Free Printable Basic and Advanced Algebra

1.

Which of these statements is/are TRUE?

I. Every integer is the coordinate of some point on the number line.

II. Every rational number is a real number.

III. Every point on the number line can be named by a rational number.

a)

Only I

b)

Only II

c)

Only I & II

d)

I, II & III

e)

None of the choices

2.

Express the inequality in interval notation:

$-5\le x$

a)

( $\infty,\ -5$ )

b)

( $-\infty,\ -5$ )

c)

[ $-5,\ \infty$ )

d)

( $\infty,\ -5$ ]

e)

None of the choices

3.

If a + b is negative, then what is the value of the

absolute value of a + b or l a + b l?

a)

0

b)

$a+b$

c)

$-a+b$

d)

$-\left(a+b\right)$

e)

None of the choices

4.

Which of the following is FALSE?

a)

$\left|8-2\right|=8-2$

b)

$\left|2-7\right|=2-7$

c)

d)

$\left|3-5\right|=-\left(3-5\right)$

e)

None of the choices

5.

The inequality $\left|x\right|\ge k$ , where $k\ge0$ is true if and only if _____.

a)

$x\le-k$ or $x\ge k$

b)

$x\le k$ or $x\ge-k$

c)

$-k\le x\le k$

d)

$x\ge k$

e)

None of the choices

6.

Which of the statements is/are TRUE for all real numbers a, b and c?

I. If a < b, then a + c < b + c.

II. If a < b, then ac < bc for c > 0.

III. If a < b, then ac > bc for c < 0.

a)

Only I

b)

Only II

c)

Only I & II

d)

I, II & III

e)

None of the choices

7.

In interval notation, what is the solution of the inequality: $-3\left(x\ +\ 1\right)\ <\ 2x\ +\ 2$ ?

a)

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

b)

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

c)

$\left(1,\ \infty\right)$

d)

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

e)

None of the choices

8.

The length of a rectangle is 2 inches less than 3 times the width.

If the length is increased by 5 in and the width decreased by 1 in,

the length will be 5 times the width.

Using x to denote the original width,

which of the following equations can be used to solve for x?

a)

$x-1=5\left(3x+3\right)$

b)

$3x-2=5x-1$

c)

$3x+3=5\left(x-1\right)$

d)

$3x+3=5x-1$

e)

None of the choices

9.

Which of the ff. is equivalent to $\left(a+b\right)^{-1}$ ?

a)

$a^{-1}\ +\ b^{-1}$

b)

$\frac{1}{a+b}$

c)

$\left(-a\right)\ +\ \left(-b\right)$

d)

$\frac{1}{a}\ +\ \frac{1}{b}$

e)

None of the choices

10.

Which of the following is/are TRUE?

I. $\left(a\right)^{-\frac{1}{2}}\ +\left(b\right)^{-\frac{1}{2}}\ =\ \frac{1}{\sqrt[]{a}}\ +\ \frac{1}{\sqrt[]{b}}$

II. $\left(-x\right)^{-\frac{1}{3}}\ =\ \left(x\right)^{\frac{1}{3}}$

III. $\left(x\right)^{\frac{3}{4}}\ =\ \left(\sqrt[3]{x}\right)^4$

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

11.

Rationalize the denominator:

$\frac{8}{\sqrt[]{5}\ -\ 1}$

a)

$8\left(\sqrt[]{5}\ +\ 1\right)$

b)

$2\left(\sqrt[]{5}\ -\ 1\right)$

c)

$2\left(\sqrt[]{5}\ +\ 1\right)$

d)

$2\ \sqrt[]{5}\ +\ 1$

e)

None of the choices

12.

Which of the following is/are TRUE?

I. $2\left(\sqrt[]{x\ +\ 1}\right)\ =\ \sqrt[]{2x\ +\ 1}$

II. $\sqrt[]{\left(x\ -\ 1\right)^2}\ =\ \left|\ x\ -\ 1\ \right|$

III. $\left(x\ +\ y\right)^{\frac{1}{3}}\ =\ \left(x\right)^{\frac{1}{3}}\ +\ \left(y\right)^{\frac{1}{3}}$

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

13.

