I'm going to run a little experiment for a while. Every Tuesday until the exams, I'm going to put out a ten-question quiz on one of the A-level modules. I'd love to have feedback on whether you find them useful, how I can make them better, and what else I ought to cover! Here's the first one - it's on Core 2.

Core 2 basic facts quiz

This quiz takes you through some of the most important rules and identities for C2. Mastering this stuff won't guarantee you a good grade in your exam, but it'll give you a great foundation to work from.
(It's designed for OCR, but works just as well for the other boards).

Start

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Question 1

If you know two sides of a triangle and the angle between them, which rule do you use to find the remaining side?

A

Rule 34

Hint:

*Looks sternly over glasses.* No.

B

Heron's rule

Hint:

Good guess. Wrong.

C

Sine rule

Hint:

No - that won't help you here!

D

A slide rule

Hint:

Possibly, if it's the 1960s. *Checks calendar*. Nope, it's not.

E

Cosine rule

Hint:

Yep!

Question 2

What's the area of a triangle, if you know two sides $a$ and $b$ and the angle $C$ between them?

A

$\frac{1}{2} bh$

Hint:

No, you don't know $h$.

B

$\frac{1}{2}ab\sin(C)$

Hint:

Boom!

C

$\frac{1}{2}ab\cos(C)$

Hint:

Nope. Wrong function!

D

$abC$

Hint:

It's not that simple.

E

$\frac{1}{2}abC$

Hint:

Not that simple, either.

Question 3

What kind of sequence might go $192,~96,~48,~24,~12,~...,~\frac{384}{2^{n}$},~...$?

A

Probably geometric, but it might be something else!

Hint:

No, it can't be something else - the general term you're given is for a geometric series.

B

Probably arithmetic, but it might be something else!

Hint:

Nope. Well, kind of. It's something else, all right.

C

Something else!

Hint:

Nope. Well, in a paradoxical kind of way, it's not something else... it's something else.

D

Geometric!

Hint:

Yep! You have a common ratio of $\frac{1}{2}$.

E

Arithmetic!

Hint:

Nope. An arithmetic series has the same difference between terms.

Question 4

For $0 \le x \lt 360º$, which values of $x$ satisfy $\cos^2(x) = \frac{1}{9}$?

A

$70.5º$, $109.5º$, $250.5º$, and $289.5º$

Hint:

Yes!

B

$70.5º$ and $250.5º$ only

Hint:

No.

C

$70.5º$ and $289.5º$ only

Hint:

No.

D

$70.5º$ and $109.5º$ only

Hint:

No.

E

$70.5º$ only

Hint:

No.

Question 4 Explanation:

You get $\cos(x) = \pm \frac{1}{3}$, which gives you results in all four quadrants.

Question 5

How else could you write $sin^2(x)$?

A

$1 - \cos^2(x)$

Hint:

Correct! Because $\cos^2(x) + \sin^2(x) \equiv 1$

B

$1 - \cos(x)$

C

$1 + \cos(x)$

D

$\cos(x)$

E

$1 + \cos^2(x)$

Question 5 Explanation:

$\cos^2(x) + \sin^2(x) = 1$ is the most important identity in A-level maths. It should be tattooed on your eyelids.

Question 6

Why does $\int_{-5}^{5} x^2 - 4x dx$ not give you the area under the curve $y = $x^2 - 4x$ between the lines $x=-5$ and $x=5$?

A

The curve goes below the $x$-axis and you need to account for that.

Hint:

That's right!

B

The limits are wrong.

Hint:

No they're not.

C

The integral goes to infinity

Hint:

No it doesn't.

D

You can't have a negative limit.

Hint:

Yes you can.

E

You don't integrate to find an area.

Hint:

Yes you do.

Question 7

What's the formula for arclength, if you know the radius $r$ and the angle $\theta$ in radians?

A

$\mathcal{l} = \frac{r^2 \theta}{2}$

Hint:

No, that's the area formula!

B

$\mathcal{l} = \theta \times \frac{180}{\pi}$

Hint:

No, that's for converting radians to degrees. It's the WRONG WAY, dammit!

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.

## Omole Musah-Eroje

Hi. Thank’s for the quiz, it’s really helpful.

However on question 10,

“If you know two sides of a triangle and the angle between them, which rule do you use?”,

you don’t say whether we are finding an angle or a side. [Spoilers redacted — CB]

## Colin

You’re quite right — I’ve now corrected the question. Thanks!

## AH

Hahahahahhahahaha Rule 34. Nice.

## Colin

Ha! I’d forgotten about that 🙂