10 Questions
If the perimeter and the area of a circle are numerically equal, what is the radius of the circle?
π units
In a locality, a single circular park is proposed to be built equal in area to the sum of areas of two circular parks with diameters 16 m and 12 m. What will be the radius of the new park?
15m
Given that sin θ = 1/2√3, what is cos θ?
a/√(b^2 - a^2)
In a right triangle, the length of the hypotenuse is 13 cm and one of the angles is 30 degrees. What is the length of the side opposite the 30-degree angle?
7$\sqrt{3}$ cm
If the speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h, what is the time taken to travel 24 km upstream?
3 hours
If two water taps can fill a tank in 9 hours together, with the larger tap taking 8 hours less than the smaller tap to fill the tank alone, how long would it take for the smaller tap to fill the tank on its own?
24 hours
In a circle with centre O, chord AB makes an angle of 30° with the radius at the point of contact. If the length of the chord is 6 cm, what is the length of the tangent PA?
3 cm
If $1 + \sin^2\theta = 3\sin\theta\cos\theta$, what is the value of $\tan\theta$?
1
If a motor boat with a speed of 18 km/h in still water takes 1 hour to travel, what is the speed of the stream if it travels in one direction?
8 km/h
Given the length-frequency table for leaves, what is the average length of the leaves to the nearest millimeter?
150 mm
Study Notes
Circle Properties
- If the perimeter and area of a circle are equal, the radius can be determined.
- The area of a circle is equal to the sum of areas of two smaller circles with diameters 16m and 12m.
Trigonometry
- If sin θ = 1/2√3, then cos θ can be calculated.
- In a right triangle, the length of the hypotenuse and one of the angles can be used to determine the length of the side opposite the angle.
Motion
- The speed of a boat in still water and the speed of the stream can be used to determine the time taken to travel upstream.
- The speed of a motor boat in still water and the time taken to travel can be used to determine the speed of the stream.
Time and Work
- If two taps can fill a tank together, and the larger tap takes less time to fill the tank alone, the time taken by the smaller tap to fill the tank alone can be determined.
Geometry
- In a circle, the angle of a chord with the radius at the point of contact can be used to determine the length of the tangent.
- The length of a chord and the angle it makes with the radius can be used to determine the length of the tangent.
Algebra
- The equation 1 + sin^2θ = 3sinθcosθ can be solved to determine the value of tanθ.
Statistics
- A length-frequency table for leaves can be used to determine the average length of the leaves to the nearest millimeter.
Test your knowledge on trigonometry and geometry concepts with this quiz. Questions involve calculations for sine, cosine, shadow lengths, circle properties, and more.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
