Exam
Review Part A
Remember
that there is Free Math Tutoring available
5:30-9:30 Sunday to Thursday at homeworkhelp.ilc.org
1. Plot and label each point on a Cartesian plane, and state which quadrant it is in.
a) A(6, 1) b) B(-5, -5) c) C(4, 0) d) D(-1, 0)
2. Complete a table of values for the following.
a)
y = -x + 4 b) 
c) 
d)
e)
Solution a Solution #2b Solution #2c
3. Determine if the point satisfies the equation of the line.
C(-4, 3) y = 3x + 4
4. Using the proper formula, find the slope of the line between pair of points
a) (5, -7) and (-3, -9) Solution 4a
b) (4, -3) and (2, -1) Solution 4b
c) (3, 6) and (-3, 6) Solution 4c
d) (-4, 12) and (-4, 5) Solution 4d
5. Write
the equation of each line in slope y-intercept form.
6. Without using a table of values, graph the following lines on the Cartesian plane.
i) 
ii)
iii)
iv)
7. Determine the equation of a line given its slope and y-intercept, b.
a)
m = 2 and b = -1 b) m = 
and b = 9
8. Determine the equation of a line given a point and its y-intercept, b.
a) (8, 0) and b = -1 b) (3, 4) and b = 9
9. Graph the line represented by each table. Label the line with its equation.
|
x |
y |
|
x |
y |
|
x |
y |
|
x |
y |
|
0 |
2 |
|
0 |
1 |
|
2 |
3 |
|
-3 |
2 |
|
1 |
4 |
|
1 |
-1 |
|
4 |
4 |
|
3 |
-2 |
|
2 |
6 |
|
2 |
-3 |
|
6 |
5 |
|
6 |
-4 |
Solution #9a Solution #9b Solution #9c Solution d
10. Find an equation in the form y = mx + b for the straight line represented by the table of values.
|
x |
y |
|
2 |
10 |
|
3 |
7 |
|
4 |
4 |
11. Express each sentence as an algebraic equation. Define your variables.
a) Bob earns $25 more than Joe does.
b) Her dogÕs mass is two kilograms more than three times his dogÕs mass.
12. The following equations are in standard form. State the values of A, B, and C.
a) 3x – 4y + 8 = 0
b) 2x – y + 1 = 0
c) 2x + 5 = 0
d) 2y + 9 = 0
13. Find the
slope and the y-intercept of the line
a) 2x + y = 4. Solution
b) 3x – y
– 6 = 0. Solution
c) 4x – 5y
+10 = 0. Solution
d) 4x + 6y
– 24 = 0. Solution
14. Write each equation in standard form, Ax + By + C = 0
a) 
Solution
b)
Solution
c) 
Solution
d) 
Solution
15. a) Find the slope of the line between the two points.
b) Find the y-intercept of the line.
c) Determine the equation of the line passing through each pair of points.
a) (-3, -7) and (4, 7) b) (-1, -5) and (2, 7)
16. Determine
whether each point is on the line
a) (2,6) b) (-3,-5)
17. Determine whether each point is on the
line 
a) (-3,-5) b) (6,2)
18. a) What is the length of line segment AB points if A has coordinates (4, 1) and B has coordinates (-6, 6)? Round to the nearest tenth. Solution a
b) Calculate the midpoint of line segment AB. Solution b
c) What is the equation of line AB? Solution c
d)) What is the equation of the line parallel to AB that passes through the point (21, 6)? Solution d
19. A communication tower located at the centre of the grid sends out signals in a circle covered by the equation x2 + y2 = 49. (Each unit on the graph represents 1 km.)
a) What is the radius of the signal?
b) If someone wanted to know if a point on the grid is on the signal boundary, what calculation would they make?
c) Does the point P (-3, 6) lie inside, on, or outside boundary signal? Justify your answer.
20. A triangle has vertices K
(–3, 1), L (1, 4), and M (4, 0).
a) Find the
lengths of all 3 three sides. Solution a
b) Find the slopes of all sides.
c) What conclusion can you make
about the triangle? Solution bc
21. Find
the equation of the straight line passing through point B and perpendicular to the straight line passing
through A(-6, 2) and B(4, 8).
22. Calculate the distance from point R(17,5) to the line y =
-½ x -3. Round to the nearest tenth.
Solution part 1 Solution part 2
Exam
Review Part B
1.
Solve the following system of
linear equations by graphing (find the point of intersection).
Solution
2.
Solve the system of equations
by graphing (find the point of intersection).
a) Write each equation in slope
y-intercept form, y = mx + b.
i) x + y – 4 = 0 ii)
x – y – 2 = 0 
b) Graph the lines to find the solution.
3. The Shape Up
fitness club charges an initiation fee of $200, plus $20 a month. The Premiere
Fitness club charges $100 initiation fee, plus $25 a month. The cost for the
Shape Up fitness club is modelled by the equation, C = 200 + 20n while the cost
for the Premiere Fitness club is modelled by the equation,
C = 100 + 25n. In both
equations, C represents the total cost and n represents the number of months of
membership since the membership started.
a) Construct a single
graph to represent the relationship of cost versus number of months for both
clubs.
b) If you joined a
club for one year, which club would be the least expensive?
c) After how many
months is the cost the same?
