbb{R}$.

$- 7x^{2} + 3x - 1 = 0$

$5x^{2} + 2x - 3 = 0$

$- 3x^{2} + 2x + 3 = 0$

$6x^{2} + 3x - 1 = 0$

9000025609

Level:

In the following list identify an equation such that one of the solutions equals $- 1$.

$5x^{2} + 2x - 3 = 0$

$5x^{2} - 2x - 3 = 0$

$5x^{2} + 2x + 3 = 0$

$5x^{2} - 2x + 3 = 0$

On their birthday students bring candies for their classmates. The birthday person gives a candy to every other student, not to himself or herself. During a year, $ 650 $ candies have been given away. Find out how many students are there in the class. (Note: All students’ birthdays were on school days.)

$ 26 $

$ 25 $

$ 27 $

$ 24 $

1003085402

Level:

The product of two consecutive even numbers is $ 2 808 $. Find their sum.

$ 106 $

$ 104 $

$ 102 $

$ 108 $

1003085407

Level:

If the area of the square is increased by $ 64\% $, by what percentage the length of its side is increased? Round the result to an integer.

$ 28 $

$ 8 $

$ 32 $

$ 16 $

1003085409

Level:

The area of the rectangle is $ 1\,269\,\mathrm{cm}^2 $. Its length is by $ 20\,\mathrm{cm} $ longer than its width. Find the sum of the length and the width of the rectangle.

$ 74\,\mathrm{cm} $

$ 35\,\mathrm{cm} $

$ 27\,\mathrm{cm} $

$ 57\,\mathrm{cm} $

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Quadratic equations and inequalities

9000025603

9000025604

9000025605

9000025606

9000025607

9000025609

1003085401

1003085402

1003085407

1003085409

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