Grima MAT 151 Chapter 2 Hybrid Practice test
#1-2; find an equation for the line with the given properties. Express your answer in slope
intercept form.1) Slope = 4; containing the point (2, 3)
2) Parallel to the line y = 5x - 4; containing the point (6,7)
3) Write the standard form of the equation of the circle with the given radius (r) and center
(h,k) then sketch a graph of the circle. r = 5 (h,k) = (2, -1)
4) Find the standard form of the equation of each circle. It may help to sketch a graph of the
circle before you start your algebra.
Center (2, -3) contains the point (2, 1)
5) Rewrite so that the equation is written in the standard form of a circle and sketch a graph.
x2 + y2 +4x + 6y = 3
8) Find the x and y-intercepts then sketch a graph (it will be enough to label two points on
your graph)
3
4
1
𝑥 − 3𝑦 = 3
#9-10; determine the type of symmetry the graph of the equation has (if any)
9) y2 = x - 4
10) y = -2x3
11) M varies inversely as the square of n. M is 3 when n is 3. Find M when n is 2.
12) Y varies jointly as the square of x and the square root of z. Y is 60 when x is 2 and z is 9.
Find Y when x is 9 and z is 4.
14) The distance (D) it takes a car to stop is directly proportional to the square of the speed (s)
it is moving. A car traveling 20 miles per hour can stop in 10 feet. How long will it take a car
traveling 30 miles per hour to stop?
Chapter 2 Hybrid Practice test
#15 – 17; Determine whether the graph is symmetric to the x-axis, y-axis, the origin, or none of
these.
15)
16)
17)
Chapter 2 Hybrid Practice test Answers
1) y = 4x – 5
2) y = 5x – 23
2
2
3) (x-2) + (y+1) = 25 (see below for graph)
4) (x-2)2 + (y+3)2 = 16
5) (x+2)2 + (y+3)2 = 16 (see below for graph)
6) there is no question 6
7) there is no question 7
8) x int (4,0) y-int (0,-9) see below for graph
9) symmetric to x-axis
10) symmetric to origin
11) m = 27/4
12) y = 810
13) there is no question 13
14) 22.5 feet
15) symmetric to y – axis 16) symmetric to x-axis 17) symmetric to origin
Graph for question 3
Graph for question 8
Graph for question 5
Grima MAT 151 Chapter 3 Hybrid Practice test
#1 –2: Determine the domain and range of each function, write your answer in interval notation when
appropriate.
1)
Domain_____________ Range_________
2)
y
4
3
(5,2)
2
(-3,1)
(2,1)
1
(0,0) (3,0)
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
x
5
6
7
8
9
10
11
-1
-2
-3
-4
Domain_____________ Range_________
Chapter 3 Hybrid Practice test
#3-5: Use algebra to find the domain of each function. Write your answer in interval notation, or in
words.
𝑥−4
3) 𝑓(𝑥) = 𝑥 2 +3𝑥+2
5) f(x) = x2 – 16
4) 𝑓(𝑥) = √𝑥 − 6
#6 – 8: let f(x) = x2 + 2x + 5 and g(x) = 3x – 1, find the following
7) (𝑔 ∘ 𝑓)(𝑥)
6) (f-g)(x)
8) (f+g)(2)
9) Find the difference quotient; that is find
𝑓(𝑥+ℎ)−𝑓(𝑥)
;
ℎ
f(x) = 2x – 3
Use the graph below to answer #10 – 15, call the function graphed below h(x)
9
8
7
6
5
4
3
2
1
-4
-3
-2
-1
y
(1,4)
(0,3)
(-1,0)
-1
-2
-3
-4
-5
-6
-7
-8
-9
1
2
10) find the x-intercepts
12) for what values of x is h(x) = 4
14) what is the domain of h
3
(3,0)
4
x
5
6
(4,-5)
11) find the y-intercept
13) find h(4)
15) what is the range of h
Chapter 3 Hybrid Practice test
Use the graph below to answer questions 18 – 23. (3 points each)
(You should also be able to find the domain and range of this graph)
16) the interval(s) where the function graphed is increasing
17) the interval(s) where the function graphed is decreasing
18) The values of x (if any) where the function has a local maximum
19) The local maximum value (if any)
20) The values of x (if any) where the function has a local minimum
21) The local minimum values (if any)
22) Find the average rate of change of f(x) = x3 + 6x2 from 0 to 2
#23-25 describe how the graph of the given function relates to the graph of a common function
23) f(x) = (x-2)2 + 4
24) f(x) = −√𝑥 + 3 + 5
25) 𝑓(𝑥) = |𝑥 + 3| − 4
26) Write the function whose graph has the same shape as the graph of f(x) = x2 but is shifted to the
right 3 units and up 2 units.
