YEAR 12 - MATH QUIZ

When Bermuda (B) , Puerto Rico(P) , and Miami (M) are joined on a map using straight lines, a triangle is formed. This triangle is known as the Bermuda triangle.

According to the map, the distance (MB) is 1650 KM, the distance MP is 1500 KM and angle BMP is 57º. The distance from Bermuda to Puerto Rico and the area of the Bermuda triangle are:

• 1510 km, 980 456 km²

• 1600 km, 4500 Km²

• 1510 km, 1 040 000 km²

• 1600 km, 1 368 982

In the following diagram, ABCD is the square base of a right pyramid with vertex V. The centre of the base is O. The diagonal of the base, AC, is 8 cm long. The sloping edges are 10 cm long.

The size of the angle that the sloping edge makes with the base of the pyramid and the area of the triangle CAV are:

• $\theta=66.42º\ ,\ area=\ 36.7\ cm^2$

• $\theta=0.4\ ,\ area\ =\ 40\ cm^2$

• $\theta=33.2º,\ area\ =\ 18.3\ cm^2$

• $\theta=45º,\ area=\ 72\ cm^2$

Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48°. Find the size of angle APB.

• $\theta=0.99$

• $\theta=48º$

• $\theta=82.2º$

• $\theta=66º$

Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.The information is shown on the diagram. The area of ABCD. is

• 4460 m²

• 1680 m²

• 93 m²

• 2594 m²

The diagram shows a triangle ABC . The size of angle CAB  is 55º and the length of AM is 10m, where M  is the midpoint of AB. Triangle CMB is isosceles with CM=MB. Find the length of CB .

• 16.4 m

• 8.1 m

• 4.5 m

• 12 m

The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of solid stone. The sides of the base are 230 m long. The diagram below represents this pyramid, labelled VABCD.

V is the vertex of the pyramid. O is the centre of the base, ABCD. M is the midpoint of AB . Angle ABV is 58.3º. Calculate the height of the pyramid, VO.

• 58 m

• 130 m

• 146 m

• 200 m