Ready? Let's go.

1. What is (2+y)³ written out?
8 + 12y + 6y² + y³6 + 8y + 4y² + y³The 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?
BernsteinBinomialThe 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?
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)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?
33The 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?
5/43/4You 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√34√348 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.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?
16cm18cmThe 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.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)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⁻²ᵗdx/dt = 16e⁻²ᵗMultiply 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 = 4e²ᵗdy/dt = 4eᵗThe 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 ruleChain ruleThe chain rule says that dy/dx = dy/dt x dt/dx.

15. Using the previous equations, what is dy/dx?
dy/dx = ¼e⁴ᵗdy/dx=4e⁴ᵗDividing 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.