Abeka Algebra 2 Test 2

What type of linear equation is x+1 = x+1

identity

Rewrite 2x + 4x² = 9 in standard form.

4x² + 2x - 9 = 0

What would a rational equation be multiplied by to clear the equation of fractions?

least common denominator (LCD)

What is the imaginary form of √-16?

4i

What type of number contains both a real part and an imaginary part, for example, 7 - 3i?

complex

Which of the following correctly states the number of solutions for |3x+20|>-12?
a. no solutions
b. all real numbers
c. one solution
d. two solutions

all real numbers

Which of the following correctly states the types of real solutions for the discriminant 16?
a. unequal, rational
b. unequal, irrational
c. equal, rational
d. equal, irrational

unequal, rational

Which of the choices correctly translates the following problem?
"The area of a yard is 24 square feet. If the width is 3 feet less than the length, state the dimensions of the yard."
a. x(3x)=24
b. x(x-3)=24
c. 3x-24=x
d. x(x-24)=3

x(x-3)=24

What type of interval best describes -2≤x<8?
a. unbounded, open
b. unbounded, closed
c. bounded, open
d. bounded, mixed

bounded, mixed

What are the values for a, b, and c in the equation -2x=-3x²+11?
a. a=3; b=-2; c=-11
b. a=-3; b=-11; c=2
c. a=11; b=3; c=-2
d. a=11; b=-2; c=-3

a=3; b=-2; c=-11

When simplifying the expression 3i/2-i, by which of the following would you multiply both numerator and denominator?
a. i-2
b. -2i
c. 2+i
d. 2i

2+i

Solve linear equation or inequality for x (show your work).
3x-4=8

3x-4=8
3x=12
x=4

Solve linear equation or inequality for x (show your work).
ax=2x+5

ax=2x+5
x(a-2)=5
x= 5/a-2

Solve linear equation or inequality for x (show your work).
2|x+2|=4

2|x+2|=4
|x+2|=2

x+2=2
x=0

-(x+2)=2
x+2=-2
x=-4

x=-4, 0

Solve each quadratic equation (show your work).
x²-3x-10=0

x²-3x-10=0
(x-5)(x+2)=0
x-5=0
x=5

x+2=0
x=-2

x=-2, 5

Solve each quadratic equation (show your work).
x²-15=1

x²-15=1
x²=16
x=±4

Solve each quadratic equation (show your work).
x²+8x+4=0

x²+8x+4=0
x²+8+16 = -4+16
(x+4)² = 12
x+4 = ±2√3
x = -4±2√3

Solve each quadratic equation (show your work).
x²+3x+8=0 √ ±

x²+3x+8=0
a = 1, b=3, c=8
x=-b±√b²-4ac / 2a
x=-(3)±√(3)²-4(1)(8) / 2(1)
x=-3±√9-32 / 2
x=-3±√-23 / 2
x=-3±i√-23 / 2

Solve inequality and graph solution. Write solution as an interval (show your work).
-8x<8
<|−−|−-|--|-| --|-|-|-|-|-|-|-|>
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-8x<8
x>-1, (-1, ∞)

Interval...........Test Point...........Check..............Solution?
(-∞, -1)................... -2 ................-8(-2)<8 ................. no
.......................................................... 16<8

(-1, ∞)....................... 2 ...................-8(2)<8 ............... yes
................................................ -16<8
(-1, ∞)

Solve inequality and graph solution. Write solution as an interval (show your work).
4≤2x≤10
<|−−|−−|−−|−|−|−|−|-|-|-|-|>
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6.

2≤x≤5, [2, 5]

Interval...........Test Point...........Check..............Solution?
(-∞, 2)................... 0 ..................4≤2(0)≤10 ................. no
................................................4≤(0)≤10

[2, 5]....................... 3 ...................4≤2(3)≤10 ............... yes
...................................................4≤6≤10

[5, ∞]....................... 6 .................. 4≤2(6)≤10 ............... no
.................................................. 4≤12≤10

[2, 5]

Solve inequality and graph solution. Write solution as an interval(show your work).
|x+1|>3

<|−−|−−|−−|−|−|−|−|-|-|-|-|>
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

x+1>3 or x-1 <-3
x>2.............x<-4
(-∞, -4) or (2, ∞)

Interval...........Test Point...........Check..............Solution?
(-∞, 4)................... -5 .................. |(-5)+1|>3 ............... yes
......................................................... |-4|>3
.......................................................... 4>3

(-4, 2) .................... 0..................... |(0)+1|>3 ................. no
............................................................|1|>3
............................................................1>3

(2, ∞)........................ 3 ................... |(3)+1|>3 ..................yes
........................................................... |4|>3
........................................................... 4>3

(-∞, 4) or (2, ∞)

Simplify: (show your work)
i¹⁵

i¹⁵
15/4 = 3 remainder 3
= i³
= -i

Simplify: (show your work)
(2+7i)-(4-8i)

(2+7i)-(4-8i)
= 2+7i-4+8i
= 2-4_7i+8i
= -2+15i

Simplify: (show your work)
(6-2i)(1+i)

(6-2i)(1+i)
= 6+6i-2i²
= 6+4i+2
= 8+4i

Simplify: (show your work)
3/6+i

3/6+i
= 3/6+i * 6-i/6-i
= 18-3i/36-6i+6i-i²
= 18-3i/36+1

= 18-3i/37
or 18/37-3/37 i

Solve equation: (show your work)
½z+3z=⁵/₃z-11

½z+3z=⁵/₃z-11
3z+18z=10z-66
21z=10z-66
11z=-66
z=-6

Solve equation: (show your work)
3/x-2 = 8/x+6

3/x-2 = 8/x+6
8x-16 = 3x+18
5x = 34
x = 34/5
or 6 ⁴/₅

Solve equation: (show your work)
2/x = 3/x+1 + 2/x+1

2/x = 3/x+1 + 2/x+1
x(x+1) (²/x) = 3x+2x
2x+2 = 5x
-3x = -2
x = ²/₃

Solve equation: (show your work)
√3x +1 = 4

√3x +1 = 4
√3x = 3
3x = 9
x = 3

Solve equation: (show your work)
√5x+5 = √4x+1

√5x+5 = √4x+1
(√5x+5)² = (√4x+1)²
5x+5 = 4x+2√4x+1
x+4 = 2√4x
(x+4)² = (2√4x)²
x²+8x+16 = 16x
x²-8x+16 = 0
(x-4)(x-4) = 0
x = 4

Solve word problem: (show your work)
The denominator of a fraction is 4 more than its numerator. If the fraction equals ¹/₃, what is the fraction?

x/x+4 = 1/3
x+4 = 3x
-2x = -4
x = 2
Numerator = x=2
Denominator = x+4
=(2)+4
=6

Fraction = 2/6