Let $f$ be the function $f(x) = \sqrt{x^2-4} + 2$, $2 \le x \le 6$.
What is the range of $f$?
A
$2 \le f(x) \le 4\sqrt{2} + 2$
B
$f(x) \ge 2$
C
$2 \le x \le 6$
D
$2 \le f(x) \le 6$
E
$0 \le f(x) \le 4 \sqrt{2}$
Question 4
What is the gradient of $y = 6e^{3x^2 - 3}$ at the point where $x=2$?
A
$\frac{dy}{dx} = 6e^{6x}$
B
$\frac{dy}{dx} = 6e^{3x^2 - 3}$
C
$\frac{dy}{dx} = 36xe^{3x^2 - 3}$
D
$\frac{dy}{dx} = 6e^{12}$
E
$y=6e^9$
F
$y = 72e^{9}$
Question 5
How else could you write the expression $3\sin(x) + 4\cos(x)$?
A
$5\sin(x + 53º)$
B
$3.5\sin(x + 37º)$
C
$5\cos(x + 37º)$
D
$3.5\cos(x - 53º)$
E
$5\sin(x + 37º)$
Question 6
What do you get if you differentiate $\frac{\ln(x)}{x}$?
A
$\frac{1 - x\ln(x)}{x}$
B
$\frac{1 - x\ln(x)}{x^2}$
C
$\frac{1}{x^2}$
D
$\frac{1 - \ln(x)}{x^2}$
E
$\ln(x)$
Question 7
What is $\frac{dy}{dx}$ if $y = \tan(x)$?
A
$\tan^2(x)$
B
$\sec^2(x)$
C
$\sec(x)$
D
-$\cot(x)$
E
$\sec(x)\tan(x)$
F
$\cot(x)$
Question 8
Given $T = 20 + 80e^{-kt}$, and that $T=50$ when $t=60$, find the exact value of $k$.
A
$k = \frac{8}{3}\ln(60)$
B
$k = 60\left(\ln(8) - \ln(3)\right)$
C
$k = {60}\left(\ln(3) - \ln(8)\right)$
D
$k = \frac{1}{60}\left(\ln(3) - \ln(8)\right)$
E
$k = \frac{1}{60}\left(\ln(8) - \ln(3)\right)$
Question 9
What's the derivative of $y = 4x \sin(x)$?
A
$\frac{dy}{dx} = 4\cos(x)$
B
$\frac{dy}{dx} = -4\sin(x) + 4x\cos(x)$
Hint:
What's the derivative of $y = 4x \sin(x)$?
C
$\frac{dy}{dx} = -4\cos(x)$
D
$\frac{dy}{dx} = 4\sin(x) + 4x\cos(x)$
E
$\frac{dy}{dx} = 4\sin(x) - 4x\cos(x)$
Question 10
Where do the lines $y=x$ and $y = | 2x-1 |$ cross?
A
$(1,1)$
Where do the lines $y=x$ and $y = | 2x-1 |$ cross?
B
$(1,1)$, $(1,-1)$, $(\frac{1}{3}, \frac{1}{3})$ and $(\frac{1}{3}, -\frac{1}{3})$
C
$(\frac{1}{3}, \frac{1}{3})$
D
$(1,1)$ and $(\frac{1}{3}, \frac{1}{3})$
E
$(0,0)$, $\frac{1}{2},0)$ and $(0,1)$
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
Get Results
There are 10 questions to complete.
←
List
→
Return
Shaded items are complete.
1
2
3
4
5
6
7
8
9
10
End
Return
You have completed
questions
question
Your score is
Correct
Wrong
Partial-Credit
You have not finished your quiz. If you leave this page, your progress will be lost.
Correct Answer
You Selected
Not Attempted
Final Score on Quiz
Attempted Questions Correct
Attempted Questions Wrong
Questions Not Attempted
Total Questions on Quiz
Question Details
Results
Date
Score
Hint
Time allowed
minutes
seconds
Time used
Answer Choice(s) Selected
Question Text
All done
Need more practice!
Keep trying!
Not bad!
Good work!
Perfect!
Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.
Jasmine Jones
I hope this is good! Absolutely bricking my mocks!
Colin
Good luck, Jasmine – let me know if there are any topics you’d like me to cover!