Quiz

BuzzFeed Staff, UK 

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<b>You might need a pen and paper to do this.</b> And a calculator.

You might need a pen and paper to do this. And a calculator.

The Hardest Maths Quiz You Will Ever Take

The trick to this one is spotting that 2³=8, though that's not as fun as multiplying the whole thing out of course.

What is (2+y)³ written out?

The [binomial expansion](http://mathworld.wolfram.com/BinomialSeries.html) gives you a formula for expanding out equations that look like (x+y)ⁿ. The [Bernstein expansion](http://mathworld.wolfram.com/BernsteinExpansion.html) is something else.

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

Which plot represents y=9ˣ?

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.

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

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.

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

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)

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

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

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

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

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

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.

A circle sector OAB has angle 0.8 radians. What is arc length AB?

The [trapezium rule](http://mathworld.wolfram.com/TrapezoidalRule.html) approximates the area under a curve as a trapezoid. Pythagoras' theorem does right angle triangles.

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

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.

What function does this plot represent?

Multiply by the power (in this case 8 x -2 = -16).

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

The power doesn't change when you differentiate e²ᵗ.

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

The [chain rule](http://mathworld.wolfram.com/ChainRule.html) says that dy/dx = dy/dt x dt/dx.

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

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.

Using the previous equations, what is dy/dx?

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!

Amazing!

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

Congratulations!

Well, we did say it was going to be hard. But hopefully you've learnt a thing or two along the way.

Better luck next time!

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The Hardest Maths Quiz You Will Ever Take

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The Hardest Maths Quiz You Will Ever Take

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