For This Section, You Do Not Have to Show Your Work

PART 1: OBJECTIVE (20 POINTS)

For this section, you do not have to show your work.

Place your final answer in the right hand column.

2. Solve for x:
5x = 10 / 2.x = 2
3. What is the general equation for a linear relation? / 3.y = mx + b
4. The equation y= ½ x + 3 represents what kind of relationship?
  1. Exponential
  2. Quadratic
  3. Linear
  4. None of the above
/ 4.A
5. Which of the following lines goes downhill from left to right?
  1. y = 2x + 5
B. y = -2x − 6
C. y = 2x
D. y = 2x + 20 / 5.B
6. What is the ordered pair (x-value, y-value) for the origin on a graph? / 6.(0 , 0)
9. Solve for y:
2y + 3 = 13 / 9.y = 5
10. Which line passes through the origin?
  1. y = 5
  1. y = x − 5
  2. y = −5x
  3. y = 2x + 1
/ 10.C
12. Solve for n:
¾ n + 2 = -4 / 12.n = - 8
15. What is the equation of a line with a y-intercept at (0, -9) and a slope of ½ ?
  1. y = ½x - 9
  2. y = -9x + ½
  3. y = ½x + 9
  4. y = −9x − ½
/ 15.A
17. The equation y= 1 + x2represents what kind of relationship?
  1. Exponential
  2. Quadratic
  3. Linear
  4. None of the above
/ 17.B
18. If m=-2 and b=+7, what is the equation of the line? / 18.y = -2 x + 7
20. What is the y-intercept of 4x - 3 = y?
A. ¾ B. 4/3C. –3D. 4 / 20.C

SOLVING BY INSPECTION (5 POINTS)

YOU DO NOT HAVE TO SHOW YOUR WORK.

1. 4x = 16 / x =4
2. x + 8 = 19 / x =11
3. x/2 = 20 / x =40
4. 9 + x = -5 / x =-14
5. x – 12 = 13 / x =25

SOLVING ONE STEP EQUATIONS (12 POINTS)

YOU MUST SHOW ALL OF YOUR WORK!

1. 3x = 36
3 3
x = 12 / 2. 9 + x = 74
-9 -9
x = 65 / 3. x – 32 = 109
+ 32 +32
x = 141
4. 5* x/5 = 60* 5
x = 300 / 5. x - 8 = -43
+8 +8
x = -35 / 6. –9x = 72
-9 -9
x = -8

PART 3: RELATIONS (16 POINTS)

Identify each of the following as Exponential (E), Quadratic (Q) or Linear (L). (16 POINTS)

Question / Answer / Question / Answer
1. y = 2x2 / 1. Q / 9. y= -1/2 x + 3 / 9. E
2.
x
/ y
-2 / -4
-1 / -2
0 / 0
1 / 2
2 / 4
/ 2.L / 10.
X
/ y
-2 / 1/9
-1 / 1/3
0 / 1
1 / 3
2 / 9
/ 10.E
3.
/ 3.E / 11.
/ 11.Q
4.
x
/ y
-2 / 4
-1 / 1
0 / 0
1 / 1
2 / 4
/ 4.Q / 12.
x / y
-2 / ¼
-1 / ½
0 / 1
1 / 2
2 / 4
/ 12.E
5.
x / y
0 / 0
1 / 3
2 / 6
3 / 9
4 / 12
/ 5.L / 13. / 13.
6. y = 3x / 6.E / 14. y = - ½ x + 9 / 14.L
7. y = 5x – 7 / 7.L / 15. / 15.
8. y= 1 + x2 / 8.Q / 16. y = -8 / 16.L

PART 4: LINEAR RELATIONS (79 POINTS)

Find the slope for each of the following:(12 POINTS)

Question

/

Answer

/

Question

/

Answer

1. (3 , 3) and (6 , 9)

/

1. m = 2

/

7. (-4 , 2) and (6 , 7)

