Buzz·Posted on Sep 11, 2014The Hardest Maths Quiz You Will Ever TakeYou might need a pen and paper to do this. And a calculator.by Kelly OakesBuzzFeed Staff, UK FacebookPinterestTwitterMailLink Ready? Let's go. Tap to play or pause GIF Tap to play or pause GIF Samuel Goldwyn Films / Via classicmovieactorss.tumblr.com 1. What is (2+y)³ written out? 8 + 12y + 6y² + y³ Correct Incorrect 8 + 12y + 6y² + y³ 6 + 8y + 4y² + y³ Correct Incorrect 6 + 8y + 4y² + y³ Correct! Wrong! 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 Correct Incorrect Bernstein Binomial Correct Incorrect Binomial Correct! Wrong! 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? Image: wolframalpha.com Correct Incorrect wolframalpha.com Image: wolframalpha.com Correct Incorrect wolframalpha.com Correct! Wrong! The other plot represents y=2ˣ. 4. Which equation would you find to solve 9ˣ=15 for x? x = ln(15)/ln(9) Correct Incorrect x = ln(15)/ln(9) x = ln(15/9) Correct Incorrect x = ln(15/9) Correct! Wrong! 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 Correct Incorrect -3 3 Correct Incorrect 3 Correct! Wrong! 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 Correct Incorrect 5/4 3/4 Correct Incorrect 3/4 Correct! Wrong! 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 Correct Incorrect 8√3 4√3 Correct Incorrect 4√3 Correct! Wrong! 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. Correct Incorrect 40 and 20. 160 and 320. Correct Incorrect 160 and 320. Correct! Wrong! 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 Correct Incorrect 16cm 18cm Correct Incorrect 18cm Correct! Wrong! 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. Correct Incorrect Trapezium rule. Pythagoras' theorem. Correct Incorrect Pythagoras' theorem. Correct! Wrong! The trapezium rule approximates the area under a curve as a trapezoid. Pythagoras' theorem does right angle triangles. mathworld.wolfram.com 11. What function does this plot represent? wolframalpha.com cos(x) Correct Incorrect cos(x) sin(x) Correct Incorrect sin(x) Correct! Wrong! 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 Correct Incorrect dx/dt = -4e⁻²ᵗ dx/dt = -16e⁻²ᵗ Correct Incorrect dx/dt = -16e⁻²ᵗ Correct! Wrong! 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 Correct Incorrect dy/dt = 4e²ᵗ dy/dt = 4eᵗ Correct Incorrect dy/dt = 4eᵗ Correct! Wrong! 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 Correct Incorrect Substitution rule Chain rule Correct Incorrect Chain rule Correct! Wrong! The chain rule says that dy/dx = dy/dt x dt/dx. 15. Using the previous equations, what is dy/dx? dy/dx = -¼e⁴ᵗ Correct Incorrect dy/dx = -¼e⁴ᵗ dy/dx=-4e⁴ᵗ Correct Incorrect dy/dx=-4e⁴ᵗ Correct! Wrong! 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.