Math 37
Mock Test 2
1.- Simplify the following expressions.
(a) −3x + 8 − x − 5
(b) −4(9 − 3x) + 26
(c) −7x − 3(2 − 2x)
(d) −2(x + 8) + 6(x − 1)
2.- Which of the following expressions are equivalent to −3x + 4.
(a) −9x − 7 + 12x + 11
(b) x + 3(x − 1) − 7x + 7
(c) 6(2 − 3x) + 5(3x − 2) + 2
(d) −x − x + (3 − x) − 1
3.- Solve the following linear equations.
(a) 3x + 1 = −11
(b) −2x + 7 + 3x = 8
(c) 5(1 − x) + 2 = −3
(d) 4x − 9 = −2x + 3
(e) 7(2x − 3) − 9x = −2 + 6
(f) 3(x − 5) + 3 = 2(x + 9)
Villalobos - Math 37 - Mock Test2 - Fall 2015
4.- Explain the difference between an Expression and an Equation. Give an example of each.
5.- Evaluate the following expressions.
(a) (a − b)(b + c)(a + c);
(b) (w + r)2 + p;
(c) −(t − y) +
w = 9,
j+k
;
w
a = −2,
b = 3,
r = −12,
t = 1,
y = −2,
c = −1
p = −3
j = −7,
k = 9,
6. Which of the following ordered pairs are solutions to
(a) (−4, −5)
(b) (4, 5)
Villalobos - Math 37 - Mock Test2 - Fall 2015
w=2
3
y = x−2
4
(c) (0, −2)
(b) (8, 4)
7.- Complete the following table and then graph all the ordered points.
(a)
y
y = −2x + 1
x
x
-4
-3
0
1
5
y
(x, y)
(b)
y
3x − 5y = 15
x
0
y
(x, y)
3
x
-5
0
10
8.- Find the x − intercept and y − intercept for the following linear equations.
(a) y = 3x + 12
(b) 5x + 4y = 20
(c) x = 7
(d) y = −1
3
(e) y = x − 3
7
(f) 4y − 3 = 5
Villalobos - Math 37 - Mock Test2 - Fall 2015
9.- Find the x − intercept and y − intercept for the following linear equations.
y
y
x
x
x − intercept :
x − intercept :
y − intercept :
y − intercept :
10.- Use the following figure to answer the following.
(a) Find the coordinates of point A
y
(b) Find the coordinates of point B
B
(c) Area of the intersection of the two pens.
A
(d) Perimeter of the union of the two pens.
x
(e) Describe how to get from point A to
point B.
(f) Which point A or B is farther from the
origin? Explain how you got your answer.
Villalobos - Math 37 - Mock Test2 - Fall 2015
11.- Write a mathematical expression/equation for the following sentences.
(a) Seven added to the product of r and m
(b) The difference of x and four is two
(c) The quotient of t and p increased by ten
(d) Twice the sum of x and y decreased by five
(e) Five more than four times a number equals to another number
12.- Set up an equation and solve the following word problems.
(a) Barney is five years older then Nemo. If the sum of their ages is 47 years, how old are
they?
Parts (b) and (c) are challenging. The problems on the exam will be more like
part (a), but it is good to challenge yourself a bit as you prepare for the exam.
(b) Lars and Jose played a 21 points basketball game. The number of points that Jose scored
was three more than twice the number of points that Lars scored. If Jose won the game (he
scored 21 poinst),How many points did Lars scored?
(c) Art, Jose and Lars collect mathematics books. Art has 5 more books than Jose. If Lars
has 4 more books than Art and their total book collections add to 53 books, how many books
does each person have?
Villalobos - Math 37 - Mock Test2 - Fall 2015
13.- Pinky is asked to simplify the following expression: 3 + 5(x + 2) + 4x. Below is Pinky’s
work. Find all the mistakes (Explain why is a mistake) and then simplify the problem correctly.
3 + 5(x − 2) − 4x
⇒ 8(x − 2) − 4x
⇒ 8x − 2 − 4x
⇒ −4x − 2
⇒ −6x
14.(a) Expression A: Fill in the missing values in the table. Then, express the steps in the
Expressions column using symbols. Finally, in the box in the lower corner of the table, set
the algebraic expression equal to y
Input, x
-3 0
Result of Step 1 0 3
Result of Step 2 0 6
Result of Step 3 1 7
Output, y =
1 7
Verbal Steps
\Input/
2
5
10
11
11
/Output\
Expression
x
y=
(b) Expression B: Express the steps using words in the Verbal Steps column based on
clues in the table of values. Then, express the steps in the Expressions column using symbols. Finally, in the box in the lower corner of the table, set the algebraic expression equal to y.
Input, x
-3 0
Result of Step 1
Result of Step 2
Output, y =
2
Verbal Steps
\Input/
Multiply the input by two
Add seven to the result of Step 1
/Output\
(c) Are Expressions A and B equivalent? Explain
Villalobos - Math 37 - Mock Test2 - Fall 2015
Expression
x
y=
15.- For the set of numbers plotted below, create an extended table of values, a 2D grid, an
evaluation machine, and a symbolic summary
0
1
2
3
Position in List
n
-1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
List Number
C(n)
4
10
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
-3 -2 -1 0 1 2 3 4 5
−1
−2
−3
Villalobos - Math 37 - Mock Test2 - Fall 2015
n
C(n)=
16.- Consider the following graph that gives the height of a child as determined by the age of
a child during the period of 1970 - 1990.
(a) Draw vertical and horizontal arrows to show how you would estimate the height
of an eight-year old child. What did you estimate for the height of an eight year old child.
(b) Depict your answer from part (a) in function notation by filling in the blanks.
f(
)=
(c) Draw vertical and horizontal arrows to show how you would estimate the age of
a child that is 60 cm in height.
Villalobos - Math 37 - Mock Test2 - Fall 2015
17.(a) Produce a table of steps for the given expression in the first column.
(b) Produce a reverse evaluation table in the second column and find the reverse expression (write this in terms of y).
(c) Use the reverse evaluation table to solve the given equation.
Expression −2(x + 7) − 2
\Input, x/
\Output, y/
Reverse expression
\Input,, y/
\Output,, x/
Villalobos - Math 37 - Mock Test2 - Fall 2015
Equation
−2(x + 7) − 2 = −4
x=