FTCE Mathematics 6-12 Practice Version 2 Day 1

​FTCE Mathematics 6-12 Practice Test Version 2 Day 1

​Knowledge of Algebra

Multiple Choice

$$5x-2\left(1+2x\right)=10-\left(x-1\right)$$ #1

• $$x=\frac{11}{10}$$

• $$x=\frac{11}{2}$$

• $$x=\frac{13}{10}$$

• $$x=\frac{13}{2}$$

Multiple Choice

What are the solutions for the quadratic equation x² + 6x = 16? #2

• -2, -8

• -2, 8

• 2, -8

• 2, 8

Multiple Choice

Solve the inequality  5(2x - 3) - 6x < 9 for x. #3

• x < -1.5

• x < 1.5

• x < 3

• x < 6

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Multiple Choice

Which statement about the graph of y = 8(0.25)^x is true? #4

• The coordinates of the x-intercept are (0.25, 0).

• The coordinates of the y-intercept are (0, 8).

• The equation of the asymptote is x = 0.

• The graph includes the point (2, 1).

Multiple Choice

Which graph best represents f(x) = 2(5)^x? #5

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year? #6

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

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Multiple Choice

Find the vertex of  f(x) = -x² - 4x + 12 #13

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Multiple Choice

What is vertex of the quadratic function x²+4x-21? #15

• (4, -21)

• (-2,-25)

• (2, -21)

• (4, -25)

Multiple Choice

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec.  This can be modeled with the function h(t) = -16t² + 96t.  When does the maximum height occur? #17

• 6 seconds

• 3 seconds

• 145 seconds

• 160 seconds

Multiple Choice

Valley Video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the video store. How many movies did she rent? Write the linear equation and solve for the number of movies. #9

• 15x + 3x = 99    and 6 movies

• 15x + 3 = 99 and 6 movies

• 3x + 15 = 99 and 28 movies

• 3x + 99 = 15 and 28 movies

Multiple Choice

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? Let "c" represent the # of people who ordered chicken and "s" represent those who ordered steak. #10

• c + s = 6 14.80c + 17s = 91

• c + s = 91 14.80c + 17s = 6

• c + s = 6 14.80s + 17c = 91

• c + s = 91 14.80s+ 17c = 6

Multiple Choice

Factor: $$5x^3-15x^2+4x\ -12$$  #20

• $$5x\left(x-3\right)$$  

• $$\left(5x^2+4\right)\left(x-3\right)$$  

• $$5\left(x^3-3x^2\right)+4\left(x-3\right)$$  

• $$5x\left(x^2-3x\right)+2\left(2x-6\right)$$  

Multiple Choice

What is the factored form of x³+7x²-2x-14? #19

• (x²-2)(x-7)

• (x²+2)(x-7)

• (x²+2)(x+7)

• (x²-2)(x+7)

Multiple Choice

Solve for x: $$\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$$   #21

• $$2$$  

• $$\frac{18}{5}$$  

• $$\frac{26}{5}$$  

• $$6$$  

Multiple Choice

$$\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}$$  #23

• $$-2$$  

• $$5$$  

• $$6$$  

• $$\frac{61}{3}$$  

Multiple Choice

Solve 3x² - 5 = -446 #24

• ±√-147

• 7i√3

• ±7i√3

• -7√3

Multiple Choice

Simplify: $$\frac{\frac{x}{x-1}+\frac{3}{x+5}}{\frac{5}{x+5}-\frac{x}{x-1}}$$  #25

• $$\frac{x^2+2x+15}{-x^2-5}$$  

• $$\frac{x^2+8x-3}{x^2+10x-5}$$  

• $$\frac{x^2+2x+15}{x^2+10x-5}$$  

• $$\frac{x^2+8x-3}{-x^2-5}$$  

Multiple Choice

Rewrite in exponential form: #30

log₉x=2

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

Multiple Choice

Simplify: $$\log_4\left(x+4\right)-\log_4\left(x-5\right)$$  #31

• $$\log_49$$  

• $$\log_4\left(2x-1\right)$$  

• $$\log_4\left(x^2-x-20\right)$$  

• $$\log_4\left(\frac{x+4}{x-5}\right)$$  

Multiple Choice

Simplify: $$2\log_3\left(11x\right)$$  #32

• $$\log_3\left(22x\right)$$  

• $$\log_3\left(121x\right)$$  

• $$\log_3\left(121x^2\right)$$  

• $$\log_3\left(11x^2\right)$$  

Match

Match the following:

Rewrite the following in the form $$\log\left(c\right)$$ #33

• $$2\log\left(5\right)$$

• $$\log\left(5\right)+\log\left(4\right)$$

• $$\log\left(35\right)-\log\left(7\right)$$

• $$3\log\left(4\right)$$

• $$\log\left(4\right)-\log\left(16\right)$$

log(25)

log(20)

log(5)

log(64)

log(.25)

