Extra Credit Math Questions
1) Determine the value of ii where i = -1. hint: eix = cos x + i sin x
x2
2)
----------------------
=
4
x2
5 -
------------x2
5 -
------5 – x2
Find all values of x that satisfy the above equation.
3) The function y = f(x) = ax2 + bx + c passes through the points (0,3),
the value of a, b, and c.
(1,11), and (2,15). Determine
4) Let a, b, c, and d be the roots of the equation 2x4 + x3 – 8x2 – x + 6 = 0 and let E(a,b,c,d) be the
expression (2 + a)(2+ b)(2 + c)(2 + d). Find the value of E(a,b,c,d).
5) Find the perimeter of the triangle whose vertices lie on the sides (faces) or vertices of a cube whose
edge length is 1 so that the perimeter of the triangle is maximal.
6) Find the solutions of the equation x2/3 – 5x1/3 + 6 = 0.
7) Let a, b, and c be integers where:
a+b+c=–6
a3 + b3 + c3 = 3
ab + ac + bc = 2
Find the value of abc.
8) Let H1 be a regular hexagon with side of length 1. Let Hn+1 be the regular hexagon formed by joining
the mid-points of the sides of hexagon H n where n  1. Find an expression for the area of hexagon H n
where n  1.
9) Let S1 = 1
Let T1 = 1 – ½S1
Extra Credit Math Questions
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Let S2 = 1 + ½S1
Let T2 = 1 – ½S2
Let S3 = 1 + ½S2
Let T3 = 1 – ½S3
...
Let Sn = 1 + ½Sn-1
Let Tn = 1 – ½Sn
a) Determine the value of Sn
b) Determine the value of Tn
10) In the diagram below, circle P has radius 4 and sector BPC has area 4/3. APC is a diameter of
circle P. Determine the exact area of ∆APB without using any trigonometric functions or  in the
expression.
B
A
C
A
P
11) Determine the area of the region in the x-y plane that satisfies the inequalities: x 2 – 6x + y2 – 8y + 21  0
and |4y + 3x|  25.
12) Find all integers x that satisfy the inequality:
log2(3x)  log3(4x)  (e2ln(1000))1/3
13) Let (n) = the number of 1's in the binary (base 2) representation of the integer n and let (n) be the
sum: (n) = (1) + (2) + (3) + … + (n). Determine the value of (1024).
14) A person is d feet from a bus stop where a bus is stopped at a red light. At the moment that the light
turns green, the person begins running toward the bus at a constant speed of v feet per second while the
bus continually accelerates at a constant acceleration of a feet per second2. Refer to your Physical
Science course for the relationships between distance, time, speed, and acceleration.
a) Show that if v > 2ad that the person can “catch” the bus at two different times and determine these
times.
b) Show that if v = 2ad that the person can “catch” the bus at a single point in time and determine that
time.
Extra Credit Math Questions
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c) Show that if v < 2ad that the person cannot “catch” the bus at all.
d) Referring to part a), discuss any problems that the person might have “catching” the bus at the later
time.
15) Given a circle of radius 1 centered at the origin and a point b on the y-axis (where b > 1 so b is
“outside” of the circle), determine the slope m (in terms of b) of the line that is tangent to the circle in the
first quadrant and also passes through the point (0, b) as shown in the diagram below:
^y
(0, b)
>x
16) Determine the full solution set of the inequality below (where x is a
Real Number):
x – 2
x
--------- > ----2(x – 3)
x + 3
17) A flask contains 120 mL of a solution. If 40 grams of the solution are added to the flask, the total
mass of the solution in the flask is 200 grams. What was the mass of the original 120 mL of solution in
the flask? extended-response question
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