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

Find the total surface of the prism, leaving in \({\rm{c}}{{\rm{m}}^2}\).

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

Find \(\theta \), correcting to the nearest degree.

\(\theta = \) degree(s)

CorrectIncorrect##### Hint

\(\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}}\)

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

Find the smallest angle in the triangle, correcting to the nearest minute.

\(\theta = \) degree(s) and minute(s)

CorrectIncorrect##### Hint

\(\cos A = \dfrac{{{b^2} + {c^2} – {a^2}}}{{2bc}}\)

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

Convert \(0.23 \) radians to degrees, correct to 3 significant figures.

degrees

CorrectIncorrect##### Hint

\(\pi \text{ radian } = 180^\circ \)

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

Find the acute angle which has the negative cosine of \(127^\circ \).

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

In which quadrant is true where \(\cos \theta \) is positive and \(\tan \theta \) is negative.

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

Find \(A\), if \(\left( {1 + {{\tan }^2}\theta } \right)\left( {1 – {{\sin }^2}\theta } \right) = A \).

\(A = \)

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

{\sin ^2}\theta + {\cos ^2}\theta &= 1\\

\dfrac{{\sin \theta }}{{\cos \theta }} &= \tan \theta

\end{align}\) - Question 8 of 10
##### 8. Question

Solve \(2\sin \theta – \cos 2\theta = 1\) for \(0^\circ \le \theta \le 360^\circ \).

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

\cos 2\theta &= {\cos ^2}\theta – {\sin ^2}\theta \\

&= 2{\cos ^2}\theta – 1\\

&= 1 – 2{\sin ^2}\theta

\end{align}\) - Question 9 of 10
##### 9. Question

Solve \(\sin \left( {x + \dfrac{\pi }{3}} \right) = \dfrac{1}{2}\) for \( – 3\pi \le x \le 3\pi \). Write six answers in ascending order, correcting to two decimal places.

\(x = \) , , , , ,

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

Solve \(\sin x + \cos x = \sqrt 2 \) for \(0^\circ \le x \le 360^\circ \). Write answers in ascending order.

\(x = \) \(^\circ\), \(^\circ\)

CorrectIncorrect##### Hint

\(\begin{align} \displaystyle

\sin 2x &= 2\sin x\cos x\\

{\sin ^2}x + {\cos ^2}x &= 1

\end{align}\)