27) A campground owner has 1000 meters of fencing. He wants to enclose a rectangular field bordering
a river, with no fencing needed along the river. Let W represent the width of the field. Follow these
steps to find the dimensions of the field that yields the largest area.
a)
b)
c)
d)
e)
Write an expression for the length of the field
Write an equation for the area of the field.
Find the value of w leading to the maximum area
Find the value of L leading to the maximum area
Find the maximum area
Chapter 3 Hybrid Practice test Answers:
1) Domain [3, ∞) Range (−∞, 0] 2) Domain {-3,0,2,3,5} Range {0,1,2}
3) Domain: All real numbers except -1, -2
4) Domain [6, ∞) 5) Domain all real numbers
6) x2 – x + 6 7) 3x2 + 6x + 14 8) 18 9) 2
10) (-1,0) (3,0) 11) (0,3) 12) x = 1 13) -5 14) [-1,4] 15) [-5,4]
16) (−∞, −1) ∪ (1, ∞) 17) (-1, 1)
18) x = -1 19) max y-value y = 4
20) x = 1 21) min y-value y = 0
22) 16
23) shifted right 2 up 4
24) reflected over x-axis, shifted left 3 up 5
25) left 3 down 4
26) g(x) = (x-3)2 + 2
27 was missed by many last semester and will likely be on your test
27a) L = 1000 – 2W
27b) A = LW or A = (1000 – 2W)W or A = 1000W – 2W2
27c) W = 250 FT
27d) L = 500 FT
27e) 125000 square feet
Grima MAT 151: Chapter 4 Hybrid Practice test
This is not a complete test review, but it is what I think I can complete in class. The review at the end of the
chapter is a more complete review. Everything on this handout should make it on the test, but the test will
be longer and have more kinds of problems than this handout. I have not written answers for this yet, but
will solve each problem in class.
1) An object fired vertically into the air with an initial velocity of 160 feet per second will be at a height
(h) in feet, t seconds after launching, determined by the equation h= – 16t2 + 160t
a) at which times will the object have a height of 144 feet?
b) how long it will take the object to return to the ground.
c) determine the maximum height the object reaches.
2) A real estate office manages an apartment complex with 100 units. When the rent is $1000 per
month, all 100 units will be occupied. However, when the rent is $1200 per month only 80 units will be
occupied. Assume the relationship between the monthly rent and the number of units occupied is
linear.
a) Write the equation giving the demand y in terms of the price p
b) Use the equation to predict the number of units occupied when the price is $1300. (round to the
nearest unit if needed)
c) What price would cause 50 units to be occupied?
