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- Question 1 of 10
##### 1. Question

Find \(A\) and \(B\) if \(\left( {2.2 \times {{10}^3}} \right) \times \left( {1.8 \times {{10}^5}} \right) = A \times {10^B}\) in scientific notation with two significant figures.

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

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

If \({t_{10}} = – \dfrac{1}{2}\) and \({t_{13}} = \dfrac{3}{4}\), find \({t_{100}}\) of the arithmetic sequence.

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

A geometric sequence has \({u_2} = – 6\) and \({u_5} = 162\). Find its general term.

CorrectIncorrect##### Hint

\({u_n} = {u_1} \times {r^{n – 1}}\)

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

Given \(2.1444 \cdots = \dfrac{a}{{90}}\), find \(a \).

\(a = \)

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

Find \(x\) and \(y\), if \(24 \times {2^3} \times {3^2} = {2^x}{3^y}\).

\(x = \) , \(y = \)

CorrectIncorrect##### Hint

\({a^p} \times {a^q} = {a^{p + q}}\)

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

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

CorrectIncorrect##### Hint

\({a^0} = 1\)

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

Solve \({4^x} – 6 \times {2^x} + 8 = 0\). There could be more than one answer.

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

Solve \({\log _{10}}x = – 5\), correcting to one significant figures.

$x=$

CorrectIncorrect##### Hint

\(a = {b^x} \Leftrightarrow x = {\log _b}a\)

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

Solve \({8^x} – 5 \times {4^x} = 0\), correct to 2 significant figures.

\(x = \)

CorrectIncorrect##### Hint

\({a^x} = y \Leftrightarrow x = {\log _a}y\)

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

Find the constant term in the expansion of \({\left( {x + \dfrac{2}{{{x^2}}}} \right)^{15}}\).

Coefficient \( = \)

CorrectIncorrect##### Hint

\({T_{k + 1}} = \left( {\begin{array}{*{20}{c}}

n\\

k

\end{array}} \right){a^{n – k}}{b^k}\)