MTH 219T Wk 3 – Midterm Exam

Complete the midterm exam. You have one attempt at the exam. So, be sure to review all previous course materials before attempting the exam.

Question 1

Suppose x is the height of a building and y is the number of rooms in the building. Which quadrant does the point (x,y) lie on?

Quadrant IV

Quadrant I

Quadrant III

Quadrant II

Question 2

If left parenthesis 3 to the power of 8 right parenthesis to the power of 4 equals 3 to the power of x , find x.

2

4

12

32

Question 3

Solve 1 third left parenthesis 3 x plus 6 right parenthesis plus 2 x equals 26 .

x equals 28 over 3

x equals 32 over 5

x equals 4

x equals 8

Question 4

Find the y-intercept of the line fraction numerator 6 y plus 2 x over denominator 5 end fraction equals 18 .

45

-15

-45

15

Question 5

Simplify fraction numerator left parenthesis x to the power of negative 3 end exponent x to the power of 5 right parenthesis left parenthesis 3 y right parenthesis cubed over denominator x to the power of negative 1 end exponent x squared end fraction .

9 x y cubed

9 x cubed y

27 x y cubed

27 x squared y cubed

Question 6

Which of the following is a polynomial?

x cubed plus x y minus 1

begin mathsize 10px style 1 over x end style

x to the power of 1 divided by 2 end exponent 12 y minus 1

fraction numerator x cubed over denominator x minus 1 end fraction

Question 7

Simplify left parenthesis x minus y minus 5 right parenthesis left parenthesis x minus 2 right parenthesis .

2 x minus y minus 3

x squared minus x y plus 7 x plus 2 y plus 10

2 x minus y minus 7

x squared minus x y minus 7 x plus 2 y plus 10

Question 8

Find the value of f left parenthesis 6 right parenthesis space i f space f left parenthesis x right parenthesis equals 1 over 6 x plus 7 .

13

6

8

7

Question 9

Solve the inequality negative x over 4 plus 2 x less or equal than 14 .

x less than 8

x greater or equal than negative 8

x greater than negative 8

x less or equal than 8

Question 10

Simplify x to the power of 8 over x to the power of 4 .

x to the power of 4

x squared

x to the power of 12

x to the power of 32

Question 11

Subtract x squared plus 4 x y space minus space 12 from 3 x squared minus 7 x y plus 4 .

2 x squared minus 3 x y minus 8

2 x squared plus 3 x y plus 8

negative 2 x squared plus 11 x y minus 16

2 x squared minus 11 x y plus 16

Question 12

Find the inequality that is illustrated in the following image:

left square bracket negative 2 comma space minus 1 right square bracket intersection left parenthesis 0.2 right parenthesis

left square bracket negative 2 comma space minus 1 right parenthesis union left parenthesis 0 comma 2 right parenthesis

left parenthesis negative 2 comma space minus 1 right square bracket union left square bracket 0 comma 2 right square bracket

left parenthesis negative 2 comma space minus 1 right square bracket intersection left square bracket 0 comma 2 right square bracket

Question 13

Which of the following steps is involved in solving 3 x plus 8 equals 14 ?

3 x plus 8 equals 14 minus 8

3 x plus 8 plus 8 equals 14 plus 8

3 x plus 8 minus 8 equals 14

3 x plus 8 minus 8 equals 14 minus 8

Question 14

Find the range of the function f left parenthesis x right parenthesis equals square root of 3 x minus 9 end root .

left curly bracket y element of straight real numbers left enclose y greater than 3 right curly bracket end enclose

left curly bracket y element of straight real numbers left enclose y greater or equal than 3 right curly bracket end enclose

left curly bracket y element of straight real numbers left enclose y greater than 0 right curly bracket end enclose

left curly bracket y element of straight real numbers left enclose y greater or equal than 0 right curly bracket end enclose

Question 15

Solve the inequality fraction numerator 3 x over denominator 2 end fraction minus 5 greater than negative 2 x .

x less than 10 over 7

x greater than 10

x greater than negative 10

x greater than 10 over 7

Question 16

Which of the following images represents the inequality x less than negative 2 ?

