MPM2DT Name: _______________________

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Midterm Exam: Grade 10 IBT Math North Park Secondary School Mr. Gordon Spring 2009 Instructions

Non-programmable, non-graphing calculators are permitted. Complete solutions are required for full marks. Provide exact answers unless a rounded answer is specifically required. Two communication marks are earned based on your ability to present your

solutions using proper form, appropriate terms, symbols, units, and mathematical conventions, as discussed in class.

Reminder First, answer questions you know how to solve. Then try the rest. Good luck! Questions 1. Solve the linear system using the method of substitution. No check is required.

2x − y = 54x + 8y = 20

Overall = _______ 63 Marks 3 1 1 1 2

Marks

1

1

Marks

4

2

MPM2DT Name: _______________________

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2. Solve the linear system using the method of elimination. No check is required.

x3+y2= 3

2x3

−3y4

= −1

3. On the provided grid, draw labeled, accurate graphs of the following lines.

Use the method indicated to graph each line.

a) 3x+ 6y = −12 x intercept is: ________________ y intercept is: ________________

b) y = 32x + 2

slope is: ________________ y intercept is: ________________

c) State the point of intersection: ( , )

Marks

5

5 4

-2

2

6

-4

-6

5 -5

MPM2DT Name: _______________________

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4. Muneeb traveled 400 km to his cottage. He traveled at 100 km/h most of the

way, until a storm forced him to reduce speed to 70 km/h . The whole trip took 5.5 hours. How far did Muneeb travel at each speed?

5. Simran invested $8900 . Part of that amount was invested at 3.5% interest, and the other part at 12% interest. In one year, the two parts earned equal amount of interest. How much did she invest at each rate?

5

Marks

3

3

For questions #4 and #5 below, define the variables using “let” statements, and write two equations. Do not solve.

D O

N O T

S O L V E

D O

N O T

S O L V E

MPM2DT Name: _______________________

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6. On the sets of axes below, draw sketches of graphs that would illustrate the

following situations: a) a linear system with infinite solutions b) a linear system with no solutions

7. Graph each quadratic relation.

a) y = −(x + 2)2 + 3 b) y = −2(x −1)2 + 8 c) y = −(x + 3)(x −1)

8. Is the relation linear, quadratic, or neither? Show your work.

∴ the relation is ______________________

_________________________________ _________________________________

4

-2

2

6

-4

-6

5 -5

4

-2

2

6

-4

-6

5 -5

Marks

2

6

2

x y -5 -34 -4 -20 -3 -10 -2 -4 -1 -2 0 -4 1 -10

1st

2nd

MPM2DT Name: _______________________

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9. Evaluate. Do not write your answer in decimal form.

a) 3−4 = ______ b) (0.912325)0 = ______ c) 32

⎛⎝⎜

⎞⎠⎟−2

= ______

10. Write an equation for the parabola

with vertex (−4, 5) , opening downward, and with a vertical stretch factor of 3. ____________________________

11. The predicted flight path of a toy rocket used in a mathematics project is defined by the relation h = −3(d − 2)(d −12) , where d is the horizontal distance, in metres, from a wall, and h is the height, in metres, above the ground. a) Sketch a graph of the path of the rocket.

b) How far from the wall is the rocket when it is launched? ________

c) How far from the wall is the rocket when it lands on the ground? ________

d) What is the maximum height of the rocket, and how far, horizontally, is it from the wall at that moment? ________ ________

12. Caesium-137 is a radioactive element used in medical imaging. Caesium-137 decays to 1

32 of its original mass every 150 years.

a) Write the fraction 132

as a power with a base of 2. _______

b) What is the remaining mass of 4 g of Caesium-137 after 150 years?

_______

Marks

3

1

2

3

2

MPM2DT Name: _______________________

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13. Expand where necessary, and simplify. You may use expanding shortcuts. a) 3(x + 7)(x − 5) b) (2x − 5)2 c) −(x − 2) − 2(3x + 6) d) (2x + 3y)(2x − 3y) 14. Factor fully, where possible. a) 13ab −15bc b) 12x2 −18xy2 c) 17a2 −11b2 + 2 d) 3m2 −15m − 2m +10 e) m2 −15m + 56 f) 12m2 − 7mn −12n2 g) 7c2 + 8c − 5

Marks

3

4

3

3

4

MPM2DT Name: _______________________

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15. Write an algebraic expression to represent the area of the figure.

Then expand and simplify.

Marks

3