Testing Enhancement Workshop MATH98
27
Testing Enhancement Workshop MATH98 Department of Mathematics and Computer Science, Coppin State University Updated on Oct 20, 2014 by Dr. Min A
Transcript of Testing Enhancement Workshop MATH98
Testing Enhancement WorkshopMATH98
Department of Mathematics and Computer Science, Coppin State University
Updated on Oct 20, 2014 by Dr. Min A
Outline
• Solve an equation(linear or quadratic).
• Solve a formula.
• Special equations and inequalities.
• Application of equation, inequality,
proportion and geometry.
• Factoring.
• Link to check answers
http://faculty.coppin.edu/pages/MA/
Linear Equation
Form A #1)
#2)
#3)
Solve a formula
Practice form A4)
Solve for b.
Try Form A 22)
Step 1: Collect all terms with the specified variable one side.
Step 2:Combine terms with the specified variable .
Step 3:Divide each side by the factor of the specified variable.
bhA2
1
bhA 2
hb
A
2
Find the perimeter of Geometric Figure
Practice Form A 6) : find the perimeter of
P = 2(L+W)
=2(9x2+9x+19+9x2-6x+11)
=2( 18x2+3x+30)
=36x2+6x +60
9x2+9x+19
9x2-6x+11
Practice Form B10) factor out the GCF.
48m9+84m6+48m2
= 12m2(4m7)+12m2(7m4)+12m2(4)
= 12m2(4m7+7m4+4)
GCF has the least exponent of all terms.
Practice test form B 12) Factor by grouping.
14 –7s –2t+st
= (14 –7s) –(2t – st) grouping
= 7(2 –s) – t(2 –s) factor separately
=(2 –s)(7 –t) factor out GCF
Practice form A 10)
7x2 – 7x – 42
=7 (x2 –x –6)
= 7 (x )(x )
= 7 (x –3 )(x+2)
Try practice form B 13)
8x2 –8x –48
Factor GCF out if there is any.
Factor ax2+bx+c: Factor out GCF
I. Difference of squares a2 −b2= (a+b)(a −b)
Practice form A 14)
25x2 −36
= (5x+6)(5x −6)
Try practice form B 14)
16x2 − 49
Practice form A 12)
x2 − 16xy + 64y2
=(x 8y)(x 8y)
=(x − 8y)(x −8y)
− 8x
− 8x
−16x
II. Factor a perfect square trinomial.a2 + 2ab+b2 = (a +b)(a +b)a2 − 2ab+b2 = (a −b)(a −b)
Practice form A 13) Solve(9y+20)(6y+19)=0
ab=0 a = 0 or b = 0
Practice form A 13) Solve(9y+20)(6y+19)=0
ab=0 a = 0 or b = 0
Practice Form A13) Solve equation by factoring.
(9y+20)(6y+19) = 0
9y+20= 0 or 6y+19 = 0
y = −20/9 or y = −19/6
The solution set is {−20/9, −19/6}.
Try form A) 14
x2 −x=6
x2 −x −6 = 0
(x −3)(x+2) = 0
x −3 = 0 or x+2 = 0
x = 3 or x = −2
The solution set is {3, −2}.
Two rational solutions.
Find numbers not in domain
Practice form A 17) Find all numbers not in the domain of the function.
Idea: denominator can not be equal to zero.
x2+4x−45 = 0
(x+9)(x −5) = 0
x+9 = 0 or x − 5 = 0
x = −9 or x = 5
The domain is {x|x ≠5 and x ≠ −9}.
454
49)(
2
2
xx
xxf
When to cancel?
Practice form A 18) express the rational expression in lowest
terms.
Practice form A 19)
x
x
3 x
x
3 )2)(3(
)2(
ax
ax
2
22
a
ax
2
22
2
x
ax
)7)(3(
)3)(9(
yy
yy
82615
432
xx
x
)25)(43(
43
xx
x
)25(
1
x
Only common factors can be cancelled.
Application of GeometryA16) The length of a rectangle frame is 3 cm more than the width. The
area is 180 square cm. Find the width.
Let x = the width
x + 3 =another dimension
Area = Length × Width
x(x + 3) = 180
x2 + 3x − 180 = 0
(x + 15)(x − 12) = 0
x + 15 = 0 or x − 12 = 0
x = −15 or x = 12
x = 12 reject the negative solution
x + 3 = 15
Check answers:18/13/15/12For factoring .
VIII. Divide rational expressions
Example 5 write in lowest terms.
Practice form A 20)
11
2
x
x
x
x
x
x
x
x )1(
)1(
2
x
23
9988
p
p
p
p
)99(
3)88( 2
p
p
p
p
)1(9
3)1(8 2
p
p
p
p
3
8p
Practice form A 21)
45
5
16 22
xxx
x
)4)(1(
5
)4)(4(
xxxx
x
)1)(4)(4(
)4(5)1(
xxx
xxx
)1)(4)(4(
2052
xxx
xxx
)1)(4)(4(
2042
xxx
xx
A22) Solve for r
P(1 + rt) = A multiply 1+rt both sides
P + Prt = A clear () by distribution
Prt = A − P subtract P both sides
r = A−P divide Pt both sides
Pt
1
AP
rt
Solve a formula
Application of ProportionA24) If 3.5 ounces of oil are to be added to 14
gallons of gasoline, then how many ounces of oil should be added to 29.2 gallons of gasoline?
Idea: mixture of oil and gasoline at the same ratioLet x= # of ounce of oil should be added
3.5(29.2) = 14x cross product 102.2 = 14x
7.3 = x divide 14 both sidesTry Form B 22
2.2914
5.3 x
Example Graph –3 ≤ x < 2.
End points from left to right : interval notation [–3,2).
Graph the inequality.
Inequalities
A25) Solve − 2x ≤ 18
x ≥ −9
[− 9,∞)
[
− 9
2
18
2
2
xreverse when div negative
Graph the solution first;Determine the direction; Always use ( -∞ or ∞) .
Practice form A 27) For the compound inequality, give the solution set in both interval and graph forms.
x≥2 and x≤5
Try Practice form B 24) For the compound inequality, give the solution set in both interval and graph forms.
x≥3 and x≤6
Practice form A 32) simplify the radical . Assume that all variables represent positive real numbers.
12 8x
Practice form A 34) multiply, then simplify the product.
)15)(15(
)1)(1()5)(1()5)(1()5)(5(
1555
15
4
F O I L
Try form B 32) )111)(111(
Practice form A 35) rationalize the denominator
2
7a
2
7a
)2)(2(
)2(7a
2
)2(7a
Practice form B 33) rationalize the denominator 5
6a
Practice form A 38) solve x2 = 9
x = or x =
x = 3 or x = −3
The solution set is {−3, 3}
Try to solve x2 −25=0
9 9
Two rational solutions.