What is the complete factored form for this expression?

$x^2\left(x\ -\ 1\right)\ -\ 2x\left(x\ -\ 1\right)\ +\ \left(x\ -\ 1\right)$

a)

$x\left(x\ -\ 2\right)\left(x\ -\ 1\right)$

b)

$\left(x\ -\ 1\right)\left(x^2\ -\ 2x\ +\ 1\right)$

c)

$\left(x\ -\ 2x\right)\left(3x\ -\ 3\right)$

d)

$\left(x\ -\ 1\right)^3$

e)

None of the choices

14.

Which of the following is/are TRUE?

I. $x^3\ -\ y^3\ =\ \left(x\ -\ 1\right)\left(x^2\ +\ y^2\right)$

II. $x^2\ +\ y^2\ =\ \left(x\ +\ y\right)\ \left(x\ +\ y\right)$

III. $4x^2\ -\ 6xy\ +\ 9y^2\ =\ \left(2x\ -\ 3y\right)^2$

a)

Only I

b)

Only II

c)

Only III

d)

Only II & III

e)

None of the choices

15.

Which of the following can be used to show that

the real number x is within 5 units of 2 on a number line?

a)

$\left|\ x\ -\ 2\ \right|\ <\ 5$

b)

$\left|\ x\ +\ 2\ \right|\ <\ 5$

c)

$\left|\ x\ -\ 5\ \right|\ <\ 2$

d)

$\left|\ x\ +\ 5\ \right|\ <\ 2$

e)

None of the choices

16.

How is 325 000 000 written in In scientific notation?

a)

$3.25\ \times\ 10^{-8}$

b)

$3.25\ \times\ 10^8$

c)

$325\ \times\ 10^6$

d)

$0.325\ \times\ 10^9$

e)

None of the choices

17.

Which of the following is/are TRUE?

I. Every integer can be written in the form a + bi, where $i\ =\sqrt[]{-1}$ .

II. Every real number is a complex number.

III. The sum, difference, and product of two complex numbers are complex numbers.

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

18.

Which of the following represents the graph shown?

a)

$\left|\ x\ +\ 4\ \right|\ \le\ 2\$

b)

$\left|\ x\ -\ 4\ \right|\ \le\ 2\$

c)

$\left|\ x\ -\ 2\ \right|\ \le\ 4\$

d)

$\left|\ x\ +\ 2\ \right|\ \le\ 4\$

e)

None of the choices

19.

Which of the following is FALSE?

a)

$\left(x\ +\ y\right)^{\frac{1}{3}}\ =\ \sqrt[3]{x\ +\ y}$

b)

$\left(x\right)^{-1}\ +\ \left(y\right)^{-1}\ =\ \frac{x\ +\ y}{xy}$

c)

$\sqrt[3]{x^9}\ =\ x^{\frac{1}{3}}$

d)

$\sqrt[]{\left(x\ -\ 1\right)^2}\ =\ \left|\ x\ -\ 1\ \right|$

e)

None of the choices

20.

Which of the following is/are TRUE?

I. $\frac{1}{i}\ =\ -i$

II. $\left(3\ -\ 2i\right)^0\ =\ 1$

III. $\frac{1\ +\ i}{1\ -\ i}\ =\ i$

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

21.

What is the equation of the line parallel to the line $2x-3y=5$

that passes through the point $(-8,\ \ 4)$ ?

a)

$y\ -\ 4\ =\ -\frac{2}{3}(x\ +\ 8)$

b)

$y\ -\ 4\ =\ \frac{2}{3}(x\ +\ 8)$

c)

$y\ -\ 4\ =\ \frac{3}{2}(x\ +\ 8)$

d)

$y\ -\ 4\ =\ -\frac{3}{2}(x\ +\ 8)$

e)

None of the choices

22.

Let $f(x)\ =\ x\ -\ 2$ .

What is $f(x-2)$ ?

a)

$x-2$

b)

$2x-2$

c)

$2x-4$

d)

$x-4$

e)

None of the choices

23.

Let $g(x)=(x-2)^2$ .

What is $\frac{g(x)-g(7)}{x-7}$ ?

a)

$x-7$

b)

$x+7$

c)

$x-3$

d)

$x+3$

e)

None of the choices

24.

