Linear Systems
Quadratic Expressions
Quadratic Relations
Quadratic Equations
Trigonometry
100
Solve the following linear system by graphing.
y = -2x + 2
y = x - 1
(Don't forget to properly label the graph!)
What is:
The solution is (1, 0).
100
Expand and/or simplify one of the following expressions.
1) 3-3 + 9-1
2) (4x - 1)(x - 6)
1) What is 2/9
2) What is 4x2 - 25x + 6
100
State the direction of opening, vertex, equation of the axis of symmetry, max/min value, domain and range of the following parabola.
y= -(x + 3)2 + 5
What is:
Direction of opening: down
Vertex: (-3, 5)
Axis of Symmetry: x = -3
Max/min value: y = 5
Domain: {x∈R}
Range: {y∈R|y≤5}
100
Solve the following quadratic relation by factoring.
-10x2 = 21x -10
What is x = -5/2 and x = 2/5
100
Prove that ΔABC and ΔEDC are similar. Then solve for the missing side lengths.
What is:
z - pattern: ∠D = ∠B
z - pattern: ∠E = ∠ A
x - pattern: ∠C = ∠C
e = 8cm d = 6cm
200
Determine the number of solutions found in this linear system (without graphing). State whether the system is intersecting, parallel & distinct, or parallel & coincident.
y = 4x - 3
3y - 5 = 12x
What is:
This linear system has no solutions and is parallel & distinct.
200
Common factor the following polynomial.
4x3y2z - 16x2y4z5 + 2x5yz3
What is 2x2yz(2xy - 8y3z4 + x3z2)
200
Graph the following equation. List all transformations from the base graph (y = x2).
y = -1/2(x - 3)2 + 1
What is:
Transformations:
- reflection on the x-axis
- vertical compression by a factor of 1/2
- horizontal shift 3 units right
- vertical shift 1 unit up
200
Put the following polynomial into Vertex Form.
y = 1/2x2 + 3x + 5/2
What is y = 1/2(x + 3)2 - 2
200
Find the value of x in the following triangle. Round to the nearest tenth, if necessary.
What is x = 27.5 cm
300
Solve the following linear system using elimination.
y = 3x + 3
2y = 4x - 1
What is:
The solution is (-7/2, -15/2).
300
Factor the following polynomials. (hint: difference of squares and perfect squares)
1) 9x4 - 64y2
2) 4x2 +12x + 9
1) What is (3x2 - 8y)(3x2 + 8y)
2) What is (2x+3)2
300
Graph the following quadratic relation.
y = 1/2(x + 3)(x - 5)
What is:
300
Put the following polynomial into Factored Form.
y = 2(x + 3.25)2 - 6.125
What is y = (x + 5)(2x + 3)
300
Find the value of side length m. Round to the nearest tenth, if necessary.
What is m = 5.3 metres
400
Solve the following linear system using substitution.
3x - y = 10
7x + y = 2
What is:
The solution is (6/5, -32/5).
400
Factor the following polynomials.
1) x2 + 11x +30
2) 3x2 + x - 10
1) What is (x + 5)(x + 6)
2) What is (x + 2)(3x - 5)
400
Find the equation for the following graph.
What is y = 7/36(x + 3)(x - 9)
or
What is y = 7/36(x - 3)2 - 7
400
Solve the following equation.
6x2 - 5 = x
What is x= 1 and x= -5/6
400
Solve the following triangle. Round to the nearest degree, if necessary.
What is:
∠A = 78°
∠B = 57°
∠C = 45°
500
Answer one of the following word problems. Round to the nearest tenth, if necessary.
1) Jessica is making a chip mix. She has two different mixtures; The first mixture is 60% Doritos and the second mixture is 3% Doritos. How much of each mixture does she need to make 12kg of a mixture that is 20% Doritos?
2) Jackie and Louis are canoeing at Point Pelee. They took 3 hours to canoe 20km with the current. When canoeing another 20km against the current they took 3.5 hours. What is the speed of the canoe in still water and the speed of the current?
1) What is:
She needs 3.6 kg of the first mixture and 8.4 kg of the second mixture.
2) What is:
The speed of the canoe in still water is 6.2km/h. The speed of the current is 0.5km/h.
500
Jenny had a square garden in her backyard that was x by x metres. She increased the size of her garden by 3 metres on one side and 10 metres on the other. What is the simplified expression for the area of Jenny's new garden? If x = 5, what is the area of Jenny's new garden?
What is:
The simplified expression for the area of Jenny's new garden is x2 + 13x + 30
If x = 5, the area of Jenny's new garden is 120m2
500
George threw a football in the air. The path of the ball can be modelled by the equation y = -x(x-4), where y is the height above the ground and x is the horizontal distance, in metres. What is the maximum height of the ball? How far has the ball travelled when it reaches the ground?
What is:
The maximum height is 4 metres. It has traveled 4 metres once it lands.
500
This year, Lola sold 100 CDs for $10 each. Next year, she plans to increase the price. Her research shows that for every $2 increase, 1 less CD will be sold. What should the selling price be to maximize revenue? What is the maximum revenue? Round answers to the nearest whole number, if necessary.
What is:
The selling price should be $105 to maximize revenue.
The max revenue is $5513.
500
Timmy went on a run. His route was in the shape of a triangle. He started at point A and ran 7km to point B. Then, he turned at an 80° angle and ran 5km to point C. How far did he run from point C to point A? Round to the nearest tenth, if necessary.
What is:
He ran 7.9km from point C to point A.