# math

What is (2+y)³ written out?

8 + 12y + 6y² + y³

6 + 8y + 4y² + y³

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

Bernstein

Binomial

3. Which plot represents y=9ˣ?

wolframalpha.com

wolframalpha.com

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

x = ln(15)/ln(9)

x = ln(15/9)

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

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

5/4

3/4

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

8√3

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.

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

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16cm

18cm

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

Trapezium rule.

Pythagoras’ theorem.

11. What function does this plot represent?

wolframalpha.com

cos(x)

sin(x)

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

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

dy/dt = 4e²ᵗ

dy/dt = 4eᵗ

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

Substitution rule

Chain rule

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

dy/dx = -¼e⁴ᵗ

dy/dx=-4e⁴ᵗ 