The Hardest Maths Quiz You Will Ever Take

1. What is (2+y)³ written out?

8 + 12y + 6y² + y³

6 + 8y + 4y² + y³
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The trick to this one is spotting that 2³=8, though that’s not as fun as multiplying the whole thing out of course.


2. What’s the name of the expansion you could use to work out the answer to the previous question?

Bernstein

Binomial
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The binomial expansion gives you a formula for expanding out equations that look like (x+y)ⁿ. The Bernstein expansion is something else.


3. Which plot represents y=9ˣ?
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The other plot represents y=2ˣ.


4. Which equation would you find to solve 9ˣ=15 for x?

x = ln(15)/ln(9)

x = ln(15/9)
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Apply a logarithm to both sides of 9ˣ=15 to get ln (9ˣ) = ln (15). That’s equivalent to x ln(9)=ln(15), which you can rearrange to get x=ln(15)/ln(9). Putting that into a calculator (or Google) gives you 1.23 to two decimal places.


5. Line AB has the equation 3x – 4y + 5 = 0. Point (p, p+2) lies on line AB. What is the value of p?

3

3
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The key to this is remembering that coordinates come in the form (x,y). That means x=p and y=p+2, so y=x+2. Plug that into the equation given and it works out at x=3.


6. What is the gradient of line AB from the previous question?

5/4

3/4
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You need to rearrange in to the form y=mx+c, where m is the gradient and c is the y intercept. In this case the rearranges equation is y=(3/4)x+(5/4)


7. Express √48 in the form n√3, where n is an integer.

8√3

4√3
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48 is 16 multiplied by 3, and √16=4. So √48 = √3 x √16 = 4√3.


8. A geometric series has first term 80 and common ratio 1/2. What are the next two terms?

40 and 20.

160 and 320.
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Multiply the first term by 1/2 to get the second term (40) and do it again to get the third (20). Ta da!


9. A circle sector OAB has angle 0.8 radians. What is arc length AB?AQA / Via filestore.aqa.org.uk

16cm

18cm
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The arc length of a circle sector with radius r and angle θ (in radians) is just rθ. So 20cm multiplied by 0.8 is 16cm.


10. What would you use to find the approximate area of an integral between certain limits?

Trapezium rule.

Pythagoras’ theorem.
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The trapezium rule approximates the area under a curve as a trapezoid. Pythagoras’ theorem does right angle triangles.


11. What function does this plot represent?

cos(x)

sin(x)
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Plots of sin(x) and cos(x) are the same, but offset by 90°. If you remember that cos(0)=1 and sin(0)=0 you can easily tell which is which.


12. A curve has parametric equations x = 8e⁻²ᵗ – 4 and y = 2e²ᵗ + 4. What is dx/dt?

dx/dt = 4e⁻²ᵗ

dx/dt = 16e⁻²ᵗ
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Multiply by the power (in this case 8 x 2 = 16).


13. Using the same equations (x = 8e⁻²ᵗ – 4 and y = 2e²ᵗ + 4) what is dy/dt?

dy/dt = 4e²ᵗ

dy/dt = 4eᵗ
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The power doesn’t change when you differentiate e²ᵗ.


14. When you have two parametric equations, what’s the name of the rule you can use to work out dy/dx?

Substitution rule

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The chain rule says that dy/dx = dy/dt x dt/dx.


15. Using the previous equations, what is dy/dx?

dy/dx = ¼e⁴ᵗ

dy/dx=4e⁴ᵗ
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Dividing dy/dt by dx/dt gives you dx/dy, as per the chain rule. Unsimplified, the answer is dy/dx = 4e²ᵗ/16e⁻²ᵗ.
Then 4 divided by 16 is ¼. And with e²ᵗ/e⁻²ᵗ you subtract the bottom power from the top, so 2t(2t)=4t.

The Hardest Maths Quiz You Will Ever Take

Amazing!
Either you’re just about to take A level maths (or higher), or you did it a few years ago and have a very impressive memory. Either way you’d still pass now, and with a decent mark. Well done!

Congratulations!
You might not have got everything right, but if this was an exam you’d have passed. Well done!

Better luck next time!
Well, we did say it was going to be hard. But hopefully you’ve learnt a thing or two along the way.
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