Math 9
JUNE FINAL EXAM
Pre test

	1.	This pattern of unit squares continues. 
Determine an equation that relates the number of unit squares, n, to the figure number, f. 

	2.	The pattern in this table continues. Write an equation that relates the term value to the term number.

Term Number, t	1	2	3	4	5	
Term Value, w	5	8	11	14	17	

	3.	The cost of a taxi ride is the sum of a fixed cost of $2.50 for the first kilometre, plus $1.75 for each additional kilometre.
a)	Write an equation that relates the cost of a taxi ride, F dollars, to the distance travelled, n.
b)	Determine the cost of a 28-km taxi ride.

	4.	Which equations represent a linear relation?
i)	
ii)	
iii)	
iv)	

	5.	This is a partially completed table of values for a linear relation.
a)	Determine the missing values of y.

x	2	3	4	5	6	
y			19	22		

b)	Write an equation that represents the linear relation.

	6.	Graph the equation .

	7.	Graph the following lines on the same grid. Label the lines.
i)	
ii)	

	8.	Graph the following lines on the same grid. What shape do they form?
i)	
ii)	
iii)	

	9.	Match each equation with a graph on the grid below.
i)	
ii)	
iii)	

	10.	This graph represents a linear relation.
a)	Determine the value of x when y = 3.
b)	Estimate the value of y when x = –2.

	11.	This graph represents a linear relation.
a)	Estimate the value of y when .
b)	Estimate the value of x when .

	12.	Is each expression a monomial, binomial, or trinomial?
a)	
b)	4x2
c)	
d)	
e)	

	13.	Name the coefficients, variable, degree, and constant term in the polynomial .

	14.	Identify the degree of each polynomial.
a)	
b)	
c)	
d)	
e)	

	15.	Combine like terms. Sketch algebra tiles if it helps.

	16.	Simplify: 

	17.	Write a polynomial to represent the perimeter of the rectangle.

	18.	Add: 

	19.	Write the perimeter of this equilateral triangle as a polynomial in simplest form.

	20.	Subtract: 

	21.	Subtract: 

	22.	Multiply: 

	23.	Divide: 

	24.	Divide: 

	25.	Divide: 

	26.	Determine the product: 

	27.	Solve: 

	28.	Solve: 

	29.	Solve: 

	30.	A rectangle has width 1.3 cm and perimeter 10.2 cm.
a)	Write an equation that can be used to determine the length.
b)	Solve the equation.

	31.	Solve: 

	32.	Solve: 

	33.	Write 4 numbers that are solutions of this inequality: 

	34.	Write 4 numbers that are solutions of this inequality: 

	35.	Write an inequality whose solution is graphed on the number line.

	36.	Write an inequality whose solution is graphed on the number line.

	37.	Which operation will you perform on each side of the inequality to isolate the variable?

	38.	Which operation will you perform on each side of the inequality to isolate the variable?

	39.	Solve and then graph this inequality: 

	40.	State whether you would reverse the inequality sign to solve each inequality.
a)	
b)	
c)	
d)	

	41.	Solve . Graph the solution.

	42.	Solve: 

	43.	Determine the scale factor for this scale drawing.

	44.	An enlargement of the shape below is made using a scale factor of 2. 
Determine the side lengths of the enlargement.

	45.	Which of rectangles A, B, and C are scale diagrams of the shaded rectangle? 
For each scale diagram you identify, state the scale factor.

	46.	Determine the scale factor of this reduction as a fraction and as a decimal.

	47.	A rectangular garden measures 15 m by 9 m. 
A similar rectangular garden is 7.5 m long. 
Calculate the width of the garden.

	48.	These quadrilaterals are similar. Determine the values of x and y°.

	49.	Determine the length of EF in these similar triangles. 

	50.	Determine the length of QR in these similar triangles.

	51.	This scale diagram shows the measurements a surveyor made to determine the height of a building. What is this height?

	52.	State the number of lines of symmetry in each design.

	53.	This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by drawing its other half.

	54.	Hexagon B is the rotation image of hexagon A. Describe the rotation.

	55.	How many lines of symmetry does a regular pentagon have?

	56.	Which figure below shows two quadrilaterals related by both rotational symmetry and line symmetry?

	57.	Determine whether the two octagons are related by line symmetry, by rotational symmetry, by both types of symmetry, or by neither.

	58.	Determine whether polygon A and its image are related by line symmetry after each transformation:
i)	a translation R3
ii)	a translation U6
iii)	a reflection in a vertical line through 4 in the x-axis
iv)	a reflection in a horizontal line through 7 in the y-axis

          Problem

	59.	a)	Write a simplified polynomial for the perimeter of each shape below.
b)	Subtract the perimeter of the rectangle from the perimeter of the triangle.
c)	If , which shape has the greater perimeter?

	60.	a)	Write the multiplication sentence modelled by this rectangle.
b)	Determine the area of the rectangle when x = 12.
	Show your work.

	61.	Simplify: .

	62.	Match each inequality with the graph of its solution below.
For the graph that does not have a match, write the inequality represented by the graph.
a)	
b)	
c)	

i)	
ii)	
iii)	
iv)	

	63.	These three rectangles are similar.
a) 	Determine the values of x and y.
b) 	Griswald draws another similar rectangle with width 70.4 cm. What is its length?

