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- 10 minutes in duration
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- A mixture of short answer and multiple-choice questions
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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.

\(A \) , \(B \)

CorrectIncorrect - Question 2 of 10
##### 2. Question

Find \(A \), if \(\dfrac{{14}}{{\left( {x – 8} \right)\left( {2x – 3} \right)}} \div \dfrac{{x – 7}}{{2\left( {x – 8} \right)}} = \dfrac{A}{{\left( {2x – 3} \right)\left( {x – 7} \right)}}\).

\(A = \)

CorrectIncorrect - Question 3 of 10
##### 3. Question

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

\(A = \)

\(B = \)

\(C = \)

CorrectIncorrect - Question 4 of 10
##### 4. Question

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

CorrectIncorrect - 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

CorrectIncorrect - Question 6 of 10
##### 6. Question

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

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

CorrectIncorrect##### Hint

\({a^p} \div {a^q} = {a^{p – q}}\)

- Question 7 of 10
##### 7. Question

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

\( x = \)

CorrectIncorrect##### Hint

\({a^{ – 1}} = \dfrac{1}{a}\)

- Question 8 of 10
##### 8. Question

Simplify \(2x{\left( {{x^2} – {y^2}} \right)^{ – 1}} – {\left( {x – y} \right)^{ – 1}}\).

CorrectIncorrect - Question 9 of 10
##### 9. Question

Solve \({4^x} – {2^x} – 2 = 0\).

CorrectIncorrect - Question 10 of 10
##### 10. Question

A sequence is defined by \({u_n} = 2 \times {3^{n – 1}}\). Find \({u_3}\).

CorrectIncorrect