MPM 2D1 Grade 10
POLYNOMIALS AND FACTORING TEST 3
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.