What is the equation of the line that passes through the point (2, –3)

and is parallel to the y-axis?

a)

$x=2$

b)

$x=-7$

c)

$y=3$

d)

$y=-3$

e)

None of the choices

25.

Which of the following statements is/are CORRECT?

I. The slope of a horizontal line is undefined.

II. The slope of a vertical line is 0.

III. The slopes of two perpendicular lines (not parallel to the coordinate axes) are negative reciprocals of one another.

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

26.

What is the equation of a line perpendicular to $2x-3y=6$ ?

a)

$2x+3y=6$

b)

$3x+2y=6$

c)

$3x-2y=6$

d)

$3y-2x=6$

e)

None of the choices

27.

What is the slope-intercept form of the line through

$(2,-3)$ and $(-1,\ \ 6)$ ?

a)

$y=3x+3$

b)

$y=-3x+3$

c)

None of the choices

d)

$y=-\frac{1}{3}x+\frac{11}{3}$

e)

$y=-3x-3$

28.

The vertices of a right triangle are at (0, 0), (x, 0), and (x, y), with (x, y) in the first quadrant.

If (5, 2) is on the hypotenuse of the triangle, then the area of the triangle as a function of x is given by:

a)

$A(x)=\frac{5}{2}x^2$

b)

$A(x)=\frac{5}{4}x^2$

c)

$A(x)=\frac{2}{5}x^2$

d)

$A(x)=\frac{1}{5}x^2$

e)

None of the choices

29.

What is the equation of a line with intercepts at $(0,\ -4)$ and $(2,\ \ 0)$ ?

a)

$2x+4y=8$

b)

$4x+2y=8$

c)

$4x+2y=-8$

d)

$2x-4y=8$

e)

None of the choices

30.

a)

$-6$

b)

5

c)

4

d)

$-5$

e)

None of the choices

31.

Consider the function defined as

$y=f(x)=\frac{\left|x-1\right|}{x-1}$

What are the domain and range of this function?

a)

domain: all x;

range: all y

b)

domain: all $x\ne1$ ;

range: all y

c)

domain: all $x\ne1$ ;

range: y = 1 or y = –1

d)

domain: all x;

range: y = 1 or y = –1

e)

None of the choices

32.

Given: the greatest integer function $y=\left[\left|x\right|\right]$ .

For $-2<x<-1$ , y = _____.

a)

$-2$

b)

2

c)

$-1$

d)

1

e)

None of the choices

33.

What are the coordinates of the vertex and the equation of the axis of symmetry

for the graph of $y=(x-2)^2-5$ ?

a)

vertex: (2, 5);

axis: x = –2

b)

vertex: (–2, –5);

axis: x = 2

c)

vertex: (2, –5);

axis: x = 2

d)

vertex: (–2, 5);

axis: x = -2

e)

None of the choices

34.

What is the range of the function given by

$y=-2(x+1)^2-3$ ?

a)

all real numbers

b)

all y ≥ 2

c)

all y $\le$ –3

d)

all y ≥ –3

e)

None of the choices

35.

The graph of $f\left(x\right)=3(x+1)^2-2$

is congruent to that of $g\left(x\right)=3x^2$ but $f\left(x\right)$ is

a)

shifted 1 unit to the right and 2 units down

b)

shifted 1 unit to the right and 2 units up

c)

shifted 1 unit to the left and 2 units down

d)

shifted 1 unit to the left and 2 units up

e)

None of the choices

36.

The function $f(x)=x^2-8x+10$ has _____.

a)

the minimum value –6 when x = 4

b)

the minimum value 26 when x = 4

c)

the minimum value 6 when x = –4

d)

the minimum value 10 when x = 8

e)

None of the choices

37.

When a border of uniform width is put around a 6-foot by 10-foot rectangle, the area is enlarged by 80 sq. ft.

Which equation can be used to find the uniform width x?

a)

x(10 + 2x) + x(6 + 2x) = 80

b)

x² + 16x – 20 = 0

c)

x² + 16x – 80 = 0

d)

x² + 8x – 20 = 0

e)

None of the choices

38.

