Question 1

Find the distance between the points of intersection of the functions
\( f(x) = 1.5x^2 – 3.2x + 11 \) and \( g(x) = -x^2 + 4.3x + 81 \).

Question 2

Find the equation of a sideways semicircle shown below.

Question 3

Find the sum of the sequence.
\( 1 + 4\frac{8}{9} + 7\frac{4}{9} + 10\frac{2}{9} + . . . + 40\frac{1}{4608} = \)

Question 4

At a dodgeball tournament this weekend, there will be 16 girls and 13 boys. 7 girls will be wearing green t-shirts, 9 girls will be wearing orange tshirts, 4 boys will be wearing purple t-shirts and the rest of the boys will be wearing brown tshirts. You pick a team of 10 kids. What is the probability that you will pick 7 girls for the team, and at least 6 of them will be wearing orange t-shirts?

Question 5

How will the volume of a cone change if its height increases by a factor of \( \frac{4}{7} \) and the radius decreases by a factor of \( \frac{2\sqrt{5}}{3} \)?

Question 6

Find the recursive formula for the nth term of the sequence:
\( 6 , 9 , 14 , 21 , 30 . . . \)

Question 7

\( 2 + \frac{2}{2 + \frac{2}{2 + \frac{2}{2 + \frac{2}{2 + \frac{2}{2 + \frac{2}{3}}}}}} = \)

Question 8

1 – 2 ( 1 – 2(1 – 2(1 – 2(1 – 2(1 – 5))))) =

Question 9

\( f(x) = -\frac{3}{2x} \), find the equation of \( f(f(f(f(f(f(f(f(x)))))))) \).

Question 10

At how many points does the function f(x) = |-|x^2 + x – 6| + 6| intersect the function g(x) = 12?

Question 11

Find the shortest distance from (-5, 4) to the circle described with the equation \( x^2 + y^2 – 14x + 10y + 10 = 0 \).

Question 12

What is the ratio between the longer leg and the shorter leg of the right triangle if its hypotenuse is 3 times longer than one of the legs?

Question 13

Find two numbers if their sum is equal to 10 and their product is equal to 22.

Question 14

\( \sqrt[4]{16} = 2 \) because \( 2^4 = 16 \)
However, \( (2i)^4 \) also equals 16.
How come \( \sqrt[4]{16} \) isn’t 2i?

Question 15

Simplify.
\( \frac{x^{32 – 1}}{x – 1} = \)