VWO / HAVO Centraal Examen (Netherlands) · Mathematics

Algebra, Polynomials and Functions

11 practice questions, each with the answer and an explanation.

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All 11 questions

What are the exact roots of the polynomial equation $x^{3} - 4 x^{2} + x + 6 = 0$ in the real domain?
What is the remainder when the polynomial $P (x) = 2 x^{4} - 3 x^{2} + 5 x - 7$ is divided by $(x - 2)$ ?
Which expression represents the horizontal asymptote of the rational function $f (x) = \frac{6 x ^{2} - 5 x + 1}{2 x ^{2} + 7 x - 4}$ as $x \to \pm \infty$ ?
What is the exact solution set of the inequality $∣2 x - 5∣ < 7$ for all real numbers $x$ ?
Evaluate the exact numerical value of the expression $lo g_{3} (54) - lo g_{3} (2)$ .
What is the domain of the real-valued function $g (x) = \frac{x - 2}{x + 4}$ ?
What is the sum of all roots of the quadratic equation $3 x^{2} - 12 x + 5 = 0$ according to Vieta's formulas?
If $f (x) = 2 x - 3$ and $g (x) = x^{2} + 1$ , what is the composite function $(g \circ f) (x)$ in standard polynomial form?
What is the exact value of the limit $lim_{x \to 0} \frac{s i n ( 5 x )}{2 x}$ ?
For which value of the parameter $k$ does the linear system $2 x + k y = 6$ and $4 x + 6 y = 12$ have infinitely many solutions?
What is the inverse function of the strictly increasing function $f (x) = ln (x - 1) + 2$ for $x > 1$ ?

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