Capebretonvictoriaregionalschool Board

CapeBretonVictoriaRegionalSchool Board

BRETON EDUCATION CENTRE

Mathematics 9 Examination

January , 2008

Ms. Mackenzie

Mr. Porter

Student Name:______

Exam Mark:_____

GOOD LUCK!!!

Math 10 Examinations: Formula Sheet

1. Symbols:2. Alge-Tiles:

___

Irrational- QX2

Rational- Q-X2

Integers- I

X

Whole - W

-X

Natural- N

1

-1

3. Pythagorean Theorem:

4. Laws of Exponents:

i) am x an = am+nii) am an = am-niii) (am)n = am xniv) (ab)m = ambm

v) = vi) a0 = 1vii) a-n = viii)

5. Area of a Rectangle:

6. Area of a Triangle:

7. Distributive Property: a(b + c) = ab + ac

(a + b)(c + d) = ac + ad + bc + bd

Selected-Response Questions

(Total Value – 25 points)

In this part of the examination, there are 25 selected-response questions, each with a value of 1 point. Read each question carefully and decide which of the responses best answers the question being asked. There is only one correct answer for each of the 25 selected response questions. Clearly circle the correct answer. If you circle more than one answer you will be marked wrong for that question.

Part A – Selected Response

1. Which of the following statements is TRUE?

a) All rational numbers are integers.

b) Every real number is either positive or negative.

c) All integers are rational numbers.

d) All real numbers are rational.

2. Which of the following is an irrational number?

a) b) c) d) -

3. What is the value of 6-2 ?

a) 36b) 12c) d)

4. What is the simplified form of (2x2y3z4)3 ?

a) 2x6y9z12b) 8x5y6z7c) 2x5y6z7d) 8x6y9z12

5. Which of the following is equal to 570 000 000 000?

a) 5.7 x 1025b) 2.9 x 1025c) 5.7 x 1011d) 2.9 x 1011

6. Which of the following is equal to (3.0 x 10-1)(2.5 x 1013) ?

a) 7.5 x 1014b) 5.5 x 1012c) 5.5 x 1014d) 7.5 x 1012

7. What can be added the expression 8x2 + 3x to generate 16x2 + 5x?

a) 8x + 2b) 8x2 + 2xc) 8x + 2xd) 8x2 + 2

8. Which algebraic expression best represents this symbolic expression?

a)-2x2 + 3x – 3b) 2x – 3x + 3c) 2x – 3x + 3d) 2x2 -3x + 3

9. Factor the following: 8x + 16y

a) xy (8 + 16)b) 8 (x + 2y)c) 8 (x + y)d) 8x + 16y

10. What is -9x – y + 1 + 5y +5x – (-10) simplified?

a) 14x + 4y + 11b) -4x + 4y – 9c) -4x + 4y + 11d) 4x – 4y – 11

11. What is the product of the two binomials (x + 9)(x + 1)?

a) x2 + 10x + 9b) x2 + 9x + 10c) 2x + 10d) x2 + 9x + 9

12. What is the product of these two polynomials x(x2 + 6x + 8)?

a) 2x3 + 7x2 + 9xb) x3 + 6x2 + 8xc) x2 + 7xd) x3 + 7x2 + 9

13. Which algebraic expression would best represent this area model?

a) x2 + 3x + 3b) x2 + 4x + 3c) 5x + 3d) 5x2 + 4

14. Simplify (5x + 10)5

a) 5x + 10b) 5x + 2 c) x + 2d) x + 5

15. Which equation is true when x = -4

a) -5 + 3x = -7b) -3x + 5 = 17c) 6x – 4 = -20d) -4x – 3 = -18

16. To enter JT’s after 9pm, you must be at least 19 years of age. Which set notation represents this condition?

a) {x | x 19, x R}b) {x | x< 19, x R}

c) {x | x 19, x R}d) {x | x> 19, x R}

17. Express the following number line in words.

a)All whole numbers less than or equal to 8.

b)All integers greater than 2 and less than or equal to 7.

c)All natural numbers greater than or equal to 2 and less than or equal to 7.

d)All real numbers greater than 2.

18. Which set notation represents the graph?

a) {x | x -1, x I}b) {x | x -1, x R}

c) {x | x> -1, x R}d) {x | x< -1, x R}

19. Which statement is true? – 4 is a solution for:

a) 2x – 4 > 8b) 4x + 8 < -1c) -2x + 3 < 7 d) x > - 4

20. Identify the solution set for the inequality 5x + 3 2x – 6.

a) {x | x -3, x R}b) {x | x 3, x R}

c) {x | x 2, x R}d) {x | x -3, x R}

21. The Maritime Phone Company charges a monthly fee of $22.00 and a long distance rate of $2.00 per minute within Canada.Terry can only budget $50.00 a month for his phone bill.What expression below represents this scenario?

a) 50 2t + 22b) 50 2t + 22c) 50 22t + 2d) 50 22t + 2

22. Choose the correct graph to represent the equation:

{x |- 3 x 1,x R}

a) b)

c)d)

Use these Matrices to answer questions 23, 24 and 25.