4. Solve the following linear systems by substitution.
a)
Solution a
b)
Solution b
c) 
Solution c
d) 
Solution d
5. Solve the following systems of linear equations by elimination.
a)
Solution a
b)
Solution b
c) 
Solution c
6) A display sign at
the entrance to a theme park is shown below.
|
Admission: Adults: $14.00 Students: $ 9.00 Children: free |
In one day, the
park collects $4140 in ticket sales. They sold 385 tickets.
Let a represent
the number of adult tickets sold, and s represent the number of student tickets
sold.
a) Which
of the following equations relates the number of tickets sold to a and s
?
14a
+ 9s = 385
a + s = 385
14a
+ 9s = 4140
a + s = 4140
b) Which
of the following equations relates the revenue collected (the total value of
ticket sales) to a and s ?
13a
+ 9s = 385
a + s = 385
14a
+ 9s = 4140
a + s = 4140
c) The
linear system of equations is
Which of
the following linear systems has the same solution?
A) 14a
+ 14s = 385
14a
+ 9s = 4140
B) 9a +
9s = 385
14a
+ 9s = 4140
C) 9a +
9s = 3465
14a
+ 9s = 4140
D) a + s
= 385
a + s = 4140
d) Which
of the following values for a and s are a solution to the linear
system ?
A) a=200,
s=185
B) a=150,
s=235
C) a=100,
s=285
D) a=135,
s=250
7) A fitness club has
an annual membership fee and also charges an amount for each session.
Renita attended 30
sessions in the year and paid $350 for the year. Calvin attended 50 sessions in
the year and paid $450. Determine the
annual membership fee and the rate per session.
8) The Peace and
Development Club invests the money collected from a walkathon. The total amount
invested is $4300. Part of it is invested in an account earning 4% per year,
simple interest. The rest is loaned out to an organization that will pay it
back with 6% per year simple interest. At the end of the year, the two
investments earn $208 in interest. How
much is invested at each rate?
9) Mary wishes to pack
a trail mix of peanuts and currants for a hiking trip organized by the parish
youth group. The grocery store sells these items in bulk. Peanuts are sold for
$5.50/kg and currants are sold for $8.20/kg.
The total mass of
peanuts and currants in her mixture is 3.9 kg, and the total cost is $26.04. What is the mass of the peanuts in the
mixture?
10) State the number of solutions for this system. Do NOT solve. Explain your reasoning
3y = x + 1
6y = 2x + 5 Solution
11) The cost of renting a car depends on
the number of days for which it is rented and the distance it is driven. The cost for one day and 240 km is
$39. The cost for 3 days and 800
km is $125. What is the cost per
day and the cost per kilometre?
Exam Review Part C
1. To determine the height of an old building, a surveyor obtains these measures. A buildingÕs shadow is 18 m long. At the same time, a 3-m tall post has a 5-m long shadow. How tall is the building?
Solution
2. Use the Pythagorean Relation to solve for each unknown. Round to 1 decimal place.
a) b)
3. A field measures 65 m by 90 m. How much shorter is it to walk diagonally across the field than along two adjoining sides?
4. Evaluate. Round your answer to four decimal places.
a) sin 25¼ b) cos 35¼ c) tan 78¼
5. Calculate the measure of each angle. Round your answer to the nearest degree.
a) sin X = 0.1812 b) tan Y = 0.2314
Consider the indicated angle in each of the triangles below. Can you label each of the sides correctly with the terms opposite, hypotenuse, and adjacent?
State the three primary trigonometric ratios of ÐA in the given triangle.
Find the three primary trigonometric ratios of each of Ð B.
If 
,
find the other two primary trigonometric ratios of the angle 
.
Hint: Draw a diagram.
Calculate the length of the unknown side in the triangle correct to one decimal place.
Calculate the length of the unknown side in the triangle correct to one decimal place.
Calculate the length of the unknown side in the triangle correct to one decimal place.
Find the value for 
to the nearest degree.
a) b)
c) d)
a) Find the measure of angle Y to the nearest degree.
b) Find the measure of angle Z and the side YZ.
a) Find the measure of side opposite angle D to 1 decimal place.
b) Find the measure of angle F and the side DE.
Solve triangle ABC.
6. Find the measure of the unknown side. Use the cosine ratio to find the measure of <C.
7. The recommended safe angle for a firefightersÕ ladder to make with the ground is 74¼. How far from the foot of a wall should the foot of a 9-m long ladder be placed?
8. A weather balloon is tethered to a
650-m line. The angle of elevation
of the line is 58¼. What is the
altitude of the balloon?
9. A boat is 100 m from the base of an 82
m cliff. Calculate the angle of elevation from the boat to the top of the
cliff.
10. Find
x, y, and z.
Find x, y, and z.
11. a) Find the measure of ÐD to the nearest tenth of a degree.
b) Use sine law to find the measure of ÐE to the nearest tenth of a degree
12. Solve triangle RST
if r =12 m, t = 8 m, and ÐS =65̊.
