Onderstaand overzicht volgt de nummering en de opgaven van de derde editie.
[antwoorden eerste editie | antwoorden tweede editie]
| a. $\mathbb{Z}$ | b. $\mathbb{R}$ | c. $\mathbb{Q}$ | d. $\mathbb{N}$ | e. $\mathbb{Z}$ | f. $\mathbb{R}$ |
| a. $\displaystyle \frac{1}{3}$ | b. $\displaystyle 1$ | c. $\displaystyle 4$ | d. $\displaystyle \frac{43}{30}$ |
Het repeterend gedeelte wordt overlijnd aangeduid.
| a. $\displaystyle 0{,}1\overline{6}$ | b. $\displaystyle 0{,}\overline{7}$ | c. $\displaystyle 0{,}0\overline{6}$ | d. $\displaystyle 3{,}\overline{142857}$ |
| a. $\displaystyle \frac{4}{9}$ | b. $\displaystyle \frac{5}{3}$ | c. $\displaystyle \frac{3}{22}$ | d. $\displaystyle \frac{374}{333}$ |
| a. $\displaystyle 123=8.14+11$ | c. $\displaystyle 54321=441.123+78$ |
| b. $\displaystyle 6465=73.88+41$ | d. $\displaystyle 80400=236.340+160$ |
| a. $\displaystyle 15=3.5$ | c. $\displaystyle 30=2.3.5$ | e. $\displaystyle 120=2^3.3.5$ |
| b. $\displaystyle 24=2^3.3$ | d. $\displaystyle 84=2^2.3.7$ | f. $\displaystyle 330=2.3.5.11$ |
| a. | $\displaystyle \mbox{kgv}(8,24)=24$ | $\displaystyle \mbox{ggd}(8,24)=8$ |
| b. | $\displaystyle \mbox{kgv}(15,84)=420$ | $\displaystyle \mbox{ggd}(15,84)=3$ |
| c. | $\displaystyle \mbox{kgv}(84,120)=840$ | $\displaystyle \mbox{ggd}(84,120)=12$ |
| d. | $\displaystyle \mbox{kgv}(24,330)=1320$ | $\displaystyle \mbox{ggd}(24,330)=6$ |
| a. $\displaystyle x>5$ | b. $\displaystyle x \le \frac{13}{6}$ | c. $\displaystyle x \le \frac{1}{5}$ |
| a. $\displaystyle \left\{-5,3\right\}$ | c. $\displaystyle \{ \, \}$ | e. $\displaystyle \left\{ \tfrac{5}{16},\tfrac{7}{8}\right\}$ |
| b. $\displaystyle \left\{ -\tfrac{5}{3},3\right\}$ | d. $\displaystyle \left\{ -5,-\tfrac{1}{3}\right\}$ | f. $\displaystyle \left\{0,\tfrac{2}{5}\right\}$ |
| a. $\displaystyle -5 < x < 3$ | b. $\displaystyle -\tfrac{5}{3} \le x \le 3$ | c. $\displaystyle x \le \tfrac{2}{3} \vee x \ge 2$ |
| a. $\displaystyle |x-6| < 2$ | b. $\displaystyle |x-3| \le \tfrac{3}{2}$ | c. $\displaystyle |x-\tfrac{9}{4}| < \tfrac{11}{4}$ |
| a. $\displaystyle 4$ | f. $\displaystyle 30\sqrt{14}$ | k. $\displaystyle 3$ | |
| b. $\displaystyle 4$ | g. $\displaystyle \tfrac{1}{4}$ | l. $\displaystyle 16$ | |
| c. $\displaystyle \tfrac{1}{16}$ | h. $\displaystyle 68-48\sqrt{2}$ | m. $\displaystyle \tfrac{1}{6}$ | |
| d. $\displaystyle \tfrac{\sqrt{2}}{2}$ | i. $\displaystyle 6$ | ||
| e. $\displaystyle 10000$ | j. $\displaystyle 5^{(5^4)}$ |
| a. $\displaystyle x^{\frac{7}{8}}$ | b. $\displaystyle a^x . b^{2y}$ | c. $\displaystyle \frac{2}{a}$ | d. $\displaystyle \frac{4b}{3a}$ |
| a. $\displaystyle \log 35$ | b. $\displaystyle \log\frac{x^3}{\sqrt{x+1}}$ | c. $\displaystyle \log\frac{2^4.3^5.5}{11^3}$ | d. $\displaystyle 1$ |
