Polynomials and Factoring Test 3

MPM 2D1 Grade 10


Knowledge & Understanding [23 marks]

1. Expand fully. Show all work for full marks.

a) -2x-3y2 [2 marks]

b) x-12+ x+32 [3 marks]

2. Factor fully. Show all work for full marks.

a) 5xy-2- 102-y [3 marks]

b) 3x2+ 30x+75 [3 marks]

c) 7+14ay+2x+4a [2 marks]

d) 6x2- 19x+15 [3 marks]

e) 12x2- 75y2 [2 marks]

f) 4x2+12xy+9y2 [1 mark]

3. Complete the square. Show all work for full marks.

a) x2+6x [1 mark]

b) 4x2- 8x+7 [3 marks]

Application [15 marks]

4. Find the simplified expression for the area of the shape below. Show all work for full marks! [4 marks]

5. A Frisbee is passed to another teammate in a game of Ultimate Frisbee. The Frisbee follows the path h= -0.02d2+ 0.4d+1, where h is the height, in metres, and d is the horizontal distance in metres that the Frisbee travelled from the thrower.

a) What is the initial height of the Frisbee (the height is it released from)? [1 mark]

b) At what horizontal distance will the Frisbee reach is maximum height? [4 marks]

6. Student council sells sweatshirts to raise funds. The students sell 500 sweatshirts a year at $45 each. They are planning to decrease the price to generate more sales. An informal survey that was taken showing that for every $1 decrease in price they can expect to sell an additional 20 sweatshirts. If the survey results are correct, what price would maximize revenue from the sweatshirt sales? [6 marks]

Thinking & Inquiry [10 marks]

7. The sum of a triangle’s base and height is 20 cm. What is the maximum possible area of this triangle? [5 marks]

8. Find the vertex given the relation y=ax2+ bx+c, a≠0.

[5 marks]