Name: 

Ginerva made the following conjecture:

1. Joshua is very fit.
2. Joshua feels happy.

      If you combine one haystack with another haystack,
      you get one haystack. Therefore, 1 + 1 = 1.

Which number should go in the grey square in this Sudoku puzzle?

Determine the sum of the measures of the angles in a 9-sided convex polygon.

In DUVW, ÐU = 50°, v = 19.4 cm, and ÐV = 45°.
Determine the length of side u to the nearest tenth of a centimetre.

In DXYZ, ÐX = 51°, x = 7.0 cm, and ÐZ = 41°.
Determine the length of side y to the nearest tenth of a centimetre.

Determine the measure of q to the nearest degree.

Determine the unknown side length to the nearest centimetre.

Determine the unknown side length to the nearest centimetre.

Determine the indicated side length to the nearest tenth of a metre.

A pear orchard has 40 trees with these heights, given in inches.
      110      105      83      84      104      92      95      98
      88      92      80      81      115      88      106      92
      97      103      100      93      98      93      93      102
      92      87      117      92      75      102      83      107
      122      92      115      86      89      98      105      125

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

Height (in.)	Frequency
70–79	1
80–89
90–99	14
100–109	9
110–119	4
120–129	2

Which histogram represents the following test scores?
Geography Test 3 Scores (our of 100)
92      85      78      67      54
92      83      78      65      53
90      83      77      62      50
88      80      75      62      48
86      80      68      60      42

Environment Canada recorded the amount of rain (in millimetres) in Victoria, BC for two months.
0      0      9.0      0      0      1.0      0
0      0      7.6      0      0      5.8      0.6
0      0      0.4      0      0      0
0      0      0      0      0      0
0      0      0      0      0      0
0      0      0      0      0      0.4
0      5.8      0      0      1.6      0.2
0      6.0      0      0      0.2      0
0      0.2      0      0      1.0      0
0      2.8      0      0      26.0      0

Determine the standard deviation, to one decimal place.

A teacher is analyzing the class results for a physics test. The marks are normally distributed with a mean (µ) of 76 and a standard deviation (s) of 4.
Determine Olivia’s mark if she scored µ – s.

Which set is normally distributed?

Interval	0–9	10–19	20–29	30–39	40–49	50–59
Set A.	100	500	850	820	450	150
Set B.	800	750	700	650	600	550
Set C.	950	420	180	220	460	990
Set D.	400	620	760	820	900	850

Determine the percent of data to the left of the z-score: z = 1.44.

Determine the percent of data to the left of the z-score: z = 0.87.

Determine the percent of data between the following z-scores:
z = –1.50 and z = 1.50.

A poll was conducted about an upcoming election. The result that 71% of people intend to vote for one of the candidates is considered accurate within ±3.0 percent points, 9 times out of 10.
State the confidence interval.

Describe the boundary lines for the following system of linear inequalities.
{y – 3x < 12, x + y 0, x   R, y R}

What system of linear inequalities is shown here?

A vending machine sells juice and pop.
• The machine holds, at most, 200 cans of drinks.
• Sales from the vending machine show that at least 3 cans of juice are sold for each can of pop.
• Each can of juice sells for $1.50, and each can of pop sells for $1.00.
Let x represent the number of cans of pop.
Let y represent the number of cans of juice.
What are the restrictions on x and y?

Jan volunteers to fold origami frogs and swans for a display.
• She has 8 squares of green paper for the frogs and 12 squares of white paper for the swans.
• It takes her 4 min to fold an origami frog and 3 min to fold an origami swan.
• There must be two swans for every frog.
Let f represent the number of frogs.
Let s represent the number of swans.
Which of the following points is in the feasible region?

Which set of data is correct for this graph?

Set	Axis of Symmetry	Vertex	Domain	Range
A.	x = –2	(–2, 6)	x Î R	y Î R
B.	x = –6	(–6, –2)	–8 £ x £ 4	–8 £ y
C.	x = –2	(–2, –6)	x Î R	–6 £ y
D.	x = 2	(2, 6)	–6 £ x £ 2	–6 £ y

What are the x- and y-intercepts for the function f(x) = x² + 7x + 10?

Solve 12x² + 11x = –2 by graphing the expressions on both sides of the equation.

Rewrite x² + 2x = –3x² + 2x + 36 in standard form. Then solve the equation in standard form by graphing.

Which relation is the factored form of f(x) = –2x² – 5x – 2?

Solve m² – 10m + 16 = 0 by factoring.

Solve 25x² – 36 = 0 by factoring.

Solve –2p² – 5p + 1 = 7p² + p using the quadratic formula.

A bridge is supported by three arches. The function that describes the arches is
h(x) = –0.2x² + 3.0x, where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres, from one end of the bridge. How tall is each arch?

A hockey arena sells premium tickets for $70. At this price, the arena will sell 150 premium tickets every game. The owners know from past years that they will sell 3 fewer premium tickets per game for each price increase of $2. What should the owners charge for a premium ticket to earn the maximum amount of money?

An 8 kg bag of potatoes costs $9.15. What is the unit rate?

Which situations could be described using the rates 15 L/min, $2.89/ft², and $3.60/100 g?

Data for triangle ABC is shown on the first line of the table.
Triangle ABC is enlarged by a scale factor of 3.5.
Which triangle is the enlargement of triangle ABC?

