Linear Systems
Quadratic Expressions
Quadratic Relations
Quadratic Equations
Trigonometry
Analytic Geometry
100
Determine the algebraic equation that would represent the following:
Seven times a number subtracted from 5 is 26
5-7x=26
100
Expand and simplify
(3x-1)(2x+10)
6x^2+28x-10
100
What is the y-intercept of the function
y=3x^2-4x-10
(0,-10)
100
What is the quadratic formula?
x=(-b+-sqrt(b^2-4ac))/(2a)
100
Determine the value of x if
sinx=0.82
55 degrees
100
Determine the coordinates of the midpoint Q(-3,-3) and R(-1,-7)
(-2, -5)
200
Solve by substitution.
x+4y=6
2x-3y=1
(2, 1)
200
Expand and simplify.
(x-5)^2-3(2x+7)
x^2-16x+4
200
State the transformations of
y=-1/2(x-2)^2+8
reflection in the x-axis
vertical compression by a factor of 1/2
horizontal shift right 2 units
vertical shift up 8 units
200
Solve by factoring.
3x^2-9x
x=0, x=3
200
ABC is a right triangle.
AB=7cm, angle B is 90 degrees, angle C is 64 degrees. Calculate the length of BC.
3.4 cm
200
Find the length of the line segment with endpoints J(2.1, 8.3) and K(-4.5, -4.7)
14.6
300
Solve using elimination
3x+2y=2
4x+5y=12
(-2,4)
300
What is the GCF of the following?
5x^2y^3-15x^2y^2+45xy^2+20xy
5xy
300
State the vertex, direction of opening, axis of symmetry and max/min value of the following:
y=8(x-3)^2-7
V=(3,-7)
opens up
x=3
min of -7
300
Determine the x-intercepts.
2x^2-x-6
(2,0), (-3/2,0)
300
Find the value of x. Round to one decimal.
x=15.9
300
For the triangle with vertices A(-2, 0), B(8, 8) and C(4, -2)
Determine the equation of the median from vertex A
y=3/8x+3/4
400
Maria had $10 000. She invested part of it in an account paying 4% per annum and remainder in bonds paying 5% per annum. If the total interest earned after 1 year was 440, how much did she invest in each account?
Maria invested $6000 at 4% and $4000 at 5%
400
Factor.
x^2-7x+10
(x-5)(x-2)
400
Find the equation of a parabola that has a vertex at (-2,-5) and goes through the point (0,-3)
y=1/2(x+2)^2-5
400
Solve using quadratic formula.
(x-2)^2+10=0
x=5.16, x=-1.16
400
Determine the value of a
a=17
400
A triangle has vertices L(8,8), M(-2,0), and N(4,-2)
Determine the equation of the altitude from vertex M.
y=-2/5x-4/5
500
Maryam has a bottle of 5% acetic acid and a bottle of 10% acetic acid. How much of each would she use to make 250 mL of 8% acetic acid?
Maryam would mix 100 mL of the 5% acetic acid with 150 mL of the 10% acetic acid.
500
Factor.
-12n^2+27m^2
-3(2n+3m)(2n-3m)
500
Determine the vertex of the parabola.
y=-5x^2+20x+2
V=(2,22)
500
A sporting goods store sells 90 ski jackets in a season for $200 each. Each $10 decrease in the price would result in five more jackets being sold. What is the max revenue?
The max revenue is $18050
500
From the hay loft door, Ted sees his dog on the ground. The angle of depression of the dog is 40ยบ. Ted's eye level is 16 feet above the ground. How many feet must the dog walk to reach the open barn door directly below Ted (to the nearest foot)?
19 feet
500
Determine the equation for the right bisector of the line segment with endpoints P(-5,-2) and Q(3,6)
y=-x+1