	64.	a) 	Reflect shape A in the oblique line through (0, 7) and (7, 0). Label the image shape B.
b) 	Reflect shape B in the vertical line through 6 on the x-axis. Label the image shape C.
c) 	Reflect shape C in the oblique line through (5, 0) and (12, 7). Label the image shape D.

	65.	a)	On the grid below, plot the points A(2, 5), B(2, 6), C(4, 8), D(6, 6), and E(5, 5). 
	Join the points to form polygon ABCDE.
b) 	Reflect polygon ABCDE in the oblique line through the points (0, 0) and (8, 8). 
	Draw the reflection image.
c) 	Write the coordinates of the larger shape formed by ABCDE and its image.
d) 	Describe the larger shape and its symmetry.

	66.	This square is part of a larger shape that is to be completed by three rotations.
a)	Rotate this square:
	i)	90° clockwise about point A
	ii)	180° about point B
	iii)	180° about point A
	Draw each rotation image.
b)	Outline the shape formed by the square and all its images. What is the order of rotational symmetry and angle of rotation symmetry for the final shape?

Math 9 Pre test
Answer Section

SHORT ANSWER

	1.	ANS:	

	2.	ANS:	

	3.	ANS:	
a)	
b)	$51.50

	4.	ANS:	
ii and iv

	5.	ANS:	
a)	
x	2	3	4	5	6	
y	13	16	19	22	25	

b)	

	6.	ANS:	

	7.	ANS:	

	8.	ANS:	

The lines intersect to form a triangle.

	9.	ANS:	
Graph A: 
Graph B: 
Graph C: 

	10.	ANS:	
a)	x = 6
b)	y = 

	11.	ANS:	
a)	
b)	

	12.	ANS:	
a)	Binomial
b)	Monomial
c)	Trinomial
d)	Binomial
e)	Binomial

	13.	ANS:	
Coefficients: 4, -6
Variable: x
Degree: 2
Constant term: 8

	14.	ANS:	
a)	1
b)	0
c)	2
d)	2
e)	1

	15.	ANS:	

	16.	ANS:	

	17.	ANS:	

	18.	ANS:	

	19.	ANS:	

	20.	ANS:	

	21.	ANS:	

	22.	ANS:	

	23.	ANS:	

	24.	ANS:	

	25.	ANS:	

	26.	ANS:	

	27.	ANS:	
-8

	28.	ANS:	
-20

	29.	ANS:	
28.7

	30.	ANS:	
a)	
b)	l = 3.8

	31.	ANS:	

	32.	ANS:	
x = 

	33.	ANS:	
Answers will vary.
Any number less than or equal to 8 is a solution. For example: -8, 0, 5, 8

	34.	ANS:	
Answers will vary.
Any number less than -5 is a solution. For example: –6, –7, –8, –8.5

	35.	ANS:	

	36.	ANS:	

	37.	ANS:	
Subtract 5 from each side.

	38.	ANS:	
Add 14 to each side.

	39.	ANS:	

	40.	ANS:	
a)	Yes  
b)	No  
c)	Yes  
d)	Yes

	41.	ANS:	

	42.	ANS:	

	43.	ANS:	
The scale factor is 3.5.

	44.	ANS:	
8 cm, 8 cm, 11.4 cm, and 16 cm

	45.	ANS:	
Rectangle B; scale factor is 2.
Rectangle C; scale factor is 1.5.

	46.	ANS:	

	47.	ANS:	
The width is 4.5 m.

	48.	ANS:	
x = 20.4
y° = 31°

	49.	ANS:	
EF = 32.4

	50.	ANS:	
QR = 15

	51.	ANS:	
77 m

	52.	ANS:	
a) 2 
b) 4

	53.	ANS:	

	54.	ANS:	
180° about the point (3, 1)

	55.	ANS:	
5 lines of symmetry

	56.	ANS:	
Figure iii

	57.	ANS:	
The two octagons are related by line symmetry (the vertical line through 4 on the x-axis) and by rotational symmetry (a 90° rotation about the point (4, 0)).

	58.	ANS:	
i)	There is no line of symmetry.
ii)	The line of symmetry is the horizontal line through 6 on the y-axis.
iii)	The line of symmetry is the vertical line through 4 on the x-axis.
iv)	The line of symmetry is the horizontal line through 7 on the y-axis.

        PROBLEM

	59.	ANS:	
a)	Perimeter of rectangle: 
	Perimeter of triangle: 
b)	Perimeter of triangle - perimeter of rectangle = 
c)	Substitute  into the polynomial for the perimeter of the rectangle.

	Substitute  into the polynomial for the perimeter of the triangle.

	So, the triangle has the greater perimeter.

	60.	ANS:	
a)	

b)	Substitute x = 12 into .
	
	The area of the rectangle when x = 12 is 300 square units.

	61.	ANS:	

	62.	ANS:	
a)	Graph iii
b)	Graph i
c)	Graph iv
The inequality represented by Graph ii is .

	63.	ANS:	
a) 	
Solve for x.
	  
So, x = 33 cm.
	Solve for y.

So, y = 55 cm.	

b) 	Let z represent the length.
	
	The length is 140.8 cm.

	64.	ANS:	

	    65.	ANS:	

c)	The shape ABCC'B'A'E has coordinates: A(2, 5), B(2, 6), C(4, 8), C'(8, 4), 
	B'(6, 2), A'(5, 2), E(5, 5)
d)	It is a seven-sided polygon with a line of symmetry along DE.

	66.	ANS:	
a)

b)	The final shape has rotational symmetry of order 4. 
	The angle of rotation symmetry is: