Simplify the following expressions:
(x^2)^5
((y^5)^5)^2)
x^10
y^50
100
What does "i" represent?
What is i^2?
i represents the square root of -1
i^2 = -1
100
What is the vertex of a parabola and how do you determine it?
How do you know if a parabola opens "up" or "down?"
The vertex is the highest or lowest point of the parabola. You find the x-value of the vertex using -b/2a. You then plug that x-value into the equation for the parabola to determine the y-value.
A parabola opens "up" if the coefficient, a, is positive and "down" if the coefficient, a, is negative.
100
What is the difference between an arithmetic and a geometric sequence? Is the following geometric or arithmetic?
3, 11, 19, 27, 35
Arithmetic: add the same number to each term to get the next term
Geometric: there is a common ratio between each term (multiplication)
3, 11, 19, 27, 35 = arithmetic (add 8)
100
f(x) = (x^3)^-2
Simplify & determine f(2)
f(x) = x^-6 = 1/x^6
f(2) = 1/64
200
Simplify the following expressions:
(m^5) * (m^6)
(f^3)*(f^2)*(f^6)
m^11
f^11
200
What is
i^0
i^1
i^2
i^3
i^4
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
200
Explain what the "roots" of a parabola are.
What are the roots of the following parabolas:
x^2+x-12
x^2-7x-60
The roots are the points at which the parabola crosses the x-axis (the points at which the parabola = 0)
x^2+x-12
Roots: 3 & -4
x^2-7x-60
Roots: -5 & 12
200
Determine the pattern in the following sequences:
1, 8, 27, 64
2, 5, 10, 17, 26
0, 1, 1, 2, 3, 5, 8, 13
Simplify the following expressions
(m^2)^5 + m^10
x^3 + x^3 + x^3
2m^10
3x^3
300
What is
i^25
i^26
i^25 = i
i^26 = -1
300
Determine the roots & vertex of the following parabola:
-x^2 + 2x
If the parabola models the trajectory of a projectile, determine the height of the projectile at 1.5 seconds.
Roots: x=0 & 2
Vertex: (1,1)
At 1.5, height = 0.75 units in y direction
300
What do you call a sequence in which each term is the sum of the previous two? Give an example.
Fibonacci
(example)
300
Determine the point at which the two linear functions cross:
y = 2x + 9
y = -3x - 8
2x + 9 = -3x - 8
Solve for x then plug the value back into one of the equations to obtain, y
Answer: (-17/5, 11/5)
400
Simplify the following expressions:
2x^3 + 5(x^2)^2 - 8x^4 + 6(x^1)^3
(5y^3)^2
8x^3 - 3x^4
25y^6
400
Rewrite as an expression involving i
The square root of negative -25
The square root of -144
5i
12i
400
What is the quadratic equation and why is it useful?
Determine the roots of the following (feel free to use a calculator):
x^2+2x-9
(It's difficult to type in this format, so please check your notes if you'd like clarification)
(-b +/- sq rt (b^2 - 4ac)) / (2a)
Roots: -4.16, 2.16
400
What is the sequence of steps in a major scale?
Which steps of the scale are diminished (made flat) to make a natural minor scale?
Simplify the following expression
(2x)^-2
What is the value when x = 2?
Simplified:
1/(4x^2) <<
500
Simplify
(i^4)^5 + i^7 * i^2
(i^4)^5 + i^7 * i^2
i^20 + i^14
1 + -1
0
500
Recall that the equation for the height of a projectile is the following:
h = (1/2)(-9.8)t^2 + voy(t) + ho
(Again, it's difficult to type in this format, so please consult your notes if you'd like clarification.)
Determine the initial y velocity of a projectile launched from ground level, if it reaches a height of 20 m in 2 seconds.
20 = (1/2)(-9.8)2^2 + v*2
v = 19.8 m/s
500
Describe the Circle of Fifths. Specifically, how does it help you determine the notes in a major and minor scale?
What is the order in which sharps are added?
What is the order in which the flats are added?
Circle of Fifths: shows the progression of accidentals (flats and sharps); can be used to relate which major key signature corresponds to which minor key signature
Sharp order: F, C, G, D...
Flat order: B, E, A, D...
500
A line passes through the points (2,4) & (5,8).
Calculate the slope & y-intercept, then determine the equation of the line
Calculate equation of a perpendicular line that pass through the point (0,9)
Slope: (8-4) / (5-2) = 4/3
Y-Intercept: y = (4/3)x+b 8 = (4/3)5 + b b = (4/3)
y = (4/3)x+(4/3)
Perpendicular line: y = (-3/4)x + 9