Pre DP Math Olympics

Logarithms and Exponents

100

2^x=200, find x

x = log₂(200) or

200

What is x for  log_x(25)=2

x = 5

300

5(log2x - log y) - (log3 + 2log5)

log(32x⁵/75y⁵)

400

Ms Sanker's bank account with $2000 grows continuously at a rate of 1.2% per year. How many years until the bank account has $3000?

34 years

500

Who discovered the constant 'e' known as euler's number?

Jacob Bernoulli

Sequences and Series

100

Name this sequence: The sequence in which each term after the first is obtained by adding a constant called the common difference to the preceding term.

Arithmetic Sequence 

200

What kind of sequence is this? (1,4,9,16, ....)

Quadratic

300

Find d given that a1=10 and a20=466

24

400

Find the sum of the first 13th terms of the sequence: {3,5,7,9…a₁₃}

195

500

Find r in this sequence:
(√2 - 1, 1, √2 +1, ....)

√2 + 1

Binomials

100

nCr (5,2) 

10

200

How many terms is in (x+y)⁷ 

8

300

What row of Pascal's Triangle do you see the number 6 for the first time?

5th row

400

What is the binomial expansion of (x+1)⁸?

x⁸ + 8x⁷ + 28x⁶ + 56x⁵ + 70x⁴ + 56x³ + 28x² + 8x + 1

500

Who generalised the binomial theorem?

Sir Issac Newton

Jokes

100

What did the triangle say to his prom date?

I think you're acute!

200

Did you hear about the over-educated circle?

It has 360°!

300

Why didn't sine and tangent go to the party?

Just cos!

400

Which tool is best for math?

The multi-pliers.

500

Why was e^x a bad partner?

Because no matter how much you begged them to change, they always remained the exact same.

Anagrams

100

KANSER

SANKER

200

ARTLNIONTSA

TRANSLATION

300

Ange TNT

Tangent

400

BORYIITABPL

PROBABILITY

500

annexion tiptoe

Exponentiation