Are you ready to take your first step toward achieving your goal?
- 10 diagnosis quiz questions
- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
- Instant feedback straight after the test
OK, let’s get started now!
Are you ready to take your first step toward achieving your goal?
- Ten diagnosis quiz questions
- Ten minutes in duration
- Required to attempt all questions
- A mixture of short-answer and multiple-choice questions
- Instant feedback straight after the quiz
OK, let’s get started now!
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- Question 1 of 10
1. Question
Find the first two values of \(t\) when \(h = 5\) given \(y = 3 + 4\cos \dfrac{\pi }{3}\left( {t – 4} \right)\).
,
CorrectIncorrect - Question 2 of 10
2. Question
Find the first two values of \(t\) when \(h = 5\) given \(y = 5 – 2\cos \dfrac{\pi }{4}\left( {t + 1} \right)\).
,
CorrectIncorrect - Question 3 of 10
3. Question
Find \(A\), if \(\left( {1 + {{\tan }^2}\theta } \right)\left( {1 – {{\sin }^2}\theta } \right) = A \).
\(A = \)
CorrectIncorrectHint
\(\begin{align} \displaystyle
{\sin ^2}\theta + {\cos ^2}\theta &= 1\\
\dfrac{{\sin \theta }}{{\cos \theta }} &= \tan \theta
\end{align}\) - Question 4 of 10
4. Question
Find \(A\), if \({\cos ^2}\theta \left( {1 + {{\tan }^2}\theta } \right) = A\).
\(A = \)
CorrectIncorrectHint
\(\begin{align} \displaystyle
{\sin ^2}\theta + {\cos ^2}\theta &= 1\\
\dfrac{{\sin \theta }}{{\cos \theta }} &= \tan \theta
\end{align}\) - Question 5 of 10
5. Question
Find \(A\), if \(\dfrac{1}{{1 – \sin \theta }} + \dfrac{1}{{\sin \theta + 1}} = \dfrac{A}{{{{\cos }^2}\theta }}\).
\(A = \)
CorrectIncorrectHint
\({x^2} – {y^2} = \left( {x – y} \right)\left( {x + y} \right)\)
- Question 6 of 10
6. Question
Find \(A\) and \(B\), if \({\sec ^4}\theta – 1 = A{\tan ^2}\theta + B{\tan ^4}\theta \).
\(A = \) , \(B = \)
CorrectIncorrectHint
- Question 7 of 10
7. Question
Solve \(\sin 2x + \sin x = 0\) where \(0^\circ \le x \le 360^\circ \).
CorrectIncorrectHint
\(\sin 2\theta = 2\sin \theta \cos \theta \)
- Question 8 of 10
8. Question
Solve \(\sin 2x – 2\cos x = 0\) where \(0^\circ \le x \le 360^\circ \).
CorrectIncorrectHint
\(\sin 2\theta = 2\sin \theta \cos \theta \)
- Question 9 of 10
9. Question
If \(\cos \theta = 0.4\) and \(\theta \) is obtuse, find the value of \(\cos \dfrac{\theta }{2}\), correcting to two decimal places.
CorrectIncorrectHint
\(\begin{align} \displaystyle
\cos 2\theta &= {\cos ^2}\theta – {\sin ^2}\theta \\
&= 2{\cos ^2}\theta – 1\\
&= 1 – 2{\sin ^2}\theta
\end{align}\) - Question 10 of 10
10. Question
Find \(a\) and \(b\), if \(\dfrac{{\sin 2\theta + \sin \theta }}{{1 + \cos 2\theta + \cos \theta }} = a\tan \left( {b\theta } \right)\).
\(a = \) , \(b = \)
CorrectIncorrectHint
\(\begin{align} \displaystyle
\cos 2\theta &= {\cos ^2}\theta – {\sin ^2}\theta \\
&= 2{\cos ^2}\theta – 1\\
&= 1 – 2{\sin ^2}\theta
\end{align}\)