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The Hardest Maths Quiz You Will Ever Take

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

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Ready? Let's go.

Samuel Goldwyn Films / Via classicmovieactorss.tumblr.com
  1. 1. What is (2+y)³ written out?

    Correct
    Incorrect
    8 + 12y + 6y² + 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. 2. What's the name of the expansion you could use to work out the answer to the previous question?

    Correct
    Incorrect
    Bernstein
    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. 3. Which plot represents y=9ˣ?

    Correct
    Incorrect
    Correct
    Incorrect
    Correct!
    Wrong!

    The other plot represents y=2ˣ.

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

    Correct
    Incorrect
    x = ln(15)/ln(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. 5. Line AB has the equation 3x - 4y + 5 = 0. Point (p, p+2) lies on line AB. What is the value of p?

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

    Correct
    Incorrect
    5/4
    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. 7. Express √48 in the form n√3, where n is an integer.

    Correct
    Incorrect
    8√3
    Correct
    Incorrect
    4√3
    Correct!
    Wrong!

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

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

    Correct
    Incorrect
    40 and 20.
    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. 9. A circle sector OAB has angle 0.8 radians. What is arc length AB?

    AQA / Via filestore.aqa.org.uk
    Correct
    Incorrect
    16cm
    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. 10. What would you use to find the approximate area of an integral between certain limits?

    Correct
    Incorrect
    Trapezium rule.
    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. 11. What function does this plot represent?

    wolframalpha.com
    Correct
    Incorrect
    cos(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. 12. A curve has parametric equations x = 8e⁻²ᵗ - 4 and y = 2e²ᵗ + 4. What is dx/dt?

    Correct
    Incorrect
    dx/dt = -4e⁻²ᵗ
    Correct
    Incorrect
    dx/dt = -16e⁻²ᵗ
    Correct!
    Wrong!

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

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

    Correct
    Incorrect
    dy/dt = 4e²ᵗ
    Correct
    Incorrect
    dy/dt = 4eᵗ
    Correct!
    Wrong!

    The power doesn't change when you differentiate e²ᵗ.

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

    Correct
    Incorrect
    Substitution rule
    Correct
    Incorrect
    Chain rule
    Correct!
    Wrong!

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

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

    Correct
    Incorrect
    dy/dx = -¼e⁴ᵗ
    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.

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