FTCE Math 6-12

​FTCE Mathematics 6-12 Test Version 1 (Day 1)

​FTCE Mathematics 6-12 Test Version 1 (Day 1)

​Knowledge of Algebra

Multiple Choice

A number twice the value of the second number equals to the sum of both numbers quantity squared.  Set up the equation, but do not solve or simplify.  Choose the best answer. #3

• $$2x=\left(x+y\right)^2$$

• $$2xy=\left(x+y\right)^2$$

• $$2x-2y=\left(x+y\right)^2$$

• $$2+x=\left(x+y\right)^2$$

• $$2x-2y=\left(x^2+y^2\right)$$

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Multiple Choice

Solve the system: #8

2x + 3y = -2

3x - 2y = 23

• (5, -4)

• (-5, 4)

• (-4, 5)

• infinite solutions

Explanation Slide...

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Multiple Choice

Setting Up Equations: Simplify the following rational expression. State any restrictions on the variable. #4

$$\frac{x^2+7x+10}{x+2}$$

• $$x+5,\ x\ne2$$

• $$x+5;\ no\ restrictions,\ x\in R$$

• $$-x-5,\ x\ne-2$$

• $$-x-5,\ x\ne2$$

• $$x+5,\ x\ne-2$$

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Multiple Choice

Solve using the Quadratic Formula: #5 $$2x^2+7x-15=0$$  

• $$x=-1.5,\ 5$$  

• No Solution

• $$x=-5,\ 1.5$$  

• $$x=0.7,\ 5$$  

Explanation Slide...

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Multiple Choice

°C = (°F-32) x (5/9)

°F = (9/5) x °C + 32

Celsius = Kelvin - 273

Kelvin = Celsius + 273

Convert the temperature:

25 C = _______ F #7

• 77 °F

• 32 °F

• 28 °F

​Advanced Algebra

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Multiple Choice

Solve for n: #2

$$\sqrt[3]{2n-8}=-4$$

• $$n=-28$$

• $$n=32$$

• $$n=-36$$

• $$n=-28\ or\ n=-36$$

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Multiple Choice

Can the operation be performed? #45

• Yes

• No

• tomato

Multiple Choice

What is the determinant for the following matrix?

#29

• 14

• 34

• -34

• -32

Multiple Choice

Find the 16th term in the geometric sequence 1024, –512, 256, … #47

• $$-\frac{1}{64}$$

• $$-\frac{1}{32}$$

• $$\frac{1}{64}$$

• $$\frac{1}{32}$$

Multiple Choice

Write the explicit formula for the following geometric sequence:

100, 50, 25, 12.5, ...#48

• a_n = 2(100)^n-1

• a_n = 100(2)^n-1

• a_n = 100(1/2)^n-1

• a_n = (1/2)(100)^n-1

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Multiple Choice

5, 11, 17, 23, 29,...

Find the 16th term. #50

• 101

• 67

• 95

• 85

Multiple Choice

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

(Hint: Write the explicit rule first, then use it to solve) #51

• -216

• -148

• -146

• -150

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Multiple Choice

Which of the following displays the full real-number solution set for a in the equation above? #1

76a³+19a²+16a=-4

• {-2, 2}

• { $$-\frac{1}{2}$$ }

• $$\left\{\frac{19}{4}\right\}$$

• $$\left\{-\frac{1}{4}\right\}$$

• $$\left\{-\frac{4}{19},\frac{4}{19}\right\}$$

Multiple Choice

Find all the real zeros of the function  f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor. #10

• x = 1/2, -6

• x = -1/2, 6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

Simplifying Complex Rational Expressions at a Glance

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Multiple Choice

$$\frac{\frac{2x}{x+1}}{\frac{3}{x+1}}$$  #94

• $$\frac{2x\left(x+1\right)}{3}$$  

• $$\frac{2x}{3}$$  

• $$\frac{3}{2x}$$  

• $$\frac{2x\left(x+1\right)}{x+1}$$  

Multiple Choice

$$\frac{x+\frac{3}{x^2}}{1-\frac{2}{x}}$$  #95

• $$\frac{x^3+3}{x^2-2x}$$  

• $$\frac{x\left(x+3\right)}{x-2}$$  

• $$\frac{x+3}{x-2}$$  

• $$\frac{x\left(x^3+3\right)}{x-2}$$  

Multiple Choice

$$\frac{\frac{x^2-x-2}{x+6}}{\frac{x^2-1}{x+6}}$$  #97

• $$-x-3$$  

• $$\frac{x^2-x-2}{x^2+1}$$  

• $$\frac{x-2}{\left(x-1\right)\left(x+1\right)}$$  

• $$\frac{x-2}{x-1}$$  

Multiple Choice

$$\frac{\frac{x}{25}+\frac{x}{5}}{\frac{5}{x}}$$  

#98

• $$\frac{25x^2}{400+4x}$$  

• $$\frac{6x^2}{125}$$  

• $$\frac{400x}{x^3-16}$$  

• $$\frac{x^2+x^3}{625}$$