Linear Systems
Quadratic Expressions
Quadratic Relations
Quadratic Equations
Trigonometry
100
How many solutions are found in the following linear system:
y=3x+6
4y=12x+24
There are infinite solutions (coincident)
100
Expand and simplify the following expression:
(3n+2)(6n+3)
(3n+2)(6n+3)
18n2+9n+12n+6
18n2+21n+6
100
If a parabola is represented by the equation y=-3(x+7)2+8, what are the coordinates of the vertex?
(-7,8)
100
Turn the following quadratic relation into factored form: y=x2+6x+8
y=x2+6x+8 +6 x8 2,4
y=(x+2)(x+4)
100
If side length a is 6, side length c is 8 of △ABC, and side length f is 24 of △DEF, what is the value of side length d?
24/8= 3
3x6= 18
d=18
200
Solve the following linear system by graphing:
y=-2x+7
y=3/2x+7/2
The solution is (1,5)
200
Common factor the following expression:
6a3b2c4-6ab3c2+12a2bc3
6abc2(a2bc2-b2+2ac)
200
Describe the transformations of the following quadratic:
y=1/3(x-6)2+13
- vertically compressed by a factor of 1/3
- horizontally translated 6 units to the right
- vertically translated 13 units up
200
Solve for the x-intercepts of the following quadratic relation: 0=2x2-8x+6
0=2x2-8x+6 +(-8) x12 -2,-6
0=(x-1)(x-3)
x-1=0 x-3=0
x=1 x=3
200
If ∠A is 50° and side length a is 6 of △ABC, what is the value of side length x?
Sinθ = opp/hyp
Sin 50 = 6/c
c sin 50 = 6
c sin 50 / sin 50 = 6 / sin 50
c = 7.83
300
Solve the following linear system by substitution:
2x-y=-6
x-2y=-9
1. 2x-y=-6
2. x-2y=-9
3. 2x+6=y
sub 3 into 2 sub x=-1 into 3
x-2(2x+6) = -9 2(-1)+6=y
x-4x-12=-9 -2+6=y
-3x-12=-9 4=y
-3x=-9+12
-3x=3
x=-1
300
Fully factor the following expression:
9x2-36y4
(3x-6y2)(3x+6y2)
300
Sketch the following quadratic:
y=-1/2(x-3)2
HINT - (start by sketching the base graph (y=x2), then apply the "a" value to a second graph, and finally the "h" and "k" values to a final graph)
300
Find the max/min value of the following equation:
y=2x2-12x+36
y=2x2-12x+36 x=b/2a
y=2(3)2-12(3)+36 x-12/2(2)
min: y=18 x=3
300
If ∠D is 59°, ∠E is 67°, ∠F is 54°, and side length f is 7 of △DEF, what is the value of side length e?
e/sinE = f/sinF
e/sin67 = 7/sin 54
e/sin67 x sin67 = 7/sin 54 x sin 67
e=7.97
400
Solve the following linear system by elimination:
12x+8y=8
12x+15y=36
the solution is (-2,4)
400
Fully factor the following expressions:
a. a2-7a+6
b. 5n2+36n+7
a. (a-1)(a-6)
b. (5n+1)(n+7)
400
Find the equation for the following graph in vertex form and standard form:
V.F.: y=-4(x-1)2-2
S.F.: y=-4x2+8x-6
400
Solve the following equation by using the quadratic formula: -4x2+19+7=0
x=-0.34, x=5.09
400
If ∠A is 105°, side length b is 12, and side length c is 15, what is the value of side length a?
a=21.50
500
Complete one of the two word problems:
1. Laura buys two containers of cashews and almonds. The first container is 30% cashews and the second is 45%. How much of each container of nuts should Laura combine to make a separate 4 kg container of 36% cashews?
2. Giuseppe and Alex go boating together in Lake Ontario. They travelled 16 km with the current and took 3.5 hrs. On the way back, the same 16 km took 4.5 hrs against the current. Find the boat's speed in still water and the speed of the current.
1. Laura will need 2.4 kg of the first container and 1.6 kg of the second container to make a 4 kg container of 36% cashews.
2. The boat's speed in still water is 4.06 km/h and the speed of the current is 0.51 km/h.
500
Nico owns a square piece of land with a side length of r. He shortens his property so that the length is decreased by 5 and the width by 7. Write a simplified algebraic expression for the area of Nico's shortened property.
r2-12r+35
500
A flying bird drops a worm. The height, h, in metres, of the worm above the ground can be modelled by the relation h=-6t2+216, where t is in seconds. How far above the ground is the bird when it drops the worm and how long does the worm take to hit the ground?
the bird is 216 m above the ground when it drops the worm. The worm hits the ground after 6 seconds.
500
A candy shop sells candy apples for $14.00 an apple, and they sell roughly 32 a day. If the store decreases the price of the candy apples by $0.50, they estimate they will sell 4 more apples each day. What price should the store charge to maximize its revenue? Also, state the max revenue.
the store should charge $9.00 an apple to receive a max revenue of $648.00 each day.
500
Two buildings are 62 m apart. From the roof of the shorter building, the angle of elevation to the top of the taller building is 35° and the angle of depression to the base of the taller building is 28°. What are the heights of the buildings?
the height of the shorter building is 32.97 m and the height of the taller building is 76.38 metres.