GCE A-Level Further Mathematics Practice Questions - Cameroon General Certificate of Education Advanced Level Further Mathematics (0775) Exam - GCE A-Level Further Mathematics Practice Questions - Cameroon General Certificate of Education Advanced Level Further Mathematics (0775) Exam

Question 1

Evaluate the complex power $(1 + i\sqrt{3})^6$ using De Moivre's theorem.

64 -64 64i -64i

Correct Answer:

Question 2

Using De Moivre's theorem, express $\cos(4\theta)$ entirely in terms of powers of $\cos\theta$.

4\cos^4\theta - 4\cos^2\theta + 1 8\cos^4\theta - 8\cos^2\theta + 1 8\cos^4\theta - 6\cos^2\theta + 1 16\cos^4\theta - 12\cos^2\theta + 1

Correct Answer:

8\cos^4\theta - 8\cos^2\theta + 1

Question 3

If $\omega = e^{i 2\pi/5}$ is a primitive fifth root of unity, what is the value of the finite sum $1 + \omega + \omega^2 + \omega^3 + \omega^4$?

1 -1 0 5

Correct Answer:

N/A

Question 4

The locus of points $z = x + iy$ in the complex plane satisfying $|z - 3| = 2|z - 3i|$ represents a circle. What are the center and radius of this circle?

Center $(1, -4)$, Radius $2\sqrt{2}$ Center $(-1, 4)$, Radius 8 Center $(3, 3)$, Radius 4 Center $(-1, 4)$, Radius $2\sqrt{2}$

Correct Answer:

Center $(-1, 4)$, Radius $2\sqrt{2}$

Question 5

Find the three distinct complex roots of the polynomial equation $z^3 = -8i$ in exponential form $r e^{i\theta}$ with $-\pi < \theta \le \pi$.

$$2e^{-i\pi/6}, 2e^{i\pi/2}, 2e^{-i5\pi/6}$ $$2e^{i\pi/6}, 2e^{i5\pi/6}, 2e^{-i\pi/2}$ $$8e^{-i\pi/6}, 8e^{i\pi/2}, 8e^{-i5\pi/6}$ $$2e^{-i\pi/2}, 2e^{i\pi/6}, 2e^{i5\pi/6}$

Correct Answer:

$$2e^{-i\pi/6}, 2e^{i\pi/2}, 2e^{-i5\pi/6}$

Question 1

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Prepare with the GCE A-Level Further Mathematics Practice Questions - Cameroon General Certificate of Education Advanced Level Further Mathematics (0775) Exam practice quiz. This question bank includes 100 questions covering theta, find, frac, evaluate, and calculate. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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GCE A-Level Further Mathematics Practice Questions - Cameroon General Certificate of Education Advanced Level Further Mathematics (0775) Exam

This practice set contains 100 questions from the matching question bank and focuses on theta, find, frac, evaluate, and calculate. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

This is an independent study resource intended for practice and review; it is not an official examination or an endorsement by any organization named in the title.

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GCE A-Level Further Mathematics Practice Questions - Cameroon General Certificate of Education Advanced Level Further Mathematics (0775) Exam

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