Name: 

Guilia created the following table to show a pattern.

Multiples of 9	18	27	36	45	54
Sum of the Digits	9	9	9	9	9

Which conjecture could Guilia make, based solely on this evidence?
Choose the best answer.

Determine the unknown term in this pattern.

1, 2, 4, ___, 16, 32, 64

Which number should appear in the centre of Figure 4?

Figure 1	Figure 2	Figure 3	Figure 4

In which diagram(s) is AB parallel to CD?

1.		2.

Which angle property proves ÐBED = 73°?

Which are the correct measures of the interior angles of DCDE?

Determine the sum of the measures of the interior angles of this polygon.

Determine the length of f to the nearest tenth of a centimetre.

Determine the measure of q to the nearest degree.

Determine the measure of q to the nearest degree.

In DQRS, q = 10.0 cm, s = 9.0 cm, and ÐS = 61°.
Determine the measure of ÐQ to the nearest degree.

How long, to the nearest inch, is the right rafter in the roof shown?

Determine the unknown side length to the nearest centimetre.

Which set of measurements can produce two possible triangles?

In DJKL, ÐJ = 115°, k = 6.2 m, and j = 5.5 m.
Which statement is true for this set of measurements?

Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and British Columbia towns from 1999 to 2008.
0.42      0.04      0.81      0.40      0.03      0.74
0.28      0.03      0.70      0.23      0.03      0.66
0.13      0.02      0.61      0.12      0.01      0.58
0.10      0.00      0.49      0.07      1.08      0.43
0.05      0.91      0.42      0.04      0.88

What value goes in the fourth row of this frequency table?

Lightning Strikes (per square kilometre)	Frequency
0.00–0.19	13
0.20–0.39	2
0.40–0.59	6
0.60–0.79
0.80–0.99	3
1.00–1.19	1

Environment Canada recorded the amount of rain (in millimetres) in The Pas, MB for two months.
0      0      10.8      7.0      31.2      1.6      0
0      6.0      0      0      0      3.1      0
0      1.4      0      0      0.2      1.0
0      0      0.3      11.6      0      0
0      0      0      1.6      1.2      1.0
2.4      0      0      3.0      0      3.4
1.0      0      0      0      0      0
1.6      0      0      0      0      0.2
0      0      0      1.4      0      0
0.4      0      0      0      1.0      0

Determine the standard deviation, to one decimal place.

The ages of participants in a bonspiel are normally distributed, with a mean of 40 and a standard deviation of 10 years. What percent of the curlers are older than 60?

Determine the z-score for the given value.
µ = 52, s = 6, x = 64

Determine the percent of data between the following z-scores:
z = –2.25 and z = 1.75.

In a recent survey of high school students, one third of those surveyed said they would vote for Melissa as student council treasurer. The survey is considered accurate to within 5 percent points, 19 times out of 20.
If a high school has 1200 students, state the range of the number of votes Melissa should expect.

Which test point is in the solution set for the linear inequality
{(x, y) | x + y < 3, x W, y W}?

Which test point is in the solution set for the linear inequality
{(x, y) | 5x – 2y 10, x R, y R}?

How would you graph the solution set for the linear inequality 2y – 2x 10?

Identify the point of intersection for the following system of linear inequalities.
{y – 3x < 12, x + y 0, x R, y R}

A football stadium has 60 000 seats.
• 70% of the seats are in the lower deck.
• 30% of the seats are in the upper deck.
• At least 40 000 tickets are sold per game.
• A lower deck ticket costs $100, and an upper deck ticket costs $60.
Let x represent the number of lower deck tickets.
Let y represent the number of upper deck tickets.
What are the restrictions on x and y?

The following model represents an optimization problem. Determine the minimum solution.
Restrictions:
x W
y   W

Constraints:
0 x 100
–50 y 50
x 25 – y
x – y 60

Objective function:
A = y – 2x + 10

Brent found spiders and grasshoppers in his barn.
• There were at most 12 spiders and at least 10 grasshoppers.
• There were no more than 36 spiders and grasshoppers, in total.
Let s represent the number of spiders and let g represent the number of grasshoppers.
Which inequality represents a restriction of s and g based on the given information?

What is the degree of a quadratic function?

What are the x- and y-intercepts for the function f(x) =x² –2x + 3?

Which set of ordered pairs satisfy the function f(x) = x² + 9x + 3?

The points (–5, 26) and (3, 26) are located on the same parabola. What is the equation for the axis of symmetry for this parabola?

Solve 2x² + 4x + 2 = 0 by graphing the corresponding function and determining the zeros.

Which set of data is correct for the quadratic relation f(x) = 4(x – 0.5)(x + 1)?

	x-intercepts	y-intercept	Axis of Symmetry	Vertex
A.	(–0.5, 0), (1, 0)	y = –2	x = 0.25	(0.25, –1.25)
B.	(0.5, 0), (–1, 0)	y = –2	x = –0.25	(–0.25, –2.25)
C.	(–0.5, 0), (1, 0)	y = 0.5	x = 0.5	(0.5, 0)
D.	(0.5, 0), (–1, 0)	y = –0.5	x = –0.5	(–0.5, –2)

Solve 9w² + 6w + 1 = 0 using the quadratic formula.

