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?

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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