/

7.m = ½

2. y = - ¼ x + 10

/

2.m = - ¼

/

8. y = 6x – 2

/

8.m = 6

3.

x

/

y

-2

/

18

-1

/

11

0

/

4

1

/

-3

/

3.m = -7

/

9.

x

/

Y

-2

/

-10

-1

/

-9

0

/

-8

1

/

-7

/

9.m = 1

4.

x

/

y

0

/

4

1

/

0

2

/

-4

3

/

-8

/

4.m = -4

/

10.

x

/

y

6

/

20

8

/

26

10

/

32

12

/

38

/

10.m = 3

Find the equation of the line with the information that is given:(24 POINTS)

Question

/

Answer

/

Question

/

Answer

1. m = -5, b = 0 /

1. y = -5x

/

7. m = - ½ , b = 6

/

7.y = - ½ x + 6

2. m = -1, b = 4

/

2. y = -x + 4

/

8. m = 2/3, b = -1

/

8.y = 2/3 x – 1

3.

x

/

y

-2

/

-12

-1

/

-10

0

/

-8

1

/

-6

/

3.y = 2x - 8

/

9.

x

/

Y

-2

/

15

-1

/

9

0

/

3

1

/

-3

/

9.y = -6x + 3

4.

x

/

y

0

/

7

1

/

5

2

/

3

3

/

1

/

4.y = -2x + 7

/

10.

x

/

y

5

/

3

10

/

13

15

/

23

/

10.y = 2x -7

5.

x / y
–1 / 9
1 / –5
2 / –12
3 / -19
4 / -26
/

5.y = -7x + 2

/

11.

/

11.y = 4x – 12

6.

/

6.y = -2x + 5

/

12.

/

12.y = -3x – 6

Create a Table of values for and graph each of the following equations: (24 POINTS)

1. y = 3x + 5 / 2. y = -½ x – 4
X / y
-3 / -4
-2 / -1
-1 / 2
0 / 5
1 / 8
2 / 11
3 / 14
/ x / y
-3 / -2.5
-2 / -3
-1 / -3.5
0 / -4
1 / -4.5
2 / -5
3 / -5.5
3. y = -x - 6 / 4. y = ¼ x + 2
x / y
-3 / -3
-2 / -4
-1 / -5
0 / -6
1 / -7
2 / -8
3 / -9
/ x / y
-3 / 1.25
-2 / 1.50
-1 / 1.75
0 / 2
1 / 2.25
2 / 2.50
3 / 2.75

Linear Word Problem (19 POINTS)

A car travels at an average speed of 90 km/hr from Yarmouth to Amherst. The towns are 520 km apart. The distance, d kilometers, from Amherst after t hours of driving is given by the equation d = 520 – 90t.

a) Complete the table:

t (h) / 0 / 1 / 2 / 3 / 4 / 5
d (km) / 520 / 430 / 340 / 250 / 160 / 70

b) Graph t on the horizontal and d on the vertical. Be sure to label you axis.

c) What is the slope? What does it represent?

-90 The speed. Distance per hour.

d) What is the d-intercept? What does it represent?

520 km It represents the distance of the trip.

e) What is the t-intercept? What does it represent?

5.8hrs It represents the length of time it takes to travel. 520 km at a speed of 90 km/hr.

Part 5: Factoring

Factor out a monomial from the following expressions:

4x2 – 4x / 4x (x – 1)
9x2 + 18y2 / 9 (x2 + 2y2)
x2y + 2y / y (x2 + 2)
121a – 11b / 11 (11a – 1b)
15a + 12b + 6c / 3 (5a + 4b + 2c)
15x2 + -50x + -10 / 5 (3x2 -10x -2)
18k + 36k2 + 9k3 / 9k (2 + 4k + k2)
x3 + x2 + x / x (x2 + x + 1)
6q + 10q2 + 8q3 / 2q (3 + 5q + 4q2)
64c3 + -56c2 + 88c / 8c (8c2 – 7c + 11)