3) h(x) = 2(x-1)2 - 4
a) describe the transformation as compared to the function f(x) = x2, specifically state if the graph is
shifted left, right, up, down and if any reflection has occurred
b) make a table of values and sketch a graph
c) state the domain of the function
d) state the intervals where the function in increasing and decreasing
4) f(x) = x2 + 6x + 5
a) Use completing the square to rewrite the problem in standard form
b) Sketch a graph, make sure to label the vertex. You may use your calculator, instead of making a table
of values to create your graph
Grima MAT 151 Chapter 5 Hybrid Practice test
1)
a)
b)
c)
d)
e)
f(x)=x3 + 2x2 – 8x
List each x-intercept (zero) and its multiplicity (round to 2 decimal places when needed)
Which function will the graph of f(x) behave like for large values of |𝑥|
Describe the end behavior
sketch a graph and approximate the turning points, also label the x-intercepts
state the intervals where the function is increasing and decreasing (round to 2 decimals)
2) f(x) = 2x3 - 3x2 – 17x - 12
a) use your graphing calculator, or the rational root theorem to find a zero of the polynomial
b) use synthetic division to completely factor the polynomial
3) Solve: 2x3 - 3x2 – 17x - 12= 0 (hint use your answer to question 2b)
4) Create a function with lead coefficient 1 that satisfies the conditions;
degree 3: zeros 6 and 5i
5) Solve: x2 + 3x – 10 < 0
6) f ( x ) 
a)
b)
c)
d)
e)
f)
Domain
Vertical Asymptote (if any)
Horizontal asymptote, or slant asymptote
x- intercept(s) if any
y-intercept(s) if any
Sketch a graph of the function : label all the features found in parts b - e
7. f ( x) 
a)
b)
c)
d)
e)
f)
2x  8
x2
x  10
x  4x  5
2
Domain
Vertical Asymptote (if any)
Horizontal asymptote, or slant asymptote
x- intercept(s) if any
y-intercept(s) if any
Sketch a graph of the function : label all the features found in parts b – e
Chapter 5 Hybrid Practice test Answers
1a) (-4,0) odd (0,0) odd (2,0) odd
1b) like x3
1c) falls to the left, rises to the right
1d)
1e) increasing (−∞, −2.43) ∪ (1.09, ∞) decreasing (-2.43, 1.09)
2a) x = 4 (also x = -1)
2b) f(x) = (x-4)(x+1)(2x+3)
3) x = 4, -1, -3/2
4) f(x) = x3 – 6x2 + 25x - 150
5) -5 < x < 2
6a)
6b)
6c)
6d)
6e)
Domain all real numbers except 2
x =2
y=2
(-4,0)
(0, -4)
Chapter 5 Hybrid Practice test Answers
6f)
7a)
7b)
7c)
7d)
7e)
7f)
Domain all real numbers except x = -5,1
x = -5 and x = 1
y=0
(-10, 0)
(0,-2)
Grima MAT 151
Chapter 6 Hybrid Practice test
1) f(x) = x2 - 2x + 1
g(x) = 7x – 5
a) (𝑔 ∘ 𝑓)(𝑥)
b) the domain of (𝑔 ∘ 𝑓)(𝑥)
2) The graph of a one to one f function is given. Draw the graph of the inverse function f-1 (5 points)
3) f(x) = x3 + 4
a) Find the inverse of f(x)
b) Check your answer by showing that (𝑓 ∘ 𝑓 −1 )(𝑥) = x
4) Describe the transformation of the graph of g(x) as compared to the graph of f(x) = ex.
a) g(x) = ex-2
b) g(x) = ex + 4
c) g(x) = -ex
d) g(x) = ex+3 - 6
#5-7: Solve
1 𝑥+1
5) 3x+2 = 81
6) (2)
1
= 16
7) deleted
8) y = log2(x+2)
a) Graph the logarithmic functions. First write the equation in exponential form, then create a table of
values and plot the points.
b) State the domain the function
c) Describe the transformation the occurs from a common function
Chapter 6 Hybrid Practice test
9) Write the expression as a single logarithm. Write your answer with only positive exponents.
2log3 x + 4 log3 y – 5log 3z
10) Expand into sums and differences of logarithms (express powers as factors).
𝑙𝑜𝑔3
𝑥2𝑦
𝑤4𝑧
#11-12: Solve the exponential equations, round your answer to 2 decimals.
11) 3x = 18
12) deleted
#13-18: Solve the logarithmic equations, round to 2 decimals when needed.
13) log3 x = 4
14) ln x = 0
15) log2(x +1) = 5
16) ln (4x-8) = ln(3x-1)
17) deleted
18) log2 (x+2)+log2 (x-2) = 5
(be sure to check for extraneous solutions)
19) How long will it take an initial investment of $10,000 to double if it is expected to earn 5% interest
compounded continuously? (Round to 1 decimal place) (use formula A = Pert).
