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

Write 1.0052637 correct to two significant figures.

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

Consider the geometric sequence $k + 3,k,4, \cdots $. Find the positive value of \(k \).

\(k = \)

CorrectIncorrect##### Hint

\({T_n} = {u_1}{r^{n – 1}}\)

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

The first term in a geometric series is 4, and the sum to infinity is 6. Find the common ratio.

CorrectIncorrect##### Hint

\({S_\infty } = \dfrac{{{u_1}}}{{1 – r}}\)

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

Find \(x\), if \(16 \times {2^5} = {2^x}\).

CorrectIncorrect##### Hint

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

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

Find \( x \) and \( y \) if \({\left( { – 3{a^2}} \right)^4} = x{a^y}\).

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

CorrectIncorrect##### Hint

\({\left( {{a^x}} \right)^y} = {a^{xy}}\)

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

Write \({2^{\frac{3}{4}}}\) as a root (surd) form.

CorrectIncorrect##### Hint

\(\sqrt[n]{{{a^m}}} = {a^{\frac{m}{n}}}\)

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

Solve \({4^x} – {2^x} – 2 = 0\).

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

Solve \({\log _{10}}x = – 1\) .

$x=$

CorrectIncorrect##### Hint

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

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

Find \(x\) if \({\log _e}{x^2} = 2.98\), correct to 3 significant figures.

CorrectIncorrect##### Hint

\({e^x} = y \Leftrightarrow x = {\log _e}y\)

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

Solve \({\log _{10}}x + {\log _{10}}\left( {x + 1} \right) = {\log _{10}}30\).

\(x = \)

CorrectIncorrect