math 404 midterm review mrs. nassif
TRANSCRIPT
MATH 404
Midterm Review
Date: _________ Time: _________
TopicsTopicsTopicsTopics Ch 1: Linear Equations
• Slope/Rate of change
• Y-intercept/Initial value
• X & Y intercept
• Parallel/Perpendicular Lines Ch 2: System of Equations
• Comparison
• Substitution
• Elimination Ch 3: Analytic Geometry
• Distance
• Midpoint
• Division Point Ch 4: Functions
• Quadratic Function
• Exponential Function
Mrs
. Nas
sif
The equation of line L is 4x + 7y – 56 = 0
Which of the following equations represents a line parallel to line L?
A) y = 7
4 x – 32
C) y = 4
7 x – 32
B) y = 7
4− x – 32
D) y = 4
7− x – 32
What is the solution to the following system of equations?
x + y = 20
7.5x + 10.25y = 183
A line in the Cartesian plane has the following characteristics:
• Its x-intercept is 12.
• Its y-intercept is 6.
What is the slope of this line?
The x-intercept of line L in the Cartesian plane is −15.
Its y-intercept is −60.
What is the slope of line L?
A)
−4
C)
4
1
B)
4
1−
D)
4
Mrs
. Nas
sif
A new bike path was recently built to connect towns C and D.
Before this new path was built, the only option for cyclists was to bike the circuit ABC.
In the following Cartesian plane:
• triangle ABC is right-angled at C
• point A is located on the y-axis
• point D is located �
� of the way along line segment AB
• the new path is represented by line segment CD
The scale of this graph is in kilometers.
What is the length of the new path?
A
C (0, 12)
D
B (60, 48)
x
y
Mrs
. Nas
sif
In 2010, Julie was doing research to find a good deal on a used car.
She found a car that was worth $24 000 when purchased new in 2006.
This car model loses 15% of its value each year in relation to the previous year.
Julie decided to buy this used car for exactly what it was worth.
She plans to sell the car the year when its value drops to below $5000.
What is the difference between the purchase price and the selling price of her used car?
It is estimated a computer loses 35% of its value each year.
Bruno spent $3200 for his new computer.
How much will his computer be worth in 5 years?
At the end of 1999, Paul bought a new car for $25 000. Each subsequent year the car lost 18% of its previous year's value.
Consider the relation between the value of the car and the number of years since the car was bought.
How much was the car worth at the end of 2002?
Mrs
. Nas
sif
In a drag race, a car accelerates in a straight line to the finish.
The function described below can be used to determine the distance traveled by a car according to the time.
f ( x ) = 2.5 x2
where x : from the moment the car set off, in seconds.
f ( x ) : the distance traveled, in metres
The length of the race is 100 m.
How long will it take the car to complete the race? A
A) 6.3 s
C) 40 s
B) 9.87 s
D) 25 000 s
Mrs
. Nas
sif
Point R is on line segment MN represented in the Cartesian plane below.
From point M, point R divides line segment MN in a ratio of 2:3.
What are the coordinates of point R?
Mrs
. Nas
sif
Point S is on line segment PQ represented in the Cartesian plane below.
From point P, point S is located 7
3of the way along segment PQ.
What are the coordinates of point S? B
A) (8.3, 27.6)
C) (14, 39)
B) (11, 33)
D) (16.7, 44.4)
P (2, 15)
Q (23, 57)
S
Mrs
. Nas
sif
Right triangle ABC is represented below in the Cartesian plane. The scale of this graph is in centimetres.
In addition,
• Point A is on the y-axis
• Point M is the midpoint of line segment AB
What is the length of line segment CM?
(56, 56)
(20, 8)
Mrs
. Nas
sif
Myriam wants to use some handmade square tiles for the backsplash of her kitchen. She is hesitating between two different models of handmade tiles. The cost of a handmade tile depends on the length of a side of the tile.
The cost of model A of a handmade tile is represented by function fA.
The cost of model B of a handmade tile is represented by function fB.
where x : length, in centimetres, of a side of the tile
fA (x) : cost of model A handmade tile, in dollars
fB (x) : cost of model B handmade tile, in dollars
The rules of functions fA and fB are of the form f (x) = ax2
Functions fA and fB are represented in the Cartesian plane below.
