NBT Mathematics Geometry and Trigonometry — Questions and Answers
Question 1: The angles in a triangle are 50 degrees and 60 degrees. What is the third angle?
- 70 degrees (Correct answer)
- 50 degrees
- 110 degrees
- 80 degrees
Correct answer: 70 degrees
Angles in a triangle add to 180 degrees. 180 - 50 - 60 = 70 degrees.
Question 2: A right-angled triangle has legs of 3cm and 4cm. What is the length of the hypotenuse?
- 7cm
- 12cm
- 5cm (Correct answer)
- 6cm
Correct answer: 5cm
By Pythagoras, hypotenuse = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5cm.
Question 3: What is the area of a rectangle that is 8m long and 5m wide?
- 13 m^2
- 26 m^2
- 45 m^2
- 40 m^2 (Correct answer)
Correct answer: 40 m^2
Area of a rectangle = length x width = 8 x 5 = 40 m^2.
Question 4: In a right-angled triangle, sin(theta) is defined as:
- opposite / hypotenuse (Correct answer)
- hypotenuse / opposite
- opposite / adjacent
- adjacent / hypotenuse
Correct answer: opposite / hypotenuse
By definition, sin(theta) = opposite side / hypotenuse (the 'SOH' in SOH-CAH-TOA).
Question 5: What is the value of cos(60 degrees)?
- 0.5 (Correct answer)
- 0
- 0.87
- 1
Correct answer: 0.5
cos(60 degrees) = 0.5, a standard value worth memorising for the NBT Maths paper.
Question 6: Two angles are complementary and one is 35 degrees. What is the other angle?
- 325 degrees
- 145 degrees
- 45 degrees
- 55 degrees (Correct answer)
Correct answer: 55 degrees
Complementary angles add to 90 degrees. 90 - 35 = 55 degrees.
Question 7: The circumference of a circle is given by which formula (r = radius)?
- 2 pi r (Correct answer)
- pi d^2
- r^2 / 2
- pi r^2
Correct answer: 2 pi r
Circumference = 2 pi r (or pi d). The area, by contrast, is pi r^2.
Question 8: A ladder leans against a wall making a 90-degree angle between the wall and the ground. The angle between the ladder and the ground is 65 degrees. What is the angle between the ladder and the wall?
- 15 degrees
- 35 degrees
- 25 degrees (Correct answer)
- 65 degrees
Correct answer: 25 degrees
The three angles of the right triangle sum to 180 degrees: 180 - 90 - 65 = 25 degrees between the ladder and the wall.
NBT Mathematics Geometry and Trigonometry
The angles in a triangle are 50 degrees and 60 degrees.
What is the third angle?