Matura (sierpień 2022, poziom podstawowy, poprawka)

$4^{-4}$4^{-4}

$4^{-50}$4^{-50}

$2^{-47}$2^{-47}

$2^{-130}$2^{-130}

$2$2

$14$14

$16$16

$24$24

$25+4\sqrt{3}$25+4\sqrt{3}

$25-4\sqrt{3}$25-4\sqrt{3}

$37+20\sqrt{3}$37+20\sqrt{3}

$37-20\sqrt{3}$37-20\sqrt{3}

$0{,}36 \cdot x$0{,}36 \cdot x złotych

$0{,}44 \cdot x$0{,}44 \cdot x złotych

$0{,}50 \cdot x$0{,}50 \cdot x złotych

$0{,}56 \cdot x$0{,}56 \cdot x złotych

$1$1

$\left(-1\right)$\left(-1\right)

$5$5

$\left(-5\right)$\left(-5\right)

$\displaystyle \left(-\infty,- \frac{3}{4} \right)$\displaystyle \left(-\infty,- \frac{3}{4} \right)

$\displaystyle \left(- \frac{3}{4},+\infty \right)$\displaystyle \left(- \frac{3}{4},+\infty \right)

$\displaystyle \left(-\infty,- \frac{3}{16} \right)$ \displaystyle \left(-\infty,- \frac{3}{16} \right)

$\displaystyle \left(- \frac{3}{16},+\infty\right)$\displaystyle \left(- \frac{3}{16},+\infty\right)

$\displaystyle \left(- \frac{7}{2} \right)$\displaystyle \left(- \frac{7}{2} \right)

$\displaystyle \left(- \frac{1}{2} \right)$\displaystyle \left(- \frac{1}{2} \right)

$\displaystyle \frac{1}{2}$\displaystyle \frac{1}{2}

$1$1

$m=-4$m=-4

$m=-2$m=-2

$m=0$m=0

$m=4$m=4

$\displaystyle m> \frac{2}{5}$\displaystyle m> \frac{2}{5}

$m>2{,}5$m>2{,}5

$m>0$m>0

$m>2$m>2

$b=-4,c=8$b=-4,c=8

$b=4,c=-8$b=4,c=-8

$b=-4,c=-8$b=-4,c=-8

$b=4,c=8$b=4,c=8

$\displaystyle \left(-\infty, \frac{1}{2} \right]$\displaystyle \left(-\infty, \frac{1}{2} \right]

$\left(-1,2\right)$\left(-1,2\right)

$\displaystyle \left(0, \frac{5}{2} \right)$\displaystyle \left(0, \frac{5}{2} \right)

$\displaystyle \left[ \frac{5}{2},+\infty \right)$\displaystyle \left[ \frac{5}{2},+\infty \right)

$\left[0,2\right)$\left[0,2\right)

$\left[-1,6\right)$\left[-1,6\right)

$\left[-3,4\right)$\left[-3,4\right)

$\left[1,3\right)$\left[1,3\right)

jest wyrazem ciągu $\left(a_n\right)$\left(a_n\right) i jest wyrazem ciągu $\left(b_n\right)$\left(b_n\right).

jest wyrazem ciągu $\left(a_n\right)$\left(a_n\right) i nie jest wyrazem ciągu $\left(b_n\right)$\left(b_n\right).

nie jest wyrazem ciągu $\left(a_n\right)$\left(a_n\right) i jest wyrazem ciągu $\left(b_n\right)$\left(b_n\right).

nie jest wyrazem ciągu $\left(a_n\right)$\left(a_n\right) i nie jest wyrazem ciągu $\left(b_n\right)$\left(b_n\right).

$1$1

$11$11

$21$21

$31$31

$800$800

$900$900

$1000$1000

$1500$1500

$\displaystyle \frac{\sqrt{5}}{5}$\displaystyle \frac{\sqrt{5}}{5}

$\displaystyle \frac{2\sqrt{5}}{5}$\displaystyle \frac{2\sqrt{5}}{5}

$\displaystyle \frac{1}{2}$\displaystyle \frac{1}{2}

$2$2

$\displaystyle \sin\alpha= \frac{1}{3}$\displaystyle \sin\alpha= \frac{1}{3} i $\displaystyle \cos\alpha= \frac{2}{3}$ \displaystyle \cos\alpha= \frac{2}{3}

$\displaystyle \sin\alpha= \frac{5}{13}$\displaystyle \sin\alpha= \frac{5}{13} i $\displaystyle \cos\alpha= \frac{12}{13}$ \displaystyle \cos\alpha= \frac{12}{13}

$\displaystyle \sin\alpha= \frac{3}{5}$\displaystyle \sin\alpha= \frac{3}{5} i $\displaystyle \cos\alpha= \frac{4}{5}$ \displaystyle \cos\alpha= \frac{4}{5}

$\displaystyle \sin\alpha= \frac{9}{15}$\displaystyle \sin\alpha= \frac{9}{15} i $\displaystyle \cos\alpha= \frac{12}{15}$ \displaystyle \cos\alpha= \frac{12}{15}

$30^\circ$30^\circ

$40^\circ$40^\circ

$50^\circ$50^\circ

$60^\circ$60^\circ

$\alpha=40^\circ$\alpha=40^\circ

$\alpha=45^\circ$\alpha=45^\circ

$\alpha=50^\circ$\alpha=50^\circ

$\alpha=60^\circ$\alpha=60^\circ

$4\sqrt{5}$4\sqrt{5}

$4\sqrt{10}$4\sqrt{10}

$80$80

$160$160

$\displaystyle m=- \frac{5}{4}$\displaystyle m=- \frac{5}{4}

$\displaystyle m=- \frac{1}{4}$\displaystyle m=- \frac{1}{4}

$\displaystyle m= \frac{5}{6}$\displaystyle m= \frac{5}{6}

$\displaystyle m= \frac{5}{4}$\displaystyle m= \frac{5}{4}

$\displaystyle \left(- \frac{1}{2}, \frac{1}{2} \right)$\displaystyle \left(- \frac{1}{2}, \frac{1}{2} \right)

$\displaystyle \left( \frac{1}{2},- \frac{3}{2} \right)$\displaystyle \left( \frac{1}{2},- \frac{3}{2} \right)

$\left(-1,2\right)$\left(-1,2\right)

$\left(-1,1\right)$\left(-1,1\right)

$3\sqrt{5}$3\sqrt{5}

$4\sqrt{5}$4\sqrt{5}

$6\sqrt{5}$6\sqrt{5}

$8\sqrt{5}$8\sqrt{5}

$y=2x-5$y=2x-5

$y=-2x-5$y=-2x-5

$y=-2x+5$y=-2x+5

$y=2x+5$y=2x+5

trójkąt.

pięciokąt.

siedmiokąt.

ośmiokąt.

$10$10

$20$20

$25$25

$30$30

$6 \cdot 10 \cdot 10$6 \cdot 10 \cdot 10

$3 \cdot 10 \cdot 10$3 \cdot 10 \cdot 10

$6 \cdot 5 \cdot 5$6 \cdot 5 \cdot 5

$3 \cdot 5 \cdot 5$3 \cdot 5 \cdot 5

$\displaystyle p= \frac{1}{18}$\displaystyle p= \frac{1}{18}

$\displaystyle p= \frac{1}{6}$\displaystyle p= \frac{1}{6}

$\displaystyle p= \frac{1}{3}$\displaystyle p= \frac{1}{3}

$\displaystyle p= \frac{2}{3}$\displaystyle p= \frac{2}{3}