FTCE 5-9 Math TEST- Foundations of Algebra Day 1

​FTCE 5-9 Math Test- Foundations of Algebra Day 1

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This is an arithmetic sequence-->

Multiple Choice

Arithmetic Sequence

Identify the common difference for this Arithmetic Sequence. #1

97, 86, 75, 64, ...

• 8

• 11

• -11

• -8

Multiple Choice

Find the common difference and the next 3 terms in the sequence; -14,-5, 4, 13 #2

• d = 13; 26, 39, 52

• d = 4; 17, 21, 25

• d = -14; -1, -15, -30

• d = 9; 22, 31, 40

Multiple Choice

In a certain arithmetic sequence, a₅ = 12 and a₆ = 16. What is a₁ ? #3

• -8

• -4

• 4

• 8

Multiple Choice

Find the 25th term of the sequence if a₁ = 5 and d = 0.5. #4

• 18

• 17

• 15

• 14

Multiple Choice

Find the explicit formula given the arithmetic sequence: #6

1, 21, 41, 61

• a_n = 1 - 20(n - 1)

• a_n = 1 + 20n

• a_n = 1 + 20(n + 1)

• a_n = 1 + 20(n - 1)

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Multiple Choice

Geometric Sequence

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ... #9

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1

Multiple Choice

Find a₁₂ for the geometric sequence defined by the following formula: #11

a_n = 6(2)^n-1

• 4096

• 24,576

• 2048

• 12,288

Multiple Choice

Find the 6th term of the following geometric sequence:

2, 8, 32, 128, ...#12

• 8192

• 2048

• 512

• 128

Multiple Choice

A geometric sequence has a common ratio(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)? #16

• 3

• 6

• 18

• 2

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Multiple Choice

Which table of values can be defined by the rule/equation

y = x – 4? #17

Multiple Select

Select all ordered pairs that satisfy the function y = 2x + 3. #19

• (-1, 1)

• (2, 6)

• (0, 2)

• (3, 9)

Multiple Choice

Which set of ordered pairs is not a function? #22

• (1, 3), (2, 7), (3, 8), (4, 11)

• (2, 3), (4, 9), (3, 8), (4, 15)

• (1, 2), (3, 5), (6, 9), (7, 11)

• (-9, 4), (-6, 3), (-2, 8), (0, 21)

Multiple Choice

Does this represent a function? #25

• Function

• Not a Function

Multiple Choice

What is the definition of a function? #29

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

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Multiple Choice

What is

$$\sqrt{144x^{16}}$$  in simplest form? #31

• $$12x^4$$  

• $$12x^8$$  

• $$72x^4$$  

• $$72x^8$$  

Multiple Choice

Simplify the following expression: $$\frac{15x^{12}y^{16}}{5x^4y^4}$$  #32

• $$3x^3y^4$$  

• $$3x^8y^{12}$$  

• $$10x^8y^{12}$$  

• $$10x^3y^4$$  

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Multiple Choice

Simplify and state the excluded values(restrictions) for the following rational expression. #33

• $$\frac{m+6}{m-3};\ m\ne3,-6$$

• $$\frac{7}{m-3};\ m\ne3,-6$$
  

• 7(m+6) $$;m\ne-3,6$$

• (m-3) $$;\ m\ne-3,6$$

Multiple Choice

State the excluded (undefined) values for the given expression. #34

• 8, -10

• 8, 9

• -8, 10

• -8, -9

Multiple Choice

$$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$$  #35

• $$\frac{x-5}{x+2}$$  

• $$\frac{x-5}{x-2}$$  

• $$\frac{x+5}{x+2}$$  

• $$\frac{x+5}{x-2}$$  

Multiple Choice

$$\frac{4}{2+\sqrt{2}}$$  Fully simplify... #39

Multiple Choice

Expand and simplify. #40

$$\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)$$  

• $$7$$  

• $$-7$$  

• $$5$$  

• $$-5$$  

Multiple Choice

Simplify: #42

• 5√6

• 25√6

• √150

• 10√15

Multiple Choice

Simplify the radical expression: #43
$$\sqrt{2x^2y^3}$$  

• $$2y\sqrt{xy}$$  

• $$2x\sqrt{y^2}$$  

• $$y\sqrt{2xy}$$  

• $$xy\sqrt{2y}$$  

Multiple Choice

Simplify the radical expression: #44
$$\sqrt{128a^3b^4}$$  

• $$8ab^2\sqrt{2a}$$  

• $$2a\sqrt{8ab^2}$$  

• $$2ab\sqrt{64ab}$$  

• $$64ab^2\sqrt{2a}$$  

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Multiple Choice

Solve for x: #51

8x−5−4x=−x+10

• 2

• 4

• 6

• 3

Multiple Choice

Solve for x: #52
4(1-x)+3x=-2(x+1)

• x = -6

• x = 6

• x = 3

Multiple Select

Choose all that correctly apply. #53

• To solve a two step equation you first isolate the term by using addition or subtraction

• The second step to solving a two step is to isolate the variable by using multiplication or division

• To isolate a term in solving a two step equation you use multiplication or division

• to isolate a variable in solving a two step equation you use addition or subtraction

Multiple Choice

What is the solution to the linear equation? #57

d – 10 – 2d + 7 = 8 + d – 10 – 3d

• -5

• -1

• 1

• 5

Multiple Choice

What is the solution to the linear equation? #59

$$\frac{2}{5}+p=\frac{4}{5}+\frac{3}{5}p$$

• p = 1

• p = 2

• p = 8

• p = 10

Multiple Choice

A formula is expressed as D = a(2 + kt). Express k in terms of D, a, and t. #61

• $$k=\frac{D}{a}-2t$$

• $$k=D-2at$$

• $$k=\frac{D-2a}{at}$$

• $$k=\frac{D-2a}{t}$$

Multiple Choice

If ba - cd = b, which expression represents a? #62

• $$a=\frac{b-cd}{b}$$

• $$a=\frac{b+cd}{b}$$

• $$a=\frac{b}{b-cd}$$

• $$a=\frac{b}{b+cd}$$

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Multiple Choice

Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4? #63

• x < –3  

• x > –3

• x < 3

• x > 3

Multiple Choice

What value of x is in the solution set of 2x – 3 > 11 – 5x? #64

• –3  

• 0

• 2

• 4

Multiple Choice

What is the solution to –4(8 – 3x) ≥ 6x – 8? #66

• $$x\ge-\frac{4}{3}$$

• $$x\le-\frac{4}{3}$$

• x ≥ 4

• x ≤ 4