Olga drove 346 km and used up 28.7 L of gas. What is her car's fuel efficiency?

The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling at 4.5 km/h?

Data for circle O is shown on the first line of the table.
Circle O is reduced by a scale factor of 0.2.
Which circle is the reduction of circle O?

Circle Name	Radius (cm)	Scale Factor	Area (cm2)
O	24.0	1	1809.56	1
P	3.6	0.2	82.73	0.03
Q	2.3	0.2	62.38	0.04
R	4.8	0.2	72.38	0.04
S	2.3	0.2	82.73	0.03

Data for rectangle ABCD is shown on the first line of the table.
Rectangle ABCD is enlarged so the width is 19.5 cm.
Which rectangle is the enlargement of rectangle ABCD?

Rectangle Name	Length (cm)	Width (cm)	Scale Factor	Area (cm2)
ABCD	9.0	13.0	1.00	117.00	1
EFGH	13.5	19.5	1.35	265.25	2.25
JKLM	12.5	19.5	1.25	253.25	2.125
NOPQ	13.5	19.5	1.50	263.25	2.25
RSTU	15.5	19.5	1.50	302.25	2.5

Tyler made the following conjecture:

Do you agree or disagree? Briefly justify your decision with a counterexample if possible.

Determine the unknown angles.

In DFGH, ÐG = 42° and GH = 9.9 cm. Calculate the height of the triangle from base GF to the nearest tenth of a centimetre.

Graph the solution set for the following system of inequalities.
{(x, y) | x + y > 0, x + y < 4, x R, y R}

Which point in the model below would result in the maximum value of the objective function H = x – y? What is the value of H at this optimal solution?

A quadratic function has an equation that can be written in the form f(x) = a(x – r)(x – s). The graph of the function has x-intercepts at (1, 0) and (3, 0) and passes through the point (–1, 16). Write the equation of the function.

Solve and verify the following equation:
13 – 100y² + 10y = 69y² – 10y – 15

How many zeros does f(x) = –0.5(x – 3)² – 18 have? Test your prediction by sketching the graph.

Solve –5x² + 2 = 3x + 2 using the quadratic formula.

Let n be the first integer.
But in checking his work, Terry found the following counterexample, so he knew he had made an error.

1 + 8 + 27 = 36

The posts of a hockey goal are 2.0 m apart. A player is standing at a point 4.5 m from one post and 6.0 m from the other post. Within what angle must the player shoot the puck to score a goal? Express your answer to the nearest degree. Show your work.

Joannie and Alex are trying to control the number of text messages they send. They record the number they send every day in April.
Joannie: 32, 14, 22, 33, 18, 25, 26, 20, 32, 16, 18, 25, 31, 34, 3, 8, 32, 28, 25, 18, 32, 21, 9, 10, 27, 18, 29, 22, 15, 20
Alex: 24, 0, 3, 14, 29, 24, 25, 30, 12, 18, 22, 30, 16, 19, 7, 12, 26, 21, 22, 27, 5, 19, 18, 8, 21, 25, 20, 18, 13, 15
a) Choose an interval width so you have seven intervals.
b) Create a frequency table for the data.

A manufacturer offers a warranty on its vacuum cleaners. The vacuum cleaners have a mean lifespan of 3.4 years, with a standard deviation of 0.4 years. For how long should the vacuum cleaners be covered by the warranty, if the manufacturer wants to repair no more than 2.5% of the vacuum cleaners sold?

a) Use confidence intervals to interpret the following statement.
A market research firm found that among online shoppers, 89% search for online for at least one other seller carrying the same product when they purchase something on the Internet. The survey is considered accurate within ±3.5 percent points, 99% of the time.
b) How could they decrease the margin of error in their result?

An advertisement for a new toothpaste states that 80% of users reported better dental check-ups. The results of the poll are accurate within 4 percent points, 9 times out of 10.
a) State the confidence level.
b) Determine the confidence interval.
c) In a focus group of 50 students, four said they already used this toothpaste and another five did not want to try it. Determine the range of the mean number of the remaining students who could expect better dental check-ups.

A refinery produces oil and gas.
• At least 1.5 L of gasoline are produced for each litre of heating oil.
• The refinery can produce up to 8.5 million litres of heating oil and 4 million litres of gasoline each day.
• Gasoline is projected to sell for $1.05 per litre. Heating oil is projected to sell for $1.90 per litre.
The company needs to determine the daily combination of gas and heating oil that must be produced to maximize revenue. Create a model to determine this combination. What would the revenue be?
Optimization Model
Let g represent the number of millions of litres of gasoline.
Let h represent the number of millions of litres of heating oil.
Let R represent the total revenue from sales in millions of dollars.
Restrictions:
g Î R, h Î R
Constraints:
g 0
h 0
g 1.5h
g 4
h 8.5
Objective function to maximize:
R = 1.05g + 1.90h

Determine the equation for this quadratic function. Write the equation in standard form. Show all your steps.

Identify and correct any errors in the following solution:


  or    or 

A window in a clothing store is 6.00 ft high and 15.00 ft long. Lee has been asked to paint a mural on the window. The mural must be the area of the window and the mural and window must be similar. The mural must also be centred on the window. Draw a scale diagram that shows the dimensions of the window, the dimensions of the mural, and where the mural should be placed.