Matura (czerwiec 2012, poziom podstawowy, dodatkowy)

$1$1

$-1$-1

$7+4\sqrt{5}$7+4\sqrt{5}

$9+4\sqrt{5}$9+4\sqrt{5}

$1$1 i $-4$-4

$1$1 i $2$2

$-1$-1 i $4$4

$-2$-2 i $2$2

dwa rozwiązania: $x=-5$x=-5, $x=3$x=3.

dwa rozwiązania: $x=-3$x=-3, $x=5$x=5.

cztery rozwiązania: $x=-5,\ x=-1,\ x=1,\ x=3$x=-5,\ x=-1,\ x=1,\ x=3.

cztery rozwiązania: $x=-3,\ x=-1,\ x=1,\ x=5$x=-3,\ x=-1,\ x=1,\ x=5.

$45\ \text{zł}$45\ \text{zł}

$2000\ \text{zł}$2000\ \text{zł}

$200\ 000\ \text{zł}$200\ 000\ \text{zł}

$450\ 000\ \text{zł}$450\ 000\ \text{zł}

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

$\left(0,-2\right)$\left(0,-2\right)

$\left(-2,0\right)$\left(-2,0\right)

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

$21^\circ$21^\circ i $105^\circ$105^\circ

$11^\circ$11^\circ i $66^\circ$66^\circ

$18^\circ$18^\circ i $108^\circ$108^\circ

$16^\circ$16^\circ i $96^\circ$96^\circ

$2\sqrt{3}$2\sqrt{3}

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

$6\sqrt{3}$6\sqrt{3}

$12$12

$3\ \text{cm}$3\ \text{cm}

$4\ \text{cm}$4\ \text{cm}

$5\ \text{cm}$5\ \text{cm}

$8\ \text{cm}$8\ \text{cm}

$150^\circ$150^\circ

$120^\circ$120^\circ

$115^\circ$115^\circ

$85^\circ$85^\circ

$ABF$ABF

$CAB$CAB

$IHD$IHD

$ABD$ABD

$\left(x-2\right)^2+\left(y-1\right)^2=9$\left(x-2\right)^2+\left(y-1\right)^2=9

$\left(x-2\right)^2+\left(y-1\right)^2=3$\left(x-2\right)^2+\left(y-1\right)^2=3

$\left(x+2\right)^2+\left(y+1\right)^2=9$\left(x+2\right)^2+\left(y+1\right)^2=9

$\left(x+2\right)^2+\left(y+1\right)^2=3$\left(x+2\right)^2+\left(y+1\right)^2=3

$\displaystyle \frac{x^2+15x+1}{\left(x-2\right)\left(x+3\right)}$\displaystyle \frac{x^2+15x+1}{\left(x-2\right)\left(x+3\right)}

$\displaystyle \frac{x+2}{\left(x-2\right)\left(x+3\right)}$\displaystyle \frac{x+2}{\left(x-2\right)\left(x+3\right)}

$\displaystyle \frac{x}{\left(x-2\right)\left(x+3\right)}$\displaystyle \frac{x}{\left(x-2\right)\left(x+3\right)}

$\displaystyle \frac{x+2}{-5}$\displaystyle \frac{x+2}{-5}

$a_8=2\sqrt{5}$a_8=2\sqrt{5}

$a_8=8$a_8=8

$a_8=5\sqrt{2}$a_8=5\sqrt{2}

$a_8=\sqrt{12}$a_8=\sqrt{12}

$a=8\sqrt{2}$a=8\sqrt{2}

$a=4\sqrt{2}$a=4\sqrt{2}

$a=8-2\sqrt{2}$a=8-2\sqrt{2}

$a=8+2\sqrt{2}$a=8+2\sqrt{2}

$\alpha<30^\circ$\alpha<30^\circ

$\alpha=30^\circ$\alpha=30^\circ

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

$\alpha>45^\circ$\alpha>45^\circ

$a=2$a=2

$a=-2$a=-2

$a=4$a=4

$a=-4$a=-4

$B=\left(5,11\right)$B=\left(5,11\right)

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

$B=\displaystyle \left( -\frac{3}{2},-5\right)$B=\displaystyle \left( -\frac{3}{2},-5\right)

$B=\left(3,11\right)$B=\left(3,11\right)

$3$3

$3{,}5$3{,}5

$4$4

$5$5

$a=14$a=14

$a=7\sqrt{2}$a=7\sqrt{2}

$a=7$a=7

$a=2\sqrt{2}$a=2\sqrt{2}

$96\pi$96\pi

$48\pi$48\pi

$32\pi$32\pi

$8\pi$8\pi

$0{,}12$0{,}12

$0{,}18$0{,}18

$0{,}6$0{,}6

$0{,}9$0{,}9

$r+h=a$r+h=a

$\displaystyle h-r= \frac{a}{2}$\displaystyle h-r= \frac{a}{2}

$\displaystyle r-h= \frac{a}{2}$\displaystyle r-h= \frac{a}{2}

$r^2+h^2=a^2$r^2+h^2=a^2