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 $(0,1)$

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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!