Question 17

Which of the following function is obtained when the graph of f left parenthesis x right parenthesis equals square root of x is transformed left 3 units and down 2 units?

g left parenthesis x right parenthesis equals square root of x minus 3 end root plus 2

g left parenthesis x right parenthesis equals square root of x plus 3 end root minus 2

g left parenthesis x right parenthesis equals square root of x minus 2 end root plus 3

g left parenthesis x right parenthesis equals square root of x plus 2 end root minus 3

Question 18

Find the domain of the function f left parenthesis x right parenthesis equals square root of 3 x plus 7 end root .

straight real numbers minus left curly bracket 0 right curly bracket

straight real numbers

All real-numbered x where x greater or equal than negative 3 over 7

All real-numbered x where x greater or equal than negative 7 over 3

Question 19

Find the set builder notation for the set of integer multiples of 17.

left curly bracket x left enclose x equals 17 n comma space w h e r e space n space element of straight integer numbers right curly bracket end enclose

left curly bracket 0 comma 17 comma 34 comma 51 comma… right curly bracket

left curly bracket 17 comma 34 comma 51 comma… right curly bracket

left curly bracket x left enclose x equals 17 plus n comma space w h e r e space n space element of straight integer numbers right curly bracket end enclose

Question 20

Find the inequality corresponding to the following number line:

x less than 1

x less or equal than 1

x greater than 1

x greater or equal than 1

Question 21

Find the value f(3) from the following graph:

0

5

2

4

Question 22

A car travels three equal sections of a highway that is 18 miles long. Which equation correctly models the situation?

x over 18 equals 3

3 x equals 18

18 x equals 3

x over 3 equals 18

Question 23

Which of the following is true about a graph?

If some horizontal line can be drawn that crosses the curve two times or more, the graph is a function.

If some vertical line can be drawn that crosses the curve two times or more, the graph is a function.

If some vertical line can be drawn that crosses the curve two times or more, the graph is not a function.

If some horizontal line can be drawn that crosses the curve two times or more, the graph is not a function.

Question 24

The number of tourists visiting a city doubles every month during the two-month period beginning in Jan. 1st and ending in Feb. 28th each year. If the number of tourists who visited the city in the beginning of January in that particular year was x, how many tourists visited the city at the end of February that year?

2 cubed x

2 x squared

2 x cubed

2 squared x

Question 25

A car is leaving New York. After 30 minutes, the car is 25 miles from New York, and after 3 hours the car is 200 miles from New York. What is the car’s average speed (miles per hour) between the 30 minute and 3 hour time frame?

60 mph

100 mph

80 mph

70 mph

Question 26

Find the equation of the line that passes through (1,5) and is parallel to the line 2y+4x=3.

y equals negative 1 half x plus 1

y equals negative 1 half x minus 9

y equals 2 x plus 9

y equals negative 2 x plus 7

Question 27

Find the domain of the function f left parenthesis x right parenthesis equals fraction numerator 5 x over denominator square root of 3 x squared minus 12 end root end fraction .

All real-numbered x such that x greater or equal than 2

All real-numbered x such that x less than negative 2 space a n d space x greater than 2

All real-numbered x such that x greater than 2

All real-numbered x such that x greater or equal than 2 space a n d space x less or equal than negative 2

Question 28

Find the domain of the function f left parenthesis x right parenthesis equals square root of fraction numerator 3 over denominator 2 x minus 18 end fraction end root .

left square bracket 9 comma infinity right parenthesis

left square bracket 3 comma infinity right parenthesis

left parenthesis 9 comma infinity right parenthesis

left parenthesis 3 comma infinity right parenthesis

Question 29

Simplify 3 x plus 6 left parenthesis 2 x minus y right parenthesis minus left parenthesis 32 minus x right parenthesis .

14 x minus 6 y minus 32

14 x plus 6 y minus 32

16 x plus 6 y minus 32

16 x minus 6 y minus 32

Question 30

Find the quotient and the remainder when x squared plus 5 x plus 2 is divided by x plus 1 .

Quotient = x-4 and Remainder = -2

Quotient = x+4 and Remainder = -2

Quotient = x-4 and Remainder = 2

Quotient = x+4 and Remainder =2