Download MAT084 Sample Final Exam The following questions appeared on a

MAT084 Sample Final Exam
The following questions appeared on a MAT084 Final Exam here at SCCC in the past.
1)
Solve for x: 1 − 3x = −5
2)
Solve for y:
3)
Simplify completely…combine all like terms:
4)
Find the slope (not the equation) of the line between the two points (−1,5) and
(2,3)
5)
Solve the following equation for y: 3x − 4 y = 12
6)
What is the slope of the equation: 3 y − 5 x = 9 ?
7)
Graph the line 2 y = 6 x − 12 . Label the x intercept and y intercepts clearly.
3 − 2( 4 − 3 y) = 10
2( x + 2 y ) + 6 x − 2 y + 1
10
y
8
6
4
2
x
-10 -8 -6 -4
-2
0
-2
-4
-6
-8
-10
2
4
6
8 10
8)
9)
 −2 x + y = −8
Find the solution to the given system of equations: 
. Put your
 2x + 3y = 12
answer in (x,y) notation.
4 x − 5 y = − 7
Solve the system of equations: 
. Put your answer in (x,y) notation.
6 x + 3 y = 21
10)
The Jimenez Television Company made $12,375 in April selling their two top selling TV models. They
sold 30 units of their best seller and 17 units of their second best seller. In May, they sold 42 units of
the best seller and 21 units of the second best seller for a total income of $13,250. Use two equations
and algebra to determine what their sales for these two models will total in June if they can sell 30 units
of the top-seller and 25 units of the second-best seller.
11)
Where does the line y =
2
1
x − cross the x axis?
3
4
12)
Where does the line y =
2
1
x − cross the y axis?
3
4
13)
What is the slope of the line: y =
14)
Find the equation in slope−intercept form of the line through the points (5,2) and
(20,32).
2
1
x− ?
3
4
15)
1 2
Which of the following numbers in the set are integers? 4,−2, ,− ,0, 3, π 
3 7


16)
What is the slope of the line shown?
y
5
4
3
2
1
x
-1
0
-1
-2
1
2
3
4
5
6
7
17)
Solve for a:
a 2
=
3 5
18)
Solve for x:
x 4−x 1
−
=
3
2
2
19)
A company pays costs for manufacturing a new coffee mug according to the
equation C = 1.25 x + 2300 where x is the number of mugs produced and C is
in dollars. How many mugs can they produce for $20,000?
20)
Simplify 6 − 4 2 + 2( 4 − 9)
21)
The equation T = t −
22)
The profit for a company manufacturing widgets is known to be the following: A
profit of 10 million dollars for selling 5 million units. A profit of 5.5 million dollars
for selling 2 million units. Find a linear equation that relates units sold to profit.
Put it in slope−intercept form.
23)
Solve the inequality −2( x + 5) < x − 4
24)
How many pounds of coffee beans selling for $2.00 per pound should be mixed
with 6 pounds of coffee beans selling for $2.80 per pound to get a mixture selling
for $2.48 per pound?
25)
The outside dimensions of a picture frame are 36 inches by 29 inches. If its
inside dimensions are 32 inches by 20 inches, find the area of just the frame.
Include proper units or your answer will not be given credit.
2f
gives the Fahrenheit air temperature at an altitude of
1000
f feet when the ground temperature, t, is known. Solve for f in terms of T and
t…simplify as much as possible.
For the last three questions, please use the following scenario:
A mathematician has developed a model indicating that a woman with x years of
education can expect to earn y = 1500 x + 16300 dollars per year.
26)
What is the y−intercept for this model and what does it mean in terms of the
model?
27)
What is the slope of the model and what does it mean in terms of the variables
used?
28)
How many years of education would be required for a woman to make $40,000
per year? Round to the nearest year.