Core 1 basics revision quiz

Mar26

Core 1 basic facts quiz

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This quiz is to help you get to grips with what you need for C1. It's not comprehensive, and it won't guarantee you an A - but it'll give you a good foundation to work from.

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Question 1

What is the (grown-up) equation of a straight line?

A	$y = mx + c$ Hint: Nope. I mean, you can use that, but it's not the one I'd recommend.
B	$y-y_0 = m(x-x_0)$ Hint: That's the badger!
C	$(x-x_0)^2+(y-y_0)^2=r^2$ Hint: No, that's a circle.
D	$m_\perp = -\frac{1}{m}$ Hint: No, that's for a perpendicular gradient.
E	$m = \frac{y_1-y_0}{x_1-x_0}$ Hint: No, that's for working out the gradient of a straight line, not the full equation.

Question 2

How do you find the gradient of a curve at a given point, if you know the equation of the curve?

A	$y=mx+c$! Hint: No. That's the equation of a straight line.
B	Differentiate and put the $x$ value into the result. Hint: Yep! You differentiate to get the gradient.
C	Differentiate and put the $y$ value into the result. Hint: No! You shouldn't get any $y$s to replace (in C1).
D	Integrate! Hint: No.
E	Put the $x$ value in to the equation. Hint: No, that will give you the $y$ value.

Question 3

What is $\sqrt{96}$ in simplified surd form?

A	About 9.8 Hint: No, that's not in surd form.
B	$4\sqrt(6)$ Hint: Yep! $96 = 16 \times 6$ so $\sqrt(96) = \sqrt{16}\times\sqrt{6} = 4\sqrt(6)$
C	$6\sqrt{4}$ Hint: No, wrong way round.
D	$16\sqrt{6}$ Hint: No.
E	$2\sqrt(24)$ Hint: True, but not as simplified as it should be.

Question 4

How can you tell if a quadratic equation has no real roots?

A	You can't factorise it. Hint: Not necessarily - $x^2-2$ doesn't factorise, but has real roots.
B	$b^2 - 4ac > 0$ Hint: No, that would give you two real roots.
C	$b^2 - 4ac < 0$ Hint: Yes - that's the discriminant and if it's negative, you can't solve it (in real numbers).
D	$b^2 - 4ac = 0$ Hint: No, that would give you one real root.
E	Complete the square and try to solve it. Hint: A roundabout way of doing things, for sure, but you can if you like.

Question 5

What does the graph of $y = -\frac{1}{x^2}$ look like?

A	A funnel, with asymptotes at $x=0$ and $y=0$ Hint: Yep - all below the $x$-axis.
B	A smiley face. Hint: No, that would be an $x^2$ on top.
C	A frowny face. Hint: No, that would be a $-x^2$ on top.
D	A sea-monster sort of shape. Hint: No, that's a cubic.
E	A sort of curvy seven shape in the bottom-left and and curvy L shape in the top right, with asymptotes at $x=0$ and $y=0$. Hint: No - that's $y = -\frac{1}{x}$.

Question 6

What is $2x^2 + 13x + 15$ in completed square form? 2(x+ 13/4)^2 - 169/16 + 240/16

A	$(2x+3)(x+5)$ Hint: No - that's factorised form
B	$2(x + \frac{13}{4}) - \frac{109}{4}$ Hint: No - something missing!
C	$2(x + \frac{13}{4})^2 - \frac{109}{4}$ Hint: Nope - you've not squared the 13/4 properly.
D	$2(x + \frac{13}{2}) - \frac{109}{4}$ Hint: Nope - a couple of mistakes.
E	$2(x + \frac{13}{4})^2 + \frac{71}{16}$ Hint: No - you've lost the 2 from outside the brackets. Easily done!
F	$2(x+\frac{13}{4})^2 - \frac{49}{8}$ Hint: Good - nasty one, that!

Question 7

What's the distance between the points $(6,3)$ and $(-2, 8)$?

A	89
B	$\sqrt(89)$ Hint: Pythagoras! It's eight across and five up, so you want $\sqrt(8^2 + 5^2)$.
C	13
D	$\sqrt(13)$
E	$\sqrt(41)$

Question 8

$x^{-\frac{1}{3}} = 2$. What is $x$?

A	$\frac{1}{8}$ Hint: Negative powers give you reciprocals, and fractional powers give you roots. This is the same as $\sqrt[3]{\frac{1}{x}}=2$.
B	$8$
C	$\frac{3}{2}$
D	$\frac{1}{6}$
E	$-8$

Question 9

$y = x^3 + \frac{9}{x}$. What is $\frac{dy}{dx}$?

A	$3x^2 - \frac{9}{x^2}$
B	$3x^2 - 9$ Hint: No - don't forget to turn $\frac{9}{x}$ into $9x^{-1}$.
C	$\frac{x^4}{4} - 18x^2+C$ Hint: No - you've tried to integrate (and you don't know how to integrate $x^{-1}$ yet.
D	$3x^2 - \frac{9}{x^2}+c$ Hint: No - you don't add a constant when you differentiate.
E	$3x^2 + \frac{9}{x^2}$ Hint: No, wrong sign.

Question 10

Where does the curve $y=2x^3 + 5x^2 + 3x$ cross the co-ordinate axes?

A	$(0,0),~(-\frac{3}{2},0),~(-1,0)$ Hint: It factorises as $y=x(2x+3)(x+1)$
B	$(0,0),~(-3,0),~(-1,0)$
C	$(0,0),~(3,0),~(1,0)$
D	$(0,0),~(\frac{3}{2},0),~(1,0)$
E	$(0,0),~(0,3),~(0,1)$ Hint: No - those are on the $y$-axis.

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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.

2 comments on “Core 1 basics revision quiz”

Scott Hazell
May 14, 2017 at 9:11 pm

Check question 6 i make it [correct answer]

Reply →
- Colin
  May 14, 2017 at 11:16 pm
  
  Hi, Scott, you’re quite right – I’ll fix that.
  
  I’ve edited spoilers out of your comment, and deleted the second one because it – presumably inaccurately – sounded like you were being a jerk.
  
  Reply →

Core 1 basic facts quiz

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