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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

Find \(A\), \(B\), \(C\) and \(D\) if \( – 3{x^2}\left( {2x + 3} \right) + x\left( {1 + x + {x^2}} \right) = A{x^3} + B{x^2} + Cx + D\).

\(A = \)

\(B = \)

\(C = \)

\(D = \)

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

Find \(A\), \(B\) and \(C\) if \(3\left( {2x + 5} \right)\left( {2x – 5} \right) = A{x^2} + Bx + C\).

\(A = \)

\(B = \)

\(C = \)

CorrectIncorrect##### Hint

\(\left( {a + b} \right)\left( {a – b} \right) = {a^2} – {b^2}\)

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

Find \(A\), \(B\), \(C\), \(D\) and \(E\) if \(- {\left( {{x^2} – 5} \right)^2} + {\left( {{x^2} – 1} \right)^2} = A{x^4} + B{x^3} + C{x^2} + Dx + E\).

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

CorrectIncorrect##### Hint

\({\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\)

\({\left( {a – b} \right)^2} = {a^2} – 2ab + {b^2}\) - Question 4 of 10
##### 4. Question

Find \(b\), given \(A = \dfrac{{a + b}}{{ab}} \) where \(A = 22\) and \(a = 11\), correcting to two significant figures in ascending order.

\(b = \)

CorrectIncorrect - Question 5 of 10
##### 5. Question

Find \(A \), if \(\dfrac{9}{{\left( {x – 1} \right)\left( {3x – 7} \right)}} \div \dfrac{{x + 3}}{{x – 1}} = \dfrac{A}{{\left( {3x – 7} \right)\left( {x + 3} \right)}}\).

\(A = \)

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

Write \({\left( {2{x^3}} \right)^{ – 5}}\) without negative exponents.

CorrectIncorrect##### Hint

\({a^{ – x}} = \dfrac{1}{{{a^x}}}\)

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

Write \(2 \times {3^3}\) as a basic numeral.

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

Find the value of \({\left( {{5^0} + {6^1} + {7^2}} \right)^0}\).

CorrectIncorrect##### Hint

\({a^0} = 1\)

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

The average of 5 numbers is 11. A new number is added, then the new average becomes 12. Find the new number added.

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

A sequence is defined by \({u_n} = {3^n}\). Find \({u_4}\).

CorrectIncorrect