Unit 1 Linear Systems
Unit 2/3 Geometry
Unit 4 Quadratic Relations
Unit 5 Quadratic Expressions
Unit 6 Quadratic Equations
100
State the solution of the linear system below.
Solution is (-1,4)
100
Determine the midpoints of the line segment with endpoints M(-3,-7) and N(-9,3).
Midpoint = (-6, -2)
100
Explain how you can determine whether a relation is quadratic from its equation, graph and table of values.
Equation: highest degree is 2
Graph: parabola
Table of Values: second differences are constant
100
Determine the GCF of
3x^3-15x^2+12x^4
3x^2
100
Determine whether x=5 is a root of the equation
x^2-5x+6=0
It is not a root.
200
Determine whether (-3,5) is a solution to the linear system below.
3x-5y=-34
-2x+y=-11
No, it is not.
200
Determine the equation of the circle centered at the origin with a radius of 9.
x^2+y^2=81
200
Given the quadratic relation,
y=-3(x+2)^2-5
state the...
1. Vertex
2. Axis of Symmetry
3. Direction of Opening
4. Max/Min Value
1. (-2,-5)
2. x=-2
3. Downward
4. Max at y=-5
200
State the both the perfect squares formulae and difference of squares formula.
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
(a+b)(a-b)=a^2-b^2
200
State the discriminant, what is it used for and how you would use it.
1. D=b^2-4ac
2. It is used to determine the number of roots to a quadratic equation.
3. When D>0 2 roots,
D=0 1 root and D<0 no roots.
300
Use substitution to determine the p.o.i of the following linear system.
3m-6n=1
m+3n=2
P.O.I is (1, 1/3)
300
triangleDEF has vertices D(1,3), E(-3,2) and F(-2,-2). Classify the triangle by its side lengths.
The triangle is isosceles.
300
State the transformations applied to the graph of
y=x^2
to form
y=-1/4(x-5)^2+9
, then state the mapping rule.
1. Reflection on the x-axis
2.Vertical compression by a factor of 1/4
3. Translation 5 units right
4. Translation 9 units up
Mapping Rule:
(x,y) -> (x+5, -1/4y+9)
300
Expand and simplify the following.
-2(x+4)+5(2x+1)^2
20x^2+18x-3
300
Determine the x-intercepts of
52x^2-35x-3=0
x=3/4 , -1/13
400
Use elimination to determine the p.o.i of the following linear system.
4x+7y=10
3x-5y=-13
P.O.I is (-1,2)
400
Given triangle ABC state the steps on how you would find the median from vertex C.
Find midpoint of AB
Find slope of median using Midpoint and C
Find y-intercept by subbing in either midpoint or C
400
Determine the equation of the parabola shown below.
y= 2(x-3)^2-4
400
Factor the following
-4x^2+8xy+3x-6y
-(x-2y)(4x-3)
400
State the vertex form of y=-1/2x^2-4x+5 , then state the vertex.
y=-1/2(x+4)^2-3
vertex= (-4,-3)
500
One lawn fertilizer is 24% nitrogen and the other 12% nitrogen. How much fertilizer should be mixed to obtain 100 kg of fertilizer that is 21% nitrogen?
75 kg of 24% of nitrogen
25 kg of 12% nitrogen
500
Explain the steps needed to find the shortest distance from a point to a line.
1. Find the equation of the line formed from the point to the given line. (negative reciprocal of slope, use point to find b value).
2. Find the point of intersection between the given line and newly formed line.
3. Find the distance from the P.O.I and given point.
500
Find a and k so that the parabola y=ax^2+k passes through (-3,11) and (4,18).
y=x^2+2
500
Factor the following
3x^2+40x-323
(3x-17)(x+19)
500
A rectangular field is to be closed by 600 m of fencing on all four sides. Determine the maximum area that can be enclosed.
22500 m^2