Download Test 3 Practice Problems

TEST 3 REVIEW
MATH 082
Chapter 6
-Factoring polynomials
Always look for a common factor first
Difference of squares
Perfect square trinomials
Trinomial w/leading coefficient of 1
Trinomial w/leading coefficient not 1
Factor by grouping
1.
2𝑥 2 − 4𝑥 + 20
8.
12𝑥 2 + 7𝑥 − 10
2.
𝑥 2 − 121
9.
10𝑥 2 − 56𝑥 − 24
3.
5𝑦 2 − 20
10.
9ℎ2 − 30ℎ + 25
4.
16𝑎2 − 49𝑏 2
11.
𝑥 3 − 4𝑥 2 + 3𝑥 − 12
5.
𝑥 2 − 21𝑥 + 110
12.
𝑦 4 + 7𝑦 3 − 9𝑦 − 63
6.
3𝑦 2 − 3𝑦 − 168
13.
𝑥 3 + 2𝑥 2 − 𝑥 − 2
7.
𝑥 2 + 16𝑥 + 64
-Solve quadratic equations by factoring
Put equation in general form, ax2 + bx + c = 0 (set equal to zero)
Then factor.
Set factors = 0
Solve (and check answers)
14.
(2𝑦 − 1)(6𝑦 + 7) = 0
15.
4𝑦 2 + 22𝑦 − 12 = 0
16.
𝑥(𝑥 − 5) = 84
-Applications with quadratic equations
Consecutive integers (odd and even)
Free-falling objects
Geometry (perimeter and area of squares, triangles, and rectangles)
Write an equation and solve each of the following:
17.
Find two positive consecutive integers, whose product is 182.
18.
Find two positive consecutive odd integers, whose product is 143.
19.
An object is dropped from a platform 64 feet above the ground. It’s height above the ground
after t seconds, is given by the equation, ℎ = −16𝑡 2 + 64. When will it hit the ground?
20.
The height of a triangle is one inch more than the base. If the area of the triangle is 45 square
inches, what is the length of the base and height?
21.
The length of a rectangular table is twice as long as it’s width. If the area of the table is 288
square inches, what are the dimensions of the table?
Chapter 7
- Find the restricted values of a rational expression. (These are the numbers that make the denominator equal
to 0)
Find the restricted values of the following rational expressions
22.
−2
𝑥 2 −3𝑥
23.
𝑥+8
𝑥 2 −25
-Simplify a rational expression
Remember to factor everything first.
Remember that b – a =  (a – b)
Simplify the following expressions.
24.
25.
26.
8𝑎2 𝑏3
−20𝑎𝑏6
3𝑥 2 −5𝑥−2
6𝑥 2 −𝑥−1
𝑦 2 +4𝑦−21
27−6𝑦−𝑦 2
-Multiply and divide rational expressions.
Remember: Only factors can be cancelled.
27.
28.
−2𝑓3
5𝑔4
𝑦−2
𝑦 2 +2𝑦
∙
∙
15𝑔
12𝑓2
𝑦 2 +8𝑦
𝑦 2 +6𝑦−16
29.
30.
𝑥+3
𝑥−4
÷
𝑥 2 −𝑥−12
𝑥 2 −2𝑥−8
𝑦2 −36
(𝑦 − 6) ÷ 𝑦+1
-Add and subtract rational expressions.
1.Find a common denominator
2. rewrite expressions
3. perform operation
4. simplify
31.
32.
33.
2𝑥
2𝑥 2 −𝑥−3
7
𝑦−3
−
3𝑥
4𝑥+1
+
5
2𝑥−3
5
3−𝑦
−
9
3𝑥−1
-Simplify a complex fraction
Change to a division problem then invert the divisor and multiply (Remember: Only factors can be cancelled.)
34.
4𝑐3
10𝑑2
16𝑐4
35𝑑3
35.
𝑥+3
𝑥−5
2𝑥+6
𝑥2 −25
-Solve Rational Equations.
multiply both sides by the LCD
36.
37.
−3
4𝑥
+
2
𝑥−7
5
𝑥2
=
=
2
4𝑥 2
30
𝑥 2 +𝑥−56
−
3
𝑥+8
38.
𝑥
2
=
𝑥+40
𝑥
-Applications of Rational Equations
Proportions
Similar Triangles
Work Rate
Motion
39.
If a high school employs 9 teachers for every 77 students, how many students are in the school
if it employs 234 teachers?
40.
Find the unknown length n for the given similar triangles.
12 cm
n cm
20 cm
15
41.
Jameson can mow the lawn in 40 minutes, while Tyler takes 30 minutes. If they mow the lawn
together how long will it take?
42.
A plane can fly 500 miles against the wind in the same amount of time that it can fly 725 miles with
the wind. If the wind speed is 45 mph, find the speed of the plane in still air.