- Description
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