Math 1090-002 Practice Test 1
Spring 2013
Instructor:Jie Ma
1.Solve the equation for x:
x−7
x−4
+1
=
5
3 −1
2x
6
2.Solve the equation for x: x−3 = 4+ x−3
3.Find the maximum and minimum of the objective function F = 5x − 2y
subject to the following constraints.
x+y ≥2
−x + 2y ≤ 4
5x − 4y ≥ 10
4.Statement: Six more than two times a number is at least as much as four
times that same number.
(1) Convert the problem into an inequality.
(2) Solve this inequality for x.
(3) Graph the solution set on the real number line.
5.Solve the following inequality and then graph the solution set on the real
2x
number line: −1 < 5− 3 ≤ 10
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6.Given an equation: 4y − x = x + 3
(1) What is the slope-intercept form of the given equation?
(2) What is the slope of the line?
(3) What is the x-intercept of the equation ?
(4) What is the y-intercept of the equation ?
(5) What is the line that passes through the point(1, 0) and is parallel to the
given line?
(6) What is the line that passes through the point(2, 5) and is perpendicular
to the given line?
(7) What is the equation of the line that is perpendicular to x = 4 and passes
through (5, 2013)?
7.Solve the following system of equations:
x + 3y = 10
3x + 9y = 6
8.Alexandra is 65 less than thress times the age of Madison.Charlie is 39 less
than two times the age of Madison.The sum of their ages is 58. How old is
Madison?
9.Market research has shown that for a sporting event, the supply equation
for tickets is20p − q = 100 and the demand equation is 4p = 6260 − 5q
(a) How many tickets will the fans purchase if the price is $30.00?
(b) How many tickets will the sponsors of the event be willing to sell if the
ticket price is $30.00?
(c) How many tickets will the fans purchase if the price is $100.00?
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(d) How many tickets will the sponsors of the event be willing to sell if the
ticket price is $100.00?
(e) What is the equilibrium point for this market for sporting even tickets?
10.The KM Book company wants to publish an adventure novel and has
determined that fixed costs would be $55, 000and variable costs are $1.60per
book. The LB Book Distribution Company will buy them for $11each.
(a) Write the cost function.
(b) Write the revenue function.
(c) Write the profit function.
(d) How many books must be sold for the publisher to break even?
(e) What profit would the publisher expect if the distributor purchased
12, 000books?
11.Solve the following system of equations:
x+y+z =3
3x − 2y = −1
2z = −6
12.Determine the Maximum and Minimum of the objective function 4x + 5y
over the feasible region:
y−x≤3
5y − 8x ≥ −3
y≥0
x≥0
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