EmSAT EmSAT Mathematics 5

Question 1

What is the formula for the area of a circle?

Accepted Answer

πr²

Answer

The area of a circle with radius r is A = πr². The circumference (perimeter) is 2πr, not the area.

Question 2

In a right triangle, if one leg is 3 and the other is 4, what is the hypotenuse?

Accepted Answer

5

Answer

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5. This is the classic 3-4-5 right triangle.

Question 3

What is sin(30°)?

Accepted Answer

1/2

Answer

sin(30°) = 1/2. This is a standard trigonometric value. In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse.

Question 4

What does the cosine rule state?

Accepted Answer

c² = a² + b² − 2ab·cos(C)

Answer

The cosine rule is c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem to non-right triangles.

Question 5

Convert 90° to radians.

Accepted Answer

π/2

Answer

To convert degrees to radians, multiply by π/180. 90 × π/180 = π/2 radians.

EmSAT Practice Test