20) The population of a city is expected to double in 20 years. The city currently has 5,000 residents.
How long will it take to get to 30,000 residents? (round final answer to 2 decimals)
(use formula P(t) = P0ekt, round k to 3 decimals)
Chapter 6 Hybrid Practice test Answers:
1a) (𝑔 ∘ 𝑓)(𝑥) = 7x2 – 14x + 2 1b) domain all real numbers or (−∞, ∞)
2)
3
3a) f-1(x)= √𝑥 − 4
3
3
3b) (𝑓 ∘ 𝑓 −1 )(𝑥) = ( √𝑥 − 4) + 4
(𝑓 ∘ 𝑓 −1 )(𝑥) = x – 4 + 4
(𝑓 ∘ 𝑓 −1 )(𝑥) = x
4a) right 2
4b) up 4
4c) reflect over x-axis 4d) left 3 down 6
5) x = 2
6) x = 3
7) deleted
8a)
8b) domain x > -2 or (−∞, −2)
9) 𝑙𝑜𝑔3
𝑥 2𝑦4
𝑧5
8c) same shape as y = log2 x , but shifted left 2
10) 2log3x + log3y - 4log3w - log3z
11) x = 2.63
12) deleted
13) x = 81
14) x = 1
15) x = 31
16) x = 7
17) deleted
18) x = 6
19) 13.9 years 20) 51.19 years
Grima MAT 151
Chapter 8 Hybrid Practice test
#1-2: Solve each system of equations using either the substitution method or the elimination method,
0 points if no work is shown even if answer is correct.
2
1
x y 3
1) 3
4
x  y 1
2)
3 x  2 y  13
x  5 y  7
3) Solve each system of equations, by hand without matrices, 0 points if no work is shown even if
answer is correct.
2𝑥 + 4𝑦 − 5𝑧 = 17
−𝑥 + 𝑦 + 2𝑧 = −5
𝑥 − 3𝑦 + 3𝑧 = −2
(pair the middle equation with the other 2 and drop out the x’s)
4) Solve the system of equations using matrices and row operations. 0 points if no matrix work is
shown even if answer is correct.
3x  2 y  16
2 x  3 y  11
#5-6 Use the following matrices to answer all the problems in this section. You may use a calculator to
solve these two problems.
4 5

1 2 
1 0 


A= 3 2


6 1 
3 2 0 
D= 

4  1 3
5) 2D – C
B= 
6) AC
1 0  1

7 2 4 
C= 
Chapter 8 Hybrid Practice test
7) Solve the system of equations using matrices and row operations, 0 points if no matrix work is shown
even if answer is correct.
𝑥+𝑦+𝑧 =9
3𝑥 − 2𝑦 + 3𝑧 = 7
5𝑥 − 4𝑦 − 3𝑧 = −15
8) Solve the system of equations using Cramer’s rule, 0 points if solved with another method, even if
answer is correct.
3x  2 y  4
2x  3y  7
D = _________________________________
Dx = _________________________________
Dy = _________________________________
X =_________ y = ______________
#9-10: Solve the following systems of equations.
9)
x y 5
x 2  y 2  13
x y 4
10) x 2  y  10
11) graph the system of linear inequalities by hand. Label the corner points.
𝑥+𝑦 ≤6
2𝑥 + 𝑦 ≤ 10
𝑥 ≥ 0, 𝑦 ≥ 0
Chapter 8 Hybrid Practice test Answers
Answers: 1) (3,4)
6)
1 0
[17 4
13 0
9)
(2,3) (3,2)
−1
5]
2
2) (3,2)
3) (4,1,-1)
7) (2,4,3)
10) (-2,6) (3,1)
4) (2,5)
8) D = 13
5 4 1 

1  4 2
5) 
Dx = 26
Dy = 13 x = 2 y = 1