Triangle Name	Length of Base (cm)	Height of Triangle (cm)	Scale Factor	Area (cm2)
ABC	5.00	3.00	1.0	7.5	1
DEF	17.50	10.50	3.5	91.875	12.25
GHI	17.50	12.25	3.5	80.75	10.5
JKL	12.25	10.50	3.5	91.875	17.5
MNO	13.50	9.875	3.5	80.75	12.25

Data for trapezoid ABCD is shown on the first line of the table.
Trapezoid ABCD is enlarged so the length of base a is 16 cm.
Which rectangle is the enlargement of trapezoid ABCD?

Trape- zoid Name	Length of Base a (cm)	Length of Base b (cm)	Height of Trape- zoid (cm)	Scale Factor	Area (cm2)
ABCD	8	6	16	1	112	1
EFGH	16	6	16	0.5	176	0.25
JKLM	16	12	32	2	448	4
NOPQ	16	16	28	2	448	4
RSTU	16	3	8	0.5	76	0.25

Marion used a deck of card to create a convex polygon with 52 equal side lengths. Determine the sum of the measures of the angles in her polygon.
Show your calculation.

Abbie is measuring the exterior angles of a convex pentagon.
So far, she has measured 90°, 90°, 120°, and 40°.
What is the measure of the last exterior angle?
Show your calculation.

Which side of the boundary line is the solution set for the linear inequality x + 2y – 1 > 0?

Graph the solution set for the linear inequality 3y – 6x < –1.

What system of linear inequalities is shown here?

Baskets of fruit are being prepared to sell.
• Each basket contains at least 8 apples and more than 4 oranges.
• Apples cost 25¢ each, and oranges cost 40¢ each.
• The budget allows no more than $6, in total, for the fruit in each basket.
Let x represent the number of apples.
Let y represent the number of oranges.
Describe any restrictions on the variables.

Determine the roots of the corresponding quadratic equation for the graph.

The scale factor for two similar rectangles is 1:5.
The sum of their areas is 78 cm².
Determine the area of each rectangle.

Jessica found an interesting numeric pattern:

Do you think the pattern will continue?
Justify your decision with a counterexample if possible.

Alexandra, Morana, Rebecca, and Yvonne play on the high school basketball team. After the first quarter of one game, Morana led Rebecca by 3 points. Yvonne led Alexandra by 5 points, and Rebecca led Alexandra by 2 points. In the second half, Alexandra got 4 points while Rebecca was scoreless. At half time, Yvonne was ahead of Morana by 4 points and Morana was 4 points ahead of Rebecca. Morana, Yvonne, and Rebecca did not play in the second half of the game. At the end of the game, Alexandra had 2 more points than Yvonne. Who finished third in scoring?

Solve this Sudoku puzzle using the numbers 1 to 9. Fill the grid so that each column, row, and block contains all the numbers. No number can be repeated within any column, row, or block.

A radio tower is supported by two wires on opposite sides. On the ground,
the ends of the wire are 84 m apart. One wire makes a 52° angle with the ground.
The other makes a 74° angle with the ground.
Draw a diagram of the situation. Then, determine the height of the tower to the nearest tenth of a metre.

In DQRS, q = 8.9 cm, r = 3.8 cm, and s = 7.2 cm. Solve DQRS by determining the measure of each angle to the nearest degree. Show your work.

The posts of a soccer goal are 24 ft apart. A player is standing at a point 50 ft from one post and 42 ft from the other post. Within what angle must the player kick the ball to score a goal? Express your answer to the nearest degree. Show your work and draw a diagram.

Three teams are travelling to a hockey tournament in cars and minivans.
• Each team has no more than 2 coaches and 18 athletes.
• Each car can take 3 team members, and each minivan can take 5 team members.
• No more than 7 minivans and 15 cars are available. The school wants to know the combination of cars and minivans that will require the maximum number of vehicles. Create and verify a model to represent this situation.
a) Use the optimization model to determine the combination of cars and minivans that will use the maximum number of vehicles.
b) How many team members can travel in the maximum number of vehicles?
Optimization Model
Let V represent the total number of vehicles.
Let c represent the number of cars.
Let m represent the number of minivans.
Restrictions:
c Î W, m Î W
Constraints:
c 0
m   0
3c + 5m 60
c 15
m 7
Objective function to maximize:
V = c + m

The height, in metres, of a fireworks rocket is modelled by the function
h(t) = –4.9t² + 25t + 10, where t is the time in seconds after the rocket is fired.
a) Determine the domain and range of the function to the nearest tenth.
b) Use technology to graph the function.

Solve –x² + 3x + 2 = –3x² – 2x + 4 by graphing.

Gravity affects the speed at which objects travel when they fall. Suppose a rock is dropped off a 7.5 m cliff on Mars. The height of the rock, h(t), in metres, over time, t, in seconds could be modelled by the function h(t) = –1.9t² + 3.0t + 7.5. (The acceleration due to gravity on Mars is 3.77 m/s.)
a) How long would it take the rock to hit the bottom of the cliff?
b) The same rock dropped off a cliff of the same height on Earth could be modelled by the function h(t) = –4.9t² + 3.0t + 7.5. Compare the time that the rock would be falling on Earth and on Mars.