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Question 1 of 10

1. Question

Find \(A \) and \(B \), if \(\dfrac{x}{{x + 1}} – \dfrac{{x – 1}}{{x – 2}} = \dfrac{{Ax + B}}{{\left( {x + 1} \right)\left( {x – 2} \right)}}\) in its simplest form of a fraction.

Find \(A\), \(B\) and \(C\) if \({\left( {x – 5} \right)^2} = A{x^2} + Bx + C\).

\(A = \) \(B = \) \(C = \)

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Incorrect

Question 4 of 10

4. Question

Find \(d\), given \(f = \dfrac{{{a^2} – {d^2}}}{{4a}}\) where \(f = 2\), and \(a = 15\).

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Incorrect

Question 5 of 10

5. Question

Sean is biking with a constant speed towards town B from town A. With the aid of wind, which has a speed of 2.5 km it takes him only one hour to reach the destination. However, on the way back to town A he has to bike against the wind, and it takes him three hours to reach town A. Find Sean’s speed.

km/h

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Incorrect

Question 6 of 10

6. Question

Find \(A \), \(B \) and \(C \), if \(\dfrac{{12{x^3} \times 4{y^8}}}{{4x \times y}} = A{x^B}{y^C}\).

\(A = \) , \(B = \) , \(C = \)

Correct

Incorrect

Hint

\({a^p} \div {a^q} = {a^{p – q}}\)

Question 7 of 10

7. Question

Find \( x \), if \({\left( {{4^{ – 2}}} \right)^{ – 1}} = {2^x}\).