The cost of one tile of model A is $7.68. Myriam will need 100 tiles for the backsplash.
How much money would she save by purchasing 100 tiles of model B of the same size?
fA
fB
Mrs
. Nas
sif
Laura has contacted a contractor that paves driveways of various
shapes and sizes.
The following function describes the cost of paving a square driveway based on the length of one of the sides.
f ( x ) = 11.5 x2
where x : length of a side of the driveway, in metres
f ( x ) : cost of paving the driveway, in dollars
Laura paid $2944 to have her driveway paved.
What is the length of a side of Laura’s driveway?
The equation of line L is 7x – 3y + 8 = 0.
Which of the following equations represents a line perpendicular to line L?
A) y = − 7x + 8 C) y = 7x + 12
B) xy7
3−= + 10 D) xy
7
3= + 16
Mrs
. Nas
sif
In the Cartesian plane represented below:
• From point Q, point P is located 12
5 of the way along line segment
QR.
• PSQR⊥
• Point S is on the x-axis.
What are the coordinates of point S?
Mrs
. Nas
sif
A study examined the populations of two neighbouring towns.
TOWN OF NORTH WESTERFIELD
Function f described below represents the population of North Westerfield in relation to the time elapsed since 2010.
f ( x ) = 5 000 (1.06)x
where x : time elapsed since 2010, in years
f ( x ) : population of North Westerfield
Today, the population of North Westerfield is 6 691.
TOWN OF SOUTHLAKE
In 2010, the population of Southlake was double the population of North Westerfield.
Every year since then, the population of Southlake has decreased by 8% in relation to the previous year.
To the nearest whole number, what is the difference between the populations of North Westerfield and Southlake today?
Mrs
. Nas
sif
In 2005, a doctor compared the number of people infected with AIDS in two African countries. In Country A, 1100 people had AIDS. This number is expected to increase by 6% per year. In Country B, there are 300 less people infected with AIDS compared to Country A. This number is expected to increase by 2% more than in Country A per year. In 5 years, which country will have more people infected with AIDS?
Mrs
. Nas
sif
Nick has a dart game in his basement. The circular target is divided into
three distinct sections: red, blue and green.
The number of points earned depends on the colour of the section in which
the dart lands.
Players earn 10 points when a dart lands in the green section
Nick, Shane and Tina played the game several times on a Saturday night.
The following table provides information of the performances of the three
players.
Number of
darts that
landed in the
red section
Number of
darts that
landed in the
blue section
Number of
darts that
landed in the
green
section
Points
scored
Nick
45
36
9
1530
Shane
33
22
12
1110
Tina
?
16
8
660
How many times did Tina hit the red section?
Mrs
. Nas
sif
Line DE and line segments AB and CD are represented below in the Cartesian plane.
• From point A, point C is located 9
4 of the way along line segment
AB.
• Point D is on the x-axis.
• The equation of line DE is 738
1+−= xy
What is the equation associated with line segment CD?
Mrs
. Nas
sif
In 1995, a large pack of wolves were re-introduced into the national park of Red River in order to control the elk population in the park.
The following is some information on the population of these two animals.
WOLVES
In 1995, there were 21 wolves introduced. Since then, the population of wolves has increased by 18.9% annually.
A few years later, there were 42 wolves in the Red River National Park.
ELKS
Function g described below represents the population of elks in relation to the time elapsed since 1995.
g (x) = a (0.90)x
where x : time elapsed since 1995, in years
g (x) : population of elks
In 1997, the population of elks was 13 608.
What was the population of elks when there were 42 wolves in the Red River National Park?
Mrs
. Nas
sif
Final Answers
1) �
2) (8,12)
3) −1/2
4)
5) 45.61
6) 7 803.16
7) $371.29 8) $13 784.20
9) A
10) 19 470.31
11) (16, 42)
12) �
13) 32.5 ��
14) $256
15) 16�
16) �
17) (456, 0)
18) 100
19) , 1472
20) 51 770
21) 17
22) � = −5� + 2920
23) 11 022
24) 52.5
25) 4
26) (73, 22)
27)
28) �
29) �
30) 20
31) (0, 40)
32) $44.31
33) 32 ��
34) 14 980
35) $816.75
36) � = 3� − 1380
37) (72, 24)
38) 5
39) 24
Mrs
. Nas
sif