Factor the following trinomials:

1. x2 + 8 x + 15

(x + 3)(x + 5)

2. x2 + x - 6

(x + 3)(x - 2)

3. m2 - 6m - 7

(m - 7)(m + 1)

4. p2 + 10p + 16

(p + 2)(p + 8)

5. w2 + 9w + 8

(w + 8)(w + 1)

6. y2 - 100

(y + 10)(y – 10)

7. n2 + 4n - 12

(n + 6)(n-2)

8. s2 + 13s + 36

(s + 9)(s + 4)

EVALUATING EXPRESSIONS (23 POINTS)

Example:This is how I will be marking the following questions. Please show you work the same way it is given in the example.

If a = -3 , b = 2 and c = -2, evaluate the following:

12a2 + 3b – 6c

12 (a)2 + 3(b) – 6(c) (1 POINT)

12 (-3)2 + 3(2) – 6(-2) (1 POINT)

12(9) + 6 – 6(-2)(1 POINT)

108 + 6 + 12 (1 POINT)

126(1 POINT)

SHOW YOUR WORK If x = 5, y = -4 and z = 2, solve the following equations:

1. 7x +y (4 POINTS)
7(x) + (y)
7(5) + (-4)
35 + -4
31 / 2. 8y + 5z (4 POINTS)
8(y) + 5(z)
8(-4) + 5(2)
-32 + 10
-22 / 3. 6z +5y – 2x (5 POINTS)
6(z) + 5(y) – 2(x)
6(2) + 5(-4) -2(5)
12 + (-20) – 10
-8 -10
-18

4. SHOW YOUR WORK

a) If x = 3, y = -2 and z = -6, evaluate the following: (5 POINTS)

2x - 5y + 4z
2(x) – 5(y) + 4(z)
2(3) – 5(-2) + 4(-6)
6 +10 -24
16 – 24
-8

SHOW YOUR WORK

b) If x = 2, y = 4 and z = -3, evaluate the following:(5 POINTS)

- x2 + y2 - z2
-(x)2 + (y)2 –(z)2
-(2)2 + (4)2 – (-3)2
-(4) + 16 – (9)
12 – 9
3

Combining Like Terms(13 POINTS)

Let = -x2 =-x  =- 1  = x2 = x  =1

Simplify the following as algebraic expressions:

1. = (3 points)

1. –x2 –x -5

2.=

(3 points)

2. 2x2 + 4

3.  =

(2 points)

3.6x -5

4. =(2 points)

4. -4x +8

5.   .

 

(3 points)

5.x2 -10x -6

MATCHING(14 POINTS)

Place the letter of the corresponding word in the blank to match the term to the definition.

A. Trinomial D. Algebra G. Variable J. Expression M. Binomial B. Constant E. Monomial H. Coefficient K. Polynomial N. Term
C. Distributive property F. Like Terms I. Algebraic Modeling L. Equation
1. F / Terms that have the same literal coefficient. 3xy and -5xy are like terms but 2x and 7x2 are not like terms.
2. B / A term in an expression that contains no symbols.
3.G / A symbol that represents a number. Usually, we use letters such as n, t, or x.
4.J / A mathematical statement that may use numbers, variables, or both.
5.K / An algebraic expression consisting of one or more terms separated by addition or subtraction signs.
6. H / The numerical part of the term, or the number factor of the term.
7.E / A polynomial with one term.
8.L / A statement formed by two expressions related by an equal sign.
9.M / A polynomial with two terms.
10.N / An expression formed by the product of numbers and symbols.
11.D / A branch of mathematics that uses mathematical statements to describe relationships between things that vary over time.
12.I / A model that represents a relationship by an equation or formula, or represents a pattern of numbers by an algebraic expression.
13.A / A polynomial with three terms.
14.C / A rule for expanding an expression within brackets by multiplying each term inside the brackets by the term outside the brackets.

