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
Evaluate \(\mathop {\lim }\limits_{x \to \infty } \dfrac{{{x^2} + 3x – 1}}{{{x^2} – 2x – 3}}\).
CorrectIncorrect - Question 2 of 10
2. Question
Differentiate \(y = \sqrt[4]{{5x – 1}}\).
CorrectIncorrect - Question 3 of 10
3. Question
Find \(a\), \(b\) and \(c\) gave that \(f\left( x \right) = 5x – 4{x^{ – 2}} + 9{x^{ – 3}} + {x^{ – 4}}\) and \(f”’\left( x \right) = 96{x^{ – 5}} – 540{x^{ – 6}} – 120{x^{ – 7}}\).
\(a = \) , \(b = \) , \(c = \)
CorrectIncorrect - Question 4 of 10
4. Question
Find \(A\) and \(B\), if the equation of the normal for \(y = \dfrac{1}{{{x^2}}}\) at \(x = 2\) is \(Ax + By – 63 = 0\).
\(A = \) , \(B = \)
CorrectIncorrectHint
\(\text{gradient of tangent } \times \text{gradient of normal } = – 1\)
- Question 5 of 10
5. Question
Find for the values of \(x\) for which \(f\left( x \right) = {x^3} + 6{x^2} + 9x + 7\) is concave downwards.
CorrectIncorrectHint
\(\begin{align} \displaystyle
y” &> 0 \to {\rm{concave upwards}}\\
y” &< 0 \to {\rm{concave downwards}} \end{align}\) - Question 6 of 10
6. Question
Find \(\dfrac{d}{{dx}}\sqrt x {\log _e}\left( {5x} \right)\).
CorrectIncorrectHint
\(\dfrac{d}{{dx}}{\log _e}f\left( x \right) = \dfrac{1}{{f\left( x \right)}} \times f’\left( x \right)\)
- Question 7 of 10
7. Question
A particle \(P\) moves in a straight line with a velocity function of \(s\left( t \right) = {t^3} – 6{t^2} + 1\) metres, where \(t \ge 0\), \(t\) in seconds. Find the total distance travelled for the first 5 seconds.
metres
CorrectIncorrect - Question 8 of 10
8. Question
Find \(p\) and \(q\), if \(\int {{{\left( {\dfrac{{5x}}{2} + 2} \right)}^3}} dx = \dfrac{1}{p}{\left( {5x + 4} \right)^q} + C\).
\(p = \) , \(q = \)
CorrectIncorrectHint
\(\int {{{\left( {ax + b} \right)}^n}} dx = \dfrac{{{{\left( {ax + b} \right)}^{n + 1}}}}{{a\left( {n + 1} \right)}} + C\)
- Question 9 of 10
9. Question
Find \(p\) and \(q\), if \(\int {\dfrac{x}{{{{\left( {{x^2} + 2} \right)}^4}}}} dx = – \dfrac{1}{{p{{\left( {{x^2} + 2} \right)}^q}}} + C\).
\(p = \) , \(q = \)
CorrectIncorrectHint
- Question 10 of 10
10. Question
A particle has velocity function \(v\left( t \right) = \cos 3t\) cm/s as it moves in a straight line. The particle is initially 0.5 cm to the right of the origin. Write a formula for the displacement function.
cm
CorrectIncorrect