Which is true for the parabola $y=-4x^2+20x-25$ ?

a)

It opens downward and has two x-intercepts.

b)

It opens downward and has one x-intercept.

c)

It opens downward and has no x-intercepts.

d)

It opens to the left and has two y-intercepts.

e)

None of the choices

39.

What are the solutions of $3x^2+6x+2=0$ ?

a)

$\frac{-3\pm\sqrt{3}}{3}$

b)

$\frac{-18\pm\sqrt{3}}{3}$

c)

$-1\pm\sqrt{2}$

d)

$-6\pm2\sqrt{3}i$

e)

None of the choices

40.

Which statement is true for this system of equations?

$2x-y=4$

$x+3y=7$

a)

The graph consists of two parallel lines.

b)

The graph consists of a single line.

c)

The graph consists of two lines that intersect in the first quadrant.

d)

The graph consists of two lines that intersect in the fourth quadrant.

e)

None of the choices

41.

Which of the following statements is/are TRUE?

I. The graph of f(x) = x² is symmetric about the y-axis.

II. The graph of f(x) = x³ is symmetric about the origin.

III. The graph of f(x) = $\frac{1}{x}$ is symmetric about the x-axis.

a)

Only I

b)

Only II

c)

Only III

d)

Only I & II

e)

None of the choices

42.

What is the equation of the horizontal asymptote for $f(x)=\frac{1}{x-3}$ ?

a)

x = 0

b)

y = 0

c)

x = 3

d)

x = –3

e)

None of the choices

43.

For h > 0, the graph of y = f(x – h) can be obtained

by shifting the graph of y = f(x) _____.

a)

h units to the right

b)

h units to the left

c)

h units upward

d)

h units downward

e)

None of the choices

44.

Which of the following is/are TRUE for the graph of $y=-\frac{1}{x^2}$ ?

I. The horizontal asymptote is x = 0.

II. The vertical asymptote is y = 0.

III. The graph is symmetric about the y-axis.

a)

Only I

b)

Only II

c)

Only III

d)

I, II & III

e)

None of the choices

45.

The table can be used to determine the position of the curve

f(x) = (x + 3)(x + 1)(x – 2) relative to the x-axis.

Reading left to right, these positions for the given intervals, are _____.

a)

above, below, above, below

b)

below, above, below, above

c)

below, below, above, above

d)

above, below, below, above

e)

None of the choices

46.

What is the equation of the vertical asymptote for $f(x)=\frac{3x^2}{x^3+x}$ ?

a)

x = 0

b)

x = –1

c)

x = 3

d)

y = 3

e)

None of the choices

47.

Working alone, Ann can complete a job in 5 hours.

Bea can complete the same job in 4 hours.

Which of these equations can be used to find out how long it will take to complete the job together?

(Use x for the time it takes them to complete the job working together.)

a)

$\frac{1}{4}+\frac{1}{x}=\frac{1}{5}$

b)

$\frac{1}{4}-\frac{1}{5}=\frac{1}{x}$

c)

$\frac{x}{4}-\frac{x}{5}=1$

d)

$\frac{1}{4}+\frac{1}{5}=\frac{1}{x}$

e)

None of the choices

48.

Solve for b if $c=\frac{a+2b}{ab}$

a)

$b=\frac{a}{ac-2}$

b)

$b=\frac{1}{c}-\frac{a}{2}$

c)

$b=a\left(c-a\right)$

d)

$b=c-1$

e)

None of the choices

49.

How many solutions does this equation have?

$\frac{9x+14}{2x^2-x-6}-\frac{1}{x-2}=\frac{2}{2x+3}$

a)

no solution

b)

only one solution

c)

exactly two solutions

d)

more than two solutions

e)

None of the choices

50.

Neglecting air resistance, the distance an object falls from rest is directly proportional to the square of the time it has fallen.

If an object falls 64 ft in the first 2 seconds, how far will it fall in the first 6 seconds?

a)

576 ft

b)

512 ft

c)

384 ft

d)

192 ft

e)

None of the choices

51.

z varies directly as x and inversely as y².