| a. $\displaystyle \frac{1}{2}$ | b. $\displaystyle \frac{2}{11}$ | c. $\displaystyle -2$ | d. $\displaystyle 4$ | e. $\displaystyle 0$ | f. $\displaystyle -\frac{11}{4}$ | g. $\displaystyle 5$ |
| a. $\displaystyle 4y$ | b. $\displaystyle \frac{5}{7}y$ | c. $\displaystyle \frac{3}{2}y$ | d. $\displaystyle 2-2y$ |
| a. $\displaystyle 9a^2-24ab+16b^2$ | d. $\displaystyle 27b^3-8a^3$ | |
| b. $\displaystyle 8a^6-12a^4+6a^2-1$ | e. $\displaystyle 3a^2-3b$ | |
| c. $\displaystyle 9a^2-16b^2$ | f. $\displaystyle 33b^4-33a^4$ |
| a. $\displaystyle (a-11)(a+11)$ | g. $\displaystyle (a-1)(b-1)$ | |
| b. $\displaystyle a(a-\sqrt{5}b)(a+\sqrt{5}b)(a^2+5b^2)$ | h. $\displaystyle (2a-b)^3$ | |
| c. $\displaystyle \tfrac{(3a+2b)^2}{100}$ | i. $\displaystyle (a-2)(a^3+4)$ | |
| d. $\displaystyle (\sqrt{3}-a)(\sqrt{3}+a)$ | j. $\displaystyle -(a+b+2)(a+b-2)$ | |
| e. $\displaystyle a^3b^3(2b-3a^2)(9a^4+6a^2b+4b^2)$ | k. $\displaystyle a(a+1)^2$ | |
| f. $\displaystyle \tfrac{a^4}{36}(3a-4)^2$ | l. $\displaystyle a(a-1)(a+2)$ |
| a. $\displaystyle 30$ | c. $\displaystyle 203$ | e. $\displaystyle (27x^2-7)k$ |
| b. $\displaystyle 72$ | d. $\displaystyle\tfrac{k}{6}(41+9k-2k^2)$ | f. $\displaystyle 18$ |
| a. $\displaystyle x^2-2x+2+\frac{1}{x-1}$ | c. $\displaystyle 4x^2+12x+9$ |
| b. $\displaystyle x^3-x^2+x-1$ | d. $\displaystyle x^3-\frac{x^2}{2}-\frac{11x}{4}+\frac{19}{8}-\frac{19}{16(x+0{,}5)}$ |
| a. $\displaystyle \frac{3x}{2}-\frac{23}{4}+\frac{143}{4(2x+5)}$ | b. $\displaystyle -3x^3-3x^2-14x-31-\frac{101x+154}{x^2-x-5}$ |
| a. Nee (de rest is 3) | b. Ja |
| a. $\displaystyle m = -3$ | b. $\displaystyle m = \frac{8}{11}$ |
| a. $\displaystyle (x-1)(x-2)$ | e. $\displaystyle (x-2)(x+1)^2(x-1)^2$ |
| b. $\displaystyle \left(x+\tfrac{11+\sqrt{77}}{2}\right) \left(x+\tfrac{11-\sqrt{77}}{2}\right)$ | f. $\displaystyle (x+\sqrt{2})(x+\sqrt{3})$ |
| c. $\displaystyle \left(x-\tfrac{3}{4}\right) \left(x-\tfrac{5}{6}\right)$ | g. $\displaystyle x(x+1)(x-1)^4$ |
| d. $\displaystyle (x+1)(x-2)(x+3)$ |
| a. $\displaystyle \left\{-\tfrac{1}{2},3 \right\}$ | h. $\displaystyle \left\{3 \right\}$ |
| b. $\displaystyle \left\{ \tfrac{2 \pm \sqrt{10}}{3} \right\}$ | i. $\displaystyle \left\{4 \right\}$ |
| c. $\displaystyle \left\{\pm \sqrt{2} \right\}$ | j. $\displaystyle \left\{-3,\tfrac{7}{4},\tfrac{9}{4} \right\}$ |
| d. $\displaystyle \left\{-2,\tfrac{1}{2},4 \right\}$ | k. $\displaystyle \left\{9 \right\}$ |
| e. $\displaystyle \left\{\sqrt[5]{\tfrac{2}{3}}\right\}$ | l. $\displaystyle \left\{2 \right\}$ |
| f. $\displaystyle \left\{-2,\pm 1, 3 \right\}$ | m. $\displaystyle \left\{8 \right\}$ |
| g. $\displaystyle \left\{13,\tfrac{5 \pm \sqrt{21}}{2} \right\}$ | n. $\displaystyle \left\{5+\tfrac{\sqrt{31}}{2} \right\}$ |
