## 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 \(x \), \(y \) and \(z \) for \(\neg q \Rightarrow \neg p\).

\( \begin{array}{|c|c|c|c|c|} \hline

p & q & \neg p & \neg q & \neg q \Rightarrow \neg p \\ \hline

\text{F} & \text{T} & x & y & z \\ \hline

\end{array} \)\(x = \) , \(y = \) , \(z = \)

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

Determine the validity of this argument:

*It is windy and Amy does not get cool. Therefore, Amy does not feel happy.*CorrectIncorrect - Question 3 of 10
##### 3. Question

Find \(x\), \(y\) and \(z\) if \(\left( {\begin{array}{*{20}{c}}

{x + 4}\\

{y-1}\\

{z-4}

\end{array}} \right) = \left( {\begin{array}{*{20}{c}}

{2-x}\\

{5-y}\\

{ -2-z}

\end{array}} \right)\)\(x = \) , \(y = \) , \(z = \)

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

Find the coordinates \(\left( {a,b,c} \right)\) of the point where the line with parametric equations \(x = 2 + 5t,{\rm{ }}y = -3-4t\) and \(z = 3 + t\) meets the \(XOY\) plane.

\(a = \) , \(b = \) , \(c = \)

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

A line has a vector equation \(\left( {\begin{array}{*{20}{c}}

x\\

y

\end{array}} \right) = \left( {\begin{array}{*{20}{c}}

3\\

6

\end{array}} \right) + t\left( {\begin{array}{*{20}{c}}

5\\

{ – 4}

\end{array}} \right)\). Find the shortest distance from \(P\left( {2,3} \right)\) to the line, correcting to three significant figures.CorrectIncorrect - Question 6 of 10
##### 6. Question

State whether two lines are parallel, intersect coincident, skew or perpendicular.

Line \(a\): \(x = 1 + s\), \(y = – 2s\) and \(z = 4 + 4s\)

Line \(b\): \(x = 7 + 2t\), \(y = 2 + 3t\) and \(z = t\)CorrectIncorrect - Question 7 of 10
##### 7. Question

Find \(a\), if \(\int_0^3 {x\sqrt {x + 1} } dx = \dfrac{a}{{15}}\).

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

Evaluate \(\int_0^1 {\dfrac{{{x^2} + 4x}}{{\sqrt[3]{{{x^3} + 6{x^2}}}}}} dx\).

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

Given \(U = \left\{ {x|2 < x \le 8,x \in N} \right\}\) and the following pair of propositions, find the truth set of \( p \veebar q \).

• \(p:\) \(x \) is even.

• \(q:\) \(x \) is devisible by 3.CorrectIncorrect - Question 10 of 10
##### 10. Question

Given \(\vec a = \left( {\begin{array}{*{20}{c}}

3\\

5\\

{ – 1}

\end{array}} \right),\vec b = \left( {\begin{array}{*{20}{c}}

1\\

3\\

{ – 4}

\end{array}} \right)\) and \(\vec c = \left( {\begin{array}{*{20}{c}}

3\\

– 2\\

7

\end{array}} \right)\), find \(\left| {\vec a – \vec b + 3\vec c} \right|\), correcting to two significant figures.CorrectIncorrect