Math Survivor ( Final Round )

if  $2x-3y+4x-7y=0,$  then the value of  $\frac{y}{x}$  is:

•  $\frac{3}{5}$  

•  $\frac{5}{3}$  

•  $\frac{5}{11}$  

•  $-\frac{3}{5}$  

A square has two of its vertices on a semicircle and the other two on the diameter of the semicircle as shown. The radius of the circle is 1cm. What is the area of the square?

• $\frac{4}{5}\ cm^2$

• $\frac{\pi}{4}\ cm^2$

• $1\ cm^2$

• $\frac{4}{3}\ cm^2$

• $\frac{2}{\sqrt{3}}cm^2$

The length of a side of one square is 1. what is the minimum distance you walk from "start" to "finish", if we can only move along the sides or diagonals of individual squares?

• $2\sqrt{5}$

• $\sqrt{10}+\sqrt{2}$

• $2+2\sqrt{2}$

• $4\sqrt{2}$

• $6$

The mean score of the students who took a mathematics test was 6. Exactly 60% of the students passes the test. The mean score of the students who passed the test was 8. What was the means score of the students who failed the test?

• $1$

• $2$

• $3$

• $4$

• $5$

M and N are the midpoints of the sides AB and AC of triangle ABC. What is the length of BC.

• $9.6\ cm$

• $10.2\ cm$

• $10.6\ cm$

• $11.2\ cm$

 $If\ x=y^a\ ,\ \ y=z^b\ ,\ \ z=x^c\ ,$  find the value of  $abc$  

•  $1$  

•  $xyz$  

•  $\left(xyz\right)^{abc}$  

•  $0$  

Opposite faces of a die always add to 7. A die rolls on a circuit as represented above. At the starting point (S) the top face is 3. Which will be the top face at the final point (F) ?

• $2$

• $3$

• $4$

• $5$

• $6$

What is the perimeter of the star if you know that the star on the picture is formed by four equal circles with radius 5cm, one square and four equilateral triangles?

• $40\ cm$

• $80\ cm$

• $120\ cm$

• $160\ cm$

• $240\ cm$

In the figure, PQ is parallel to AC. Given that BQ=4 cm, BC=10 cm area of triangle BPQ is 8 cm², find the area of triangle PQC.

• $10\ cm^2$

• $12\ cm^2$

• $16\ cm^2$

• $20\ cm^2$

 $The\ area\ oftriangle\ B\ by\ the\ formula\ \frac{1}{2}\times b\times h$ 

•  $3\ unit^2$  

•  $4\ unit^2$  

•  $5\ unit^2$  

•  $6\ unit^2$