| a. $\displaystyle \left\{\tfrac{17}{12}\right\}$ | g. $\displaystyle \left\{\tfrac{5}{3}\right\}$ |
| b. $\displaystyle \left\{\tfrac{\log 5-4 \log 7}{3\log 5 + 2 \log 7}\right\}$ | h. $\displaystyle \left\{\tfrac{379}{124}\right\}$ |
| c. $\displaystyle \left\{4\right\}$ | i. $\displaystyle \left\{21^{\tfrac{2}{5}}\right\}$ |
| d. $\displaystyle \left\{0,2\right\}$ | j. $\displaystyle \left\{\sqrt[3]{3}\right\}$ |
| e. $\displaystyle \left\{3\right\}$ | k. $\displaystyle \left\{3,9\right\}$ |
| f. $\displaystyle \left\{-5,-1\right\}$ | l. $\displaystyle \left\{-4,-3,-2,-1,0,8 \right\}$ |
| a. $\displaystyle x \le -1 \vee x \ge 1$ | e. $\displaystyle x \le 2 \vee x \ge 5$ |
| b. $\displaystyle 1 < x < 3$ | f. $\displaystyle x > 0$ |
| c. $\displaystyle x \le -2$ | g. $\displaystyle x < -\tfrac{3}{2} \vee -1 \le x \le 1$ |
| d. $\displaystyle -5 \le x \le 7$ | h. $\displaystyle -3 \le x < -\sqrt{5} \vee -2 \le x \le 1 \vee x > \sqrt{5}$ |
| a. $\displaystyle 3 < x \le \tfrac{17}{5}$ | e. $\displaystyle x > 5$ |
| b. $\displaystyle -1 \le x \le 0 \vee x \ge 1$ | f. $\displaystyle 3-\sqrt{11} \le x < 5 \vee x \ge 3+\sqrt{11}$ |
| c. $\displaystyle x \ge 3$ | g. $\displaystyle -11 \le x \le -4$ |
| d. $\displaystyle x < -1 \vee x >2$ |
De koppels worden in de vorm $(x,y)$ genoteerd.
| a. $\displaystyle \left\{\left(-\tfrac{1}{25},\tfrac{11}{5}\right)\right\}$ | e. $\displaystyle \left\{\left(0,-2\right),\left(-2,0\right)\right\}$ |
| b. $\displaystyle \left\{\left(5+2y,y\right) | y \in \mathbb{R}\right\}$ | f. $\displaystyle \left\{\,\right\}$ |
| c. $\displaystyle \left\{\,\right\}$ | g. $\displaystyle \left\{\left(3,5\right),\left(\tfrac{4}{3},0\right)\right\}$ |
| d. $\displaystyle \left\{\,\right\}$ | d. $\displaystyle \left\{\left(-5,-4\right),\left(-1,-\tfrac{4}{3}\right),\left(1,0\right),\left(2,\tfrac{2}{3}\right)\right\}$ |
| a. $\displaystyle -22+7i$ | f. $\displaystyle -5+2i$ | k. $\displaystyle 28+96i$ |
| b. $\displaystyle 2i$ | g. $\displaystyle \frac{1-i}{2}$ | l. $\displaystyle 2+2i$ |
| c. $\displaystyle 0$ | h. $\displaystyle \frac{-3-11i}{26}$ | m. $\displaystyle \frac{-8-2i}{17}$ |
| d. $\displaystyle 7-i$ | i. $\displaystyle \frac{3-29i}{50}$ | n. $\displaystyle 1$ |
| e. $\displaystyle 4-6i$ | j. $\displaystyle -46-5i$ |
| a. $\displaystyle \left\{\pm \sqrt{3}i\right\}$ | e. $\displaystyle \left\{-1,\frac{-1 \pm \sqrt{15}i}{2}\right\}$ |
| b. $\displaystyle \left\{2 \pm i\right\}$ | f. $\displaystyle \left\{2,3\pm 4i\right\}$ |
| c. $\displaystyle \left\{\frac{3 \pm \sqrt{7}i}{2}\right\}$ | g. $\displaystyle \left\{-3,1,\pm \sqrt{3}i\right\}$ |
| d. $\displaystyle \left\{1 \pm \sqrt{3}i\right\}$ | d. $\displaystyle \left\{\pm i,\pm \sqrt{3}i\right\}$ |
| $\displaystyle w=\tfrac{4}{25}+\tfrac{3}{25}i$ |