Matura (maj 2022, poziom podstawowy, Formuła 2015)

$2$2

$1$1

$26$26

$14$14

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

$\displaystyle \frac{13}{6}$\displaystyle \frac{13}{6}

$\displaystyle \frac{6}{13}$\displaystyle \frac{6}{13}

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

$6\log_{4}{10}$6\log_{4}{10}

$16$16

$5$5

$6\log_{4}{16}$6\log_{4}{16}

$98\ 732$98\ 732 zł

$97\ 200$97\ 200 zł

$95\ 266$95\ 266 zł

$94\ 478$94\ 478 zł

$3^2 \cdot \sqrt[4]{3}$3^2 \cdot \sqrt[4]{3}

$\sqrt[4]{3^3}$\sqrt[4]{3^3}

$3^2+\sqrt[4]{3}$3^2+\sqrt[4]{3}

$3^2+\sqrt{3^4}$3^2+\sqrt{3^4}

$x_0>0$x_0>0 i $y_0>0$y_0>0

$x_0>0$x_0>0 i $y_0<0$y_0<0

$x_0<0$x_0<0 i $y_0>0$y_0>0

$x_0<0$x_0<0 i $y_0<0$y_0<0

$(-\infty,0)$(-\infty,0)

$(0, +\infty)$(0, +\infty)

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

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

$\left(-3\right)$\left(-3\right)

$3$3

$0$0

$9$9

$\left(-12\right)$\left(-12\right)

$\left(-8\right)$\left(-8\right)

$0$0

$16$16

$g(x)=f(x)-2$g(x)=f(x)-2

$g(x)=f(x-2)$g(x)=f(x-2)

$g(x)=f(x)+2$g(x)=f(x)+2

$g(x)=f(x+2)$g(x)=f(x+2)

$\left(-3\right)$\left(-3\right)

$\displaystyle \frac{9}{2}$\displaystyle \frac{9}{2}

$5$5

$12$12

$f(x)=3(x-3)^2+2$f(x)=3(x-3)^2+2

$f(x)=3(x+3)^2+2$f(x)=3(x+3)^2+2

$f(x)=(x-3)^2+2$f(x)=(x-3)^2+2

$f(x)=(x+3)^2+2$f(x)=(x+3)^2+2

$\left(-196\right)$\left(-196\right)

$\left(-32\right)$\left(-32\right)

$\left(-26\right)$\left(-26\right)

$\left(-16\right)$\left(-16\right)

$\left(-7\right)$\left(-7\right)

$\left(-19{,}4\right)$\left(-19{,}4\right)

$7$7

$19{,}4$19{,}4

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

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

$\displaystyle \frac{2}{9}$\displaystyle \frac{2}{9}

$\displaystyle \frac{9}{2}$\displaystyle \frac{9}{2}

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

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

$\displaystyle \frac{\sqrt{3}}{2}$\displaystyle \frac{\sqrt{3}}{2}

$1$1

$\displaystyle \frac{\alpha}{2} +\gamma-180^\circ$\displaystyle \frac{\alpha}{2} +\gamma-180^\circ

$\displaystyle 180^\circ- \frac{\alpha}{2}-\gamma$\displaystyle 180^\circ- \frac{\alpha}{2}-\gamma

$180^\circ-\alpha-\gamma$180^\circ-\alpha-\gamma

$\alpha+\gamma-180^\circ$\alpha+\gamma-180^\circ

$6\pi$6\pi

$9\pi$9\pi

$10\pi$10\pi

$12\pi$12\pi

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

$4\sqrt{3}$4\sqrt{3}

$27\sqrt{3}$27\sqrt{3}

$36\sqrt{3}$36\sqrt{3}

$30\sqrt{3}$30\sqrt{3}

$30$30

$60\sqrt{3}$60\sqrt{3}

$60$60

$9$9

$\left(-9\right)$\left(-9\right)

$\left(-4\right)$\left(-4\right)

$4$4

proste $k$k oraz $l$l.

proste $k$k oraz $n$n.

proste $l$l oraz $m$m.

proste $m$m oraz $n$n.

$b=-28$b=-28

$b=-14$b=-14

$b=-24$b=-24

$b=-10$b=-10

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

$4\sqrt{2}$4\sqrt{2}

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

$4\sqrt{7}$4\sqrt{7}

$560 \text{ cm}^3$560 \text{ cm}^3

$280\text{ cm}^3$280\text{ cm}^3

$\displaystyle \frac{280}{3} \text{ cm}^3$\displaystyle \frac{280}{3} \text{ cm}^3

$\displaystyle \frac{560}{3} \text{ cm}^3$\displaystyle \frac{560}{3} \text{ cm}^3

$a^2$a^2

$\displaystyle \frac{3\sqrt{3}}{2} \cdot a^2$\displaystyle \frac{3\sqrt{3}}{2} \cdot a^2

$\displaystyle \frac{3}{2}a^2$\displaystyle \frac{3}{2}a^2

$\displaystyle \frac{3+\sqrt{3}}{2} \cdot a^2$\displaystyle \frac{3+\sqrt{3}}{2} \cdot a^2

$9 \cdot 8 \cdot 7 \cdot 2$9 \cdot 8 \cdot 7 \cdot 2

$9 \cdot 10 \cdot 10 \cdot 1$9 \cdot 10 \cdot 10 \cdot 1

$9 \cdot 10 \cdot 10 \cdot 2$9 \cdot 10 \cdot 10 \cdot 2

$9 \cdot 9 \cdot 8 \cdot 1$9 \cdot 9 \cdot 8 \cdot 1

$x=-1$x=-1

$x=7$x=7

$x=-6$x=-6

$x=6$x=6