Canada Lynx contest template

Probability

100

A fair coin is flipped twice. What is the probability of getting exactly one head?

1/2

200

A bag has 3 red and 2 blue marbles. One marble is drawn. What is the probability it is red?

3/5

300

Two dice are rolled. What is the probability that the sum is 8?

5/36

400

A 3-digit code is formed using digits 1–9 with no repetition. What is the probability the code starts with an odd digit?

5/9

500

Ten students line up randomly. What is the probability that three particular students sit together in any order?

1/15

Geometry

100

Find the area of a right triangle with a base of length 3 units and a height of length 4 units.

6 units²

200

A circle has radius 5. What is its area?

25π

300

The slope of a line is 2, and it passes through (1,3). What is its equation?

y=2x+1

400

A triangle has sides 7, 24, and 25. Is it right-angled?

Yes, since 7² +24² = 25²

500

A right triangle has legs of length 9 and 12. Find the length of the altitude to the hypotenuse.

36/5

Algebra & Functions

100

Expand: (x+2)(x+3)

x²+5x+6

200

Solve for x: 2x+5=11

x=3

300

If f(x)=2x²−3x, find f(4).

20

400

Solve for x: 3^x=81

x=4

500

Solve for real x: 2^x+1 +2^x = 48

x=4

Sequences And Series

100

What is the 10th term of the sequence 2,4,6,8,...?

20

200

Find the sum: 1+2+3+...+20.

210

300

A geometric sequence has first term 3 and ratio 2. Find the 5th term.

48

400

A sequence is defined by a_n= 3n−1. Find a₁₅.

44

500

The first term of an arithmetic sequence is 4 and the common difference is 3.
Find the 20th term.  

61