Download Cape Breton Victoria Regional School Board BRETON EDUCATION

Cape Breton Victoria Regional
School 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
___
- Q
X2
Rational
- Q
-X2
Integers
- I
Whole
- W
Natural
- N
X
-X
1
-1
3. Pythagorean Theorem: c2 = a2 +b2
4. Laws of Exponents:
i) am x an = am+n
m
 am 
a
v)   =  m 
b
b 
ii) am  an = am-n
0
vi) a = 1
5. Area of a Rectangle:
A  lw
6. Area of a Triangle:
1
A  bh
2
iii) (am)n = am x
n
 1 
vii) a =  m 
a 
-n
7. Distributive Property: a(b + c) = ab + ac
(a + b)(c + d) = ac + ad + bc + bd
8. Set Notation:
9.
iv) (ab)m = ambm
a
viii)  
b
m
b
 
a
m
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)
9
_
b) 1.3
c)
7
6
d) -
c)
1
36
d)
6
3. What is the value of 6-2 ?
a) 36
b) 12
1
12
4. What is the simplified form of (2x2y3z4)3 ?
a) 2x6y9z12
b) 8x5y6z7
c) 2x5y6z7
d) 8x6y9z12
5. Which of the following is equal to 570 000 000 000?
a) 5.7 x 1025
b) 2.9 x 1025
c) 5.7 x 1011
d) 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 1014
b) 5.5 x 1012
c) 5.5 x 1014
d) 7.5 x 1012
7. What can be added the expression 8x2 + 3x to generate 16x2 + 5x?
a) 8x + 2
b) 8x2 + 2x
c) 8x + 2x
d) 8x2 + 2
8. Which algebraic expression best represents this symbolic expression?
a)-2x2 + 3x – 3
b) 2x – 3x + 3
c) 2x – 3x + 3
d) 2x2 -3x + 3
c) 8 (x + y)
d) 8x + 16y
9. Factor the following: 8x + 16y
a) xy (8 + 16)
b) 8 (x + 2y)
10. What is -9x – y + 1 + 5y +5x – (-10) simplified?
a) 14x + 4y + 11
b) -4x + 4y – 9
c) -4x + 4y + 11
d) 4x – 4y – 11
11. What is the product of the two binomials (x + 9)(x + 1)?
a) x2 + 10x + 9
b) x2 + 9x + 10
d) x2 + 9x + 9
c) 2x + 10
12. What is the product of these two polynomials x(x2 + 6x + 8)?
a) 2x3 + 7x2 + 9x
b) x3 + 6x2 + 8x
c) x2 + 7x
d) x3 + 7x2 + 9
13. Which algebraic expression would best represent this area model?
a) x2 + 3x + 3
b) x2 + 4x + 3
c) 5x + 3
d) 5x2 + 4
c) x + 2
d) x + 5
14. Simplify (5x + 10)  5
a) 5x + 10
b) 5x + 2
15. Which equation is true when x = -4
a) -5 + 3x = -7
b) -3x + 5 = 17
c) 6x – 4 = -20
d) -4x – 3 = -18
16. Which equation is true when y =
a) 15y – 6 = 11
1
?
3
b) 3y – 3 = 6
c) 12y + 3 = 7
d) 4y + 5 = 9
17. 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}
c) {x | x  19, x  R}
b) {x | x < 19, x  R}
d) {x | x > 19, x  R}
18. Express the following number line in words.
–2 –1 0
1
2
3
4
5
6
7
8
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.
19. Which set notation represents the graph?
–4 –3 –2 –1 0
1
2
3
4
a) {x | x  -1, x  I}
c) {x | x > -1, x  R}
5
6
b) {x | x  -1, x  R}
d) {x | x < -1, x  R}
20. Which statement is true? – 4 is a solution for:
a) 2x – 4 > 8
b) 4x + 8 < -1
c) -2x + 3 < 7
d) x > - 4
21. Identify the solution set for the inequality 5x + 9  2x – 6.
a) {x | x  -3, x  R}
c) {x | x  2, x  R}
b) {x | x  3, x  R}
d) {x | x  -3, x  R}
22. 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 + 22
b) 50  2t + 22
c) 50  22t + 2
23. Choose the correct graph to represent the equation:
{x |- 3  x  3,x  R}
a)
b)
c)
d)
d) 50  22t + 2
Use these Matrices to answer questions 24 and 25.
2
A= 
 3
2

5
C= 
 4

 3
1

0 
7

1
6 

8 
 3 1
B= 

 2 3
 2 3


2 0 

D=
1 3


 5 8 
24. What are the dimensions of matrix C?
a) 2 x 2
b) 2 x 3
c) 2 x 4
d) 4 x 2
c) R2, C1
d) R1, C2
25. Where is 3 in matrix B?
a) R2, C2
b) R1, C1
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)
1 1 1
 
6 4 3
3. Use the Law of Exponents to express each of the following as a single
power, if possible. Then evaluate.
a) (42)3
b) 27 x 23 ÷ 26
c)
311 ×38  31
39 ×35
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 + 8
b) 18x3 + 12x2 + 6x
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)  2
b) (x2 + 3x)  x
c) (63y3 – 27 y2 + 81y)  9y
11. Solve each equation. Verify your answers (CHECK!!!)
a) -3x + 16 = 5x
b) 6x + 8 = 4x – 10
c) x2 + 14 = 50
12. What is the value of x in each of the following?
a)
3
1
x–2= x+4
2
4
b) 2(3x – 4) =
1
(6x + 8)
2
13. For house calls, a plumber charges $25 per visit plus $15 per hour.
a. Write an algebraic expression to describe the charges for one
house call. Explain what your variable represents.
b. Use your expression to find the total charge for a repair job
that takes 3.5 hours.
c. Suppose all charges are doubled for evenings, weekends, and
holidays. Write a simplified expression for these charges.
d. 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 < 13
b) 5x – 2 < 3x + 6
d) 5(x + 2)  9(x + 2)
d)
5
2
x–2  x+2
6
3
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.