Exam
Review Part D
1. Simplify each of the following
a) 
b)
c)
d) 
e)
f)
g) 
h)
Solution ab Solution cd Solution ef Solution gh
2. Simplify.
a) 
b)
c)
d) 
e)
3. Find each product.
a) 
b)
c)
d) 
e)
f)
g) 
h)
i)
Solution a Solution bc Solution d
4. Simplify.
a) 
b)
c)
Solution a Solution b Solution c
5. Expand and simplify.
a) 
b)
c) 
d)
e) 
f)
g) 
Solution a Solution b Solution cd Solution ef
6. Expand and simplify.
a) 
b)
7. Factor each polynomial by finding a common factor.
a) 12x2 + 36x b) 9a3b – 12a2b3 – 6ab6
8. Factor each difference of squares.
a) x2 – 16 b) x2 – 100
9. Factor each trinomial.
a) 
b)
c)
d) 
e) x2
– 2x – 15 f) x2
+ 12x – 64
g) x2 + 2x + 1
Solution a Solution b Solution c Solution d
Solution e Solution f Solution g
10. Factor each of the following:
a) 
b)
c) 
d)
e) 4x² - 25 f) 3x² - 3x – 6
Solution a Solution b Solution c Solution d
Exam
Review Part E
- Is the vertex of each
quadratic function a maximum or a minimum point of the parabola?
a) y = 4x2 – 2 b) y = -(x + 5)2 + 1 c) y =
Solution
- The following quadratic equations are translations of y=x2.
a) Identify the vertex of each function.
b) Write the equation of the function.
Solution a Solution bc Solution de
3. State the coordinates of the vertex of
each parabola.
a) y = x2
– 5 b) y = -(x – 9)2 + 1 c) y = -3(x + 7)2
4. Write an equation for the quadratic
function that can be graphed as follows.
a) Move the graph of y = x2 ten units upward.
b) Move the graph of y = x2 two units downward, and
the graph is concave down.
c) Move the graph of y = x2 four units to the right,
and one unit upward.
d) Move the graph of y = x2 nine units to the left,
and eight units downward.
5. Graph
the set of three quadratic functions on the same set of axes without a table of
values.
a)
y = x2 - 3 b)
y = -(x + 4)2 c)
y = 
Solution a Solution b Solution c
6. Describe in words how the quadratic
functions y = 
and y = 
would
appear similar on graph paper, and how they would appear different.
7. An emergency flare is shot vertically into
the air with a speed of 60m/s. Its
height, h, in metres, after t seconds is given by the function h = -5(t –
6)2 + 180.
Without
graphing, tell when the flare reaches its maximum height and what that height
is.
8. Find the y-intercept of each quadratic
function.
a) y = -2x2 + 13x
– 4 b) y = 
9. Find the x-intercepts of each quadratic
function. Show all steps!
a) y = x2 - x
- 20 b) y = x2
– 4
10. For the following quadratic
function, y = (x + 3)2 – 4
a) give the coordinates of the vertex.
b) rewrite the function in standard
form, y = ax2 + bx +
c.
(expand!)
c) Find the y-intercept.
d) Determine the x-intercepts.
e)
Graph the parabola.
11. Solve each quadratic equation by
the method stated. Give
exact values only.
a) x²
- 25 = 0 algebraically
b)
x² - 2x = 15 (factoring)
c) x²
- x - 5 = 0 (quadratic
formula)) d)
x2 - 9x = 0 by factoring
e) 2(x
- 3)2 - 18 = 0
algebraically f)
9x2 - 3x = 2 by
factoring
g) 2x2
+ 8x + 8 = 0 by
factoring h)
2x2 + 5x - 12 = 0 using
the quadratic formula
Solution a Solution b Solution c Solution d
Solution e Solution f Solution g Solution h
12. A ball is thrown up from the top
of a building. The height h, in
metres above the ground, of the ball after t seconds have elapsed is given by: h = - 5t2 + 30t +
30
a)
Complete the square to put the equation in the vertex form. Solution a
b) How
high is the ball after 2 seconds have elapsed? Solution b
c) WhatÕs
the height of the building? Solution c
d) WhatÕs
the maximum height the ball reaches?
e) How
many seconds after the ball is released does it reach its maximum height?
f) For
how many seconds to the nearest hundredth of a second is the ball in the air
above 50 metres
13. Find
two consecutive even integers such that the square of the second, decreased by
twice the first, is 52.
14. The
length of a rectangular field is 3 m more than the width. The area is 108 m2.
Find the dimensions of the field.
15. The
height of a triangle is 3 cm more than the base. The area of the triangle is 17
cm2. Find the base to the nearest hundredth of a cm.
16. Describe, then plot, the graph of y
= – 3(x - 2)2
+ 12 by first determining:
a) what
shape the graph will be
b) the
vertex
c) the
direction of opening
d) the
equation of the axis of symmetry
e) the
equation of a function congruent to this one
f) maximum
or minimum value
g) value
of x when y is at the maximum or minimum
h) the
y-intercept
i) the
x-intercepts (exactly)