A = B =

C = D =

23. What are the dimensions of matrix C?

a) 2 x 2b) 2 x 3c) 2 x 4d) 4 x 2

24. Where is 3 in matrix B?

a) R2, C2b) R1, C1c) R2, C1d) R1, C2

25. What do you get when you add matrix A to matrix B?

Constructed-Response Questions

(Total Value – 70 Points)

Read each question carefully and write your response in the space provided.

Show all of your work, as points will be given for correct method as well as for a correct answer. The method used to solve a problem must be clearly shown even when using a calculator.

Part 2 – Constructed Response – Short/ Long Answer

1. Place "X"s in the chart to classify the numbers into the correct number sets.

2. Evaluate each of the following using (ORDER OF OPERATIONS!!)

** Keep all fractions as fractions… do not change them to decimals!

a) -2 (-4 + 7) + 2(1-5) b)

3. Use the Law of Exponents to express each of the following as a single power, if possible. Then evaluate.

a) (42)3b) 27 x 2326c)

4. Simplify, keeping your answers in scientific notation.

a) (0.7 x 104) + (2.3 x 103)b) (5 x 103) x (3.2 x 102)

4 x 10-1

5. Simplify the following.

a)(4x + 4) + (-3x – 2)b) (3x2 – 10x) – (-2x2 + 5x)

6. Combine like terms and express your answer symbolically as well as algebraically.

a)

+ =

______+ ______= ______

b)

+=

______+ ______= ______

7. Fully factor each of the following polynomials using either the Area Model method (alge-tiles) or by finding the greatest common factor.

a) 4x + 8b) 6x2 + 12x

8. Expand and SIMPLIFY the following expressions.

a) 2(x + 4) b) 3(x2 – 4x + 3)

c) (x + 3)(x + 5)d) 3(x + 2) + 4(x – 5)

9. For each rectangle,

i)write an expression for the area

ii)expand your expression

iii)find the area when the variable is 3 meters

10. Simplify the following using the method of your choice.

a) (4x + 6) 2b) (x2 + 3x) x c) (63y3 – 27 y2 + 81y)9y

11. Solve each equation. Verify your answers (CHECK!!!)

a) -3x + 16 = 5xb) 6x + 8 = 4x – 10c) x2 + 14 = 50

12. What is the value of x in each of the following?

a) x – 2 = x + 4b) 2(3x – 4) = (6x + 8)

13. For house calls, a plumber charges $25 per visit plus $15 per hour.

1. Write an algebraic expression to describe the charges for one house call. Explain what your variable represents.

1. Use your expression to find the total charge for a repair job that takes 3.5 hours.

1. Suppose all charges are doubled for evenings, weekends, and holidays. Write a simplified expression for these charges.

1. Use this expression to calculate the cost of a 2 hour repair job on Christmas day.

14. Solve each inequality and verify your solution.

a) 4x + 3 < 13b) 5x – 2 < 3x + 6

d) 5(x + 2) 9(x + 2)d) x – 2 x + 2

15. Write a set notation for each description and plot on a number line

a)All natural numbers greater than 11 but less than or equal to 18.

______

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

b) All Whole numbers less than 5.

______

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

c) All real numbers greater than -2 and less than or equal to 3.

______

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

16. A rectangular garden is 12 m longer than its width. The perimeter of the garden is to be greater than 68 m but less than or equal to 112 m.

a)Draw a diagram and label the dimensions

b)What are the possible dimensions for the width of the garden?

17. In Antigonish, the Campus Bookstore at St. F. X. decides to buy out the stock of the College Bookstore downtown. The inventories are as follows.

Campus Bookstore:

Hardcover: textbooks – 2280; fiction – 680; nonfiction – 1320; reference – 890

Paperback: textbooks - 940; fiction – 930; nonfiction – 700; reference – 1061

College Bookstore:

Hardcover: textbooks – 1345; fiction – 540; nonfiction – 329; reference – 762

Paperback:textbooks – 750; fiction – 876; nonfiction – 455; reference – 623

a) Express each bookstore’s inventory as a 4 x 2 matrix for the campus bookstore.

b) Express each bookstore’s inventory as a 4 x 2 matrix for the college bookstore.

c)Using the matrices you have developed to determine the total inventory that the Campus Bookstore will now have.