• log(25)

• log(20)

• log(5)

• log(64)

• log(.25)

Multiple Choice

Which property of logarithms is demonstrated below: 

$$\log_920\ =\ \frac{\log20}{\log9}$$  #36

• Product property

• Quotient property

• Power property

• Change of Base Property

Math Response

Solve.

$$\log_2\left(x+4\right)-\log_27=2$$ #37

Type answer here

Correct Answer: 24

Deg^°

Rad

Multiple Choice

log₂(x² - 6) = log₂(2x+2) #39

• 4, -2

• No Solution

• 4

• -2

Multiple Choice

The dimensions of a rectangular prism are represented by the polynomials $$2x+1$$ , $$x+3$$ , and $$4x-2$$ . Which polynomial represents the volume of the prism? #44

• $$8x^3+24x^2-2x-6$$  

• $$8x^3+30x^2+2x-6$$  

• $$8x^3-26x^2-2x-6$$  

• $$8x^3-26x^2+2x-6$$  

Multiple Choice

Mrs. Smith is using 8 in. by 12 in. sheets of construction paper to make jelly bean baskets for her second-grade students. She cuts congruent squares from each corner of the paper and folds up the sides to create the open basket. Express the volume of the basket, in terms of x. #45

• 4x² - 40x + 96

• 4x² + 40x + 96

• 4x³ + 40x² + 96x

• 4x³ - 40x² + 96x

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Multiple Choice

This work shows $$x^2-3x+5\div x-2$$  . What information does this reveal? #47

• x-2 is not a factor of $$x^2-3x+5$$   since the remainder is 3.

• x-2 is a factor of $$x^2-3x+5$$   since the remainder is 3.

Match

Match the following: #48

• is a factor of $$5x^2-10x-40$$  

• is a solution of $$5x^2-10x-40$$  

• 0

• x+2

x + 2...

-2...

The remainder is...

5x² -10x - 40 is being divided by...

• x + 2...

• -2...

• The remainder is...

• 5x² -10x - 40 is being divided by...

Multiple Choice

Which binomial is a factor of f(x)= x³ -6x² +3x +10? #49

• x + 1

• x + 2

• x + 5

• x + 10

Multiple Choice

Find the sum. (5-2i) + (-7+8i) #42

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Match

Match the following problems with their correct answer. #41

• $$x^2=-36$$  

• $$x^2=36$$  

• $$x^2=-100$$  

• $$x^2=100$$  

a.  

d.  

b.   

c.  

• a. $$x=\pm6i$$  

• d. $$x=\pm6$$  

• b. $$x=\pm10i$$   

• c. $$x=\pm10$$  

Multiple Choice

Multiply (3i)(-2+4i) #43

• -6+12i

• -12-6i

• -2+7i

• 12+6i

Multiple Choice

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

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

• -515

• -490

• -535

• 460

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) #52

• -216

• -148

• -146

• -150

Multiple Choice

What is the common ratio for the following sequence:

3, 15, 75, 375, ... #53

• 12

• 1/5

• 5

• 3

Multiple Choice

Write the explicit formula for the following geometric sequence:

10, 20, 40, 80, ... #54

• a_n = 10(2)^n-1

• a_n = 2(10)^n-1

• a_n = 10(2)ⁿ

• a_n = 2(10)ⁿ

Multiple Choice

Find the domain of the rational function

f(x) = x / (x²-25). #67

• ( $$-\infty$$  , -5) U (5, $$\infty$$  )

• ( $$-\infty$$  , -5) U (-5, 5) U (5, $$\infty$$  )

• ( $$-\infty$$  , 5) U (5, $$\infty$$  )

• ( $$-\infty$$  , 25) U (25, $$\infty$$  )

Multiple Choice

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)). #68

• f(g(x))= -6x²+31

• f(g(x))= -6x²+24

• f(g(x))=18x²-84x+6

• f(g(x))=9x²-42x-1

Multiple Choice

f(x) = 3x + 10 g(x) = x - 2 Find (f∘g)(0) #69

• 16

• 4

• -4

• None of these.

Multiple Choice

Find the domain of

$$f\left(x\right)\ =\ \frac{x-1}{x^2+1}$$ . #70

• $$\left(-\infty,\ \infty\right)$$  

• $$\left(-\infty,-1\right)\cup\left(-1,\infty\right)$$  

• $$\left(-\infty,1\right)\cup\left(1,\infty\right)$$  

• $$\left(-\infty,-1\right)\cup\left(-1,1\right)\cup\left(1,\infty\right)$$