Y13 End of Year Jeopardy

Differentiation

100

Differentiate ln(3x² + 2)

6x/(3x²+2)

200

Differentiate x²y with respect to x

x²(dy/dx) + 2xy

300

State the formula for differentiation from first principles

dy/dx = lim_h->0((f(x + h) - f(x))/h)

400

Differentiate 3x² - 5xy + e^3y with respect to x

6x - 5x(dy/dx) - 5y + 3e^3y(dy/dx)

500

The point P lies on the curve with equation y = 2 + ln(3 - 2x) with x-ordinate 1.

Find the equation of the tangent to the curve at point P.

y = -2x + 4

Integration

100

Integrate 1/(x²) with respect to x

-x^-1 + c

200

Integrate -cos(x) with respect to x

-sin(x) + c

300

State the by parts formula

Integral of uv' = uv - integral of vu'

400

Find the integral of (sinx)/(cos²x) with respect to x

sec(x) + c

500

Integrate ln(x) with respect to x

xln(x) - x + c

Mental Maths

100

18 x 7

126

200

8³

512

300

9432 - 816

8616

400

log₇(16807)

5

500

2³ - 5³ + 8²

-53

Logarithms

100

Solve 2log₂(x) - log₂(5) = 1

x = sqrt(10)

200

Solve ln(2x + 5) = 1

x = (e-5)/2

300

Given that y = log₂(x), rewrite log₈(x) as an expression in terms of y

y/3

400

Solve 2e^y + 15e^-y = 11

y = ln(5/2) AND y = ln(3)

500

Solve simultaneously

e^2y = x + 1

ln(x - 2) = 2y - 1

Answers to 2d.p.

x = 3.75

y = 0.78

Miss Fancy's Interests

100

An anime recently adapted to a live action show by Netflix - featuring Luffy, Zoro, etc.

One Piece

200

The members of the band Queen are Freddie Mercury, Brian May, John Deacon and....

Roger Taylor

300

In Star Trek: The Original Series, what is the name of the chief engineer?

Montgomery Scott (Scotty)

400

Name any three characters from the recent smash hit video game, Baldur's Gate 3

Shadowheart, Wyll, Astarion, Karlach, Gale, Lae'zel, Halsin, Minthara etc.

500

From what song do these lyrics originate:

"To avoid complications
She never kept the same address
In conversation
She spoke just like a baroness"

Killer Queen