1. a)(y + 4)(y + 2) = y2 + 6y + 8b)(x + 1)(x + 1) = x2 + 2x + 1c) (y + 2x)(y + x) = y2 + 3xy + 2x2

2. a) (3y + 4)(2y + 1) = 6y2 + 11y + 4b) (2x + 1)(2y + 2) = 4xy + 2y + 4x + 2

c)x2 + 3x + 2d) 2y2 + 7y + 6e) 16 + 8y + y2

3. a) –6 – 2c + 3d + cdb) 10k – k2 – 9c)a2 + 2ab + b2d)m2 – 2mn + n2

e) –81p2 + 4f) –3m2 – 19m + 72g) 12 + 6d – 6d2h) 2m3 + m2n + 2mn2 + n3

4. a)i)y2 + 4y + 4ii)y2 – 4y + 4iii) y2 – 4

b)i)m2 + 12m + 36ii)m2 – 12m + 36iii)m2 – 36

  • When you multiply two binomials where each term is positive, the term that is not squared will be positive.
  • When you multiply two binomials where one term is negative, the term that is not squared will be negative.
  • When you multiply two binomials where one term is negative and the second binomial is the opposite, the term that does not have a square will be eliminated.

5. 8n2 – 14n – 15

6. a) (x– 1)(x–4)b) (p+3)(p–8)c) (w–7)(w–5)d) (y– 7)(y+4)

7. a) (x + 4)b) (y – 2)c) (z + 3)d) (c + 8)

8. a) 3x2 – 10xb) –x2 – 8x + 5c) 2y2 – 44d) 3x3 + 5x2 – 21x + 10

1.a)

(x, y) in PQRS / (x, y) in PQRS
P(4, 3) / P(1, 5)
Q(–1, 3) / Q(–4, 5)
R(–1, –1) / R(–4, 1)
S(4, –1) / S(1, 1)

b)(x, y)  (x – 3, y + 2)

2.b)

(x, y) in ∆ABC / (x, y) in ∆ABC
A(2, 4) / A(1, 2)
B(0, –4) / B(0, –2)
C(8, 4) / C(4, 2)

c)(x, y) (0.5x, 0.5y)

3.c)

(x, y) in TUVW / (x, y) in TUVW / (x, y) in TUVW
T(4, 1) / T(1, –4) / T(–1, 4)
U(–2, 3) / U(3, 2) / U(–3, –2)
V(–4, –1) / V(–1, 4) / V(1, –4)
W(2, –3) / W(–3, –2) / W(3, 2)

d)90 clockwise: (x, y) (y, –x)

90 counterclockwise: (x, y)(–y, x)

4.a)translation; (x, y) (x, y + 5)

b)reflection in y-axis; (x, y) (–x, y)

c)reflection in y = x; (x, y) (y, x)

d)rotation 90 counterclockwise; (x, y) (–y, x)

5.Original coordinates are G(–1, –2), I(–5, –3), H(–2, –4); (x, y)  (–y, –x)

1.similar; A = X, B = Z, C = Y, , ∆ABC~∆XZY

2.Answers will vary. For example, all three corresponding sides are proportional, or all three angles are equal.

3.a)a = 9 cm

b)b = 9 cm

c)c = 3 cm

d)d =12 m

4.a)No, he only needs to know the value of two pairs of corresponding angles because the three angles in a triangle always add to 180.

b)No, all she needs to know is the two pairs of corresponding angles, as all angles in a triangle add to 180. The pair of corresponding sides is extra information.

5.15 m

6.0 < h 1.5 m, where h is the height of the fence.

7.a)AB = 4, BC = 2.2, AC = 3.6,
AB = 8, BC = 4.5, AC = 7.2,
A = 34º, B = 64º, C = 82º,
A = 34º, B = 64º, and C = 82º

b)A = A, B = B, C = C and all corresponding sides are proportional.

c)2

d)(0, 0)