Lesson G3
G3 Area enclosed by a polar curve Quiz: AQA Further Maths, Unit 2
20 questions
In partnership with Revision Ninja
Lesson G3, Area enclosed by a polar curve: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.
Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.
The 20 questions
-
Which formula gives the area enclosed by a polar curve r = f(θ)?
- ½ ∫ r² dθ
- ∫ r² dθ
- ∫ r dθ
- ½ ∫ r dθ
-
What is the area enclosed by the circle r = a?
- pi a^2
- pi a^2/2
- 2 pi a^2
- pi a
-
Find the area enclosed by r = 2 for 0 <= theta <= pi/2.
- pi/2
- 2 pi
- 4 pi
- pi
-
What is the area enclosed by the full cardioid r = 1 + cos(theta)?
- pi
- 3 pi
- 3 pi/2
- 2 pi
-
What is the area enclosed by the full curve r = 2 cos(theta)?
- 2 pi
- pi/2
- pi
- 4 pi
-
Find the area enclosed by r = 3 for 0 <= theta <= pi/3.
- 3 pi
- pi/2
- 3 pi/2
- 9 pi/2
-
What is the area of one petal of the rose r = sin(2 theta)?
- pi/8
- pi/4
- pi/2
- pi/16
-
What is the area enclosed by the full curve r = 2(1 - cos(theta))?
- 6 pi
- 2 pi
- 12 pi
- 3 pi
-
Find the area enclosed by the full curve r = 4 sin(theta).
- 2 pi
- pi
- 8 pi
- 4 pi
-
What integrand is used to calculate the area enclosed by r = 2 + cos(θ)?
- (2 + cos θ)²
- 2 + cos² θ
- ½ (2 + cos θ)²
- ½ (2 + cos θ)
-
How does the area of a thin polar sector depend on its radius r?
- Independent of r
- Proportional to r²
- Proportional to r
- Proportional to 1/r
-
Which limits of theta give one complete traversal of the circle r = a?
- 0 to pi/2
- -pi/2 to pi/2
- 0 to pi
- 0 to 2 pi
-
Find the area enclosed by r = 3 sin(theta).
- 9 pi/4
- 3 pi/4
- 9 pi/2
- 3 pi
-
Find the area enclosed by r = 1 + cos(theta) for 0 <= theta <= pi.
- 3 pi/2
- pi/2
- pi
- 3 pi/4
-
Find the area enclosed by r = 4 for 0 <= theta <= pi.
- 2 pi
- 4 pi
- 8 pi
- 16 pi
-
Find the area enclosed by r = 2 for pi/4 <= theta <= pi/2.
- pi
- pi/2
- pi/4
- 2 pi
-
Find the area of the region between the curves r = 2 and r = 4 for 0 <= theta <= pi/2.
- 3 pi
- 6 pi
- 12 pi
- pi
-
Find the area enclosed by r = 2 sin(theta) for pi/6 <= theta <= pi/2.
- 2 pi/3 + sqrt(3)/2
- pi/3 + sqrt(3)/4
- pi/6 + sqrt(3)/8
- pi/3 - sqrt(3)/4
-
A sector of the circle r = 5 spans theta from 0 to 2 radians. What is its area?
- 5
- 12.5
- 50
- 25
-
What is the area enclosed by one loop of the curve r = cos(3 theta)?
- pi/24
- pi/12
- pi/4
- pi/6
Related quizzes
- Proof by mathematical induction Quiz · A1 · 20 questions
- Solving polynomial equations and complex conjugates Quiz · B1-B3 · 20 questions
- Argand diagrams, modulus-argument form and loci Quiz · B4-B7 · 20 questions
- De Moivre's theorem, exponential form and roots of unity Quiz · B8-B11 · 20 questions
- Matrix operations, zero and identity matrices Quiz · C1-C2 · 20 questions
- Linear transformations and invariant points Quiz · C3-C4 · 20 questions
- Determinants, inverse matrices and factorising determinants Quiz · C5, C6, C9 · 20 questions
- Solving three simultaneous equations with matrices Quiz · C7-C8 · 20 questions
- Eigenvalues and eigenvectors Quiz · C10 · 20 questions
- Diagonalisation of matrices Quiz · C11 · 20 questions