Zadania otwarte

KOD UCZNIA
Zadania otwarte/ problems
Instrukcja dla ucznia
1. Wpisz swój kod na każdej kartce.
2. Rozwiązania zadań 1., 2. i 3. zapisz czytelnie i starannie w wyznaczonych
miejscach.
Powodzenia!
Zadanie 1.
Jack has twice as many brothers as sisters and his sister Sophia has five times as many brothers
as sisters. How many children do their parents have? Show all your work. (Show all your
calculations).
KOD UCZNIA
Zadanie 2. (zadanie matura z matematyki PP, sierpień 2014)
In a triangle ABC |AC| > |BC|. Points D and E are located on sides AC and BC, respectively, so
that |CD| = |CE|. Lines AB and DE intersect at point F (see the diagram).
Prove that | ∡BAC| = |∡ABC| - 2· |∡AFD|.
KOD UCZNIA
Zadanie 3.
The pyramid ABDE (see the diagram) is cut out from a cube ABCDEFGH. The edge of the
cube is a units long. Find the ratio of the volume of the pyramid ABDE to the volume of the
rest of the cube. Show all your work.