If z = 60 when x = 3 and y = $\frac{1}{2}$ ,

then what is the value of z when x = 6 and y = 4?

a)

1920

b)

30

c)

$\frac{45}{2}$

d)

$\frac{15}{8}$

e)

None of the choices

52.

When the synthetic division at the left is completed, what is the remainder?

a)

0

b)

7

c)

21

d)

-7

e)

None of the choices

53.

Which of the following is a set of possible rational roots of

f(x) = 2x³ – 8x² + 7x – 10?

a)

±1, ±2, ±5, ±10

b)

±1, ±1/2, ±2, ±5/2, ±5, ±10

c)

±2, ±10

d)

±1, ±2, ±10

e)

None of the choices

54.

Consider the decomposition of $\frac{6x^2+x-37}{(x-3)(x+2)(x-1)}$ into partial fractions $\frac{A}{(x-3)}+\frac{B}{(x+2)}+\frac{C}{(x-1)}$ . What is the value of A?

a)

0

b)

1

c)

2

d)

3

e)

None of the choices

55.

The equation $x^4-6x^3+14x^2-16x+8=0$ has 2 as a double root.

What are the remaining roots?

a)

$1\pm i$

b)

$1\pm\sqrt{3}$

c)

$5\pm5i$

d)

$\pm5$

e)

None of the choices

56.

For a given function, $f(x)\ \longrightarrow\ ∞$ as x approaches c from the left.

From this we can conclude that _____.

a)

x = c is a vertical asymptote

b)

y = c is a horizontal asymptote

c)

x = –c is a vertical asymptote

d)

y = –c is a horizontal asymptote

e)

None of the choices

57.

For a given function, $f(x)\ \longrightarrow\ k$ as $x\ \longrightarrow\ \infty$ .

From this we can conclude that _____.

a)

x = k is a vertical asymptote

b)

y = k is a horizontal asymptote

c)

x = –k is a vertical asymptote

d)

y = –k is a horizontal asymptote

e)

None of the choices

58.

What is the oblique asymptote for $f(x)=\frac{x^2+3x-1}{x-2}$ ?

a)

x = 2

b)

y = x – 2

c)

y = x² + 3x – 1

d)

y = x + 5

e)

None of the choices

59.

According to Descartes’ Rule of Signs, find the number of possible positive zeros of

$p(x)=x^4-3x^3-x^2+2x+1$

a)

2

b)

2 or 0

c)

4, 2 or 0

d)

4

e)

None of the choices

60.

The graph of $f(x)=x^3+2x+1$ has how many x-intercepts?

a)

0

b)

1

c)

2

d)

3

e)

None of the choices

61.

The circle $x^2\ +\ y^2\ +\ 3y\ =\ -\frac{1}{4}$ has _____.

a)

center at $\left(0,\ \frac{3}{2}\right)$ and

radius $r=\frac{1}{2}$

b)

center at $\left(0,\ -3\right)$ and

radius $r=2$

c)

center at $\left(3,\ 0\right)$ and

radius $r=\frac{1}{2}$

d)

center at $\left(0,\ -\frac{3}{2}\right)$ and

radius $r=\sqrt[]{2}$

e)

None of the choices

62.

What is the equation of the circle with center at (2, —3) and radius r = 4?

a)

$\left(x+2\right)^2+\left(y-3\right)^2=16$

b)

$\left(x-2\right)^2+\left(y+3\right)^2=4$

c)

$\left(x-2\right)^2+\left(y+3\right)^2=16$

d)

$\left(x+2\right)^2+\left(y-3\right)^2=4$

e)

None of the choices

63.

How many solutions does this equation have?

$\sqrt[]{x^2-9x}+\sqrt[]{3x}=x$

a)

None

b)

One

c)

Two

d)

Three

e)

None of the choices

64.

The graph of $y=\frac{1}{\sqrt[]{x-1}}$ is found

by shifting the graph of $y=\frac{1}{\sqrt[]{x}}$ _____.

a)

One unit downward

b)

One unit upward

c)

One unit to the left

d)

One unit to the right

e)

None of the choices

65.

For which of the following functions is both the domain and the range the set of all real numbers greater than or equal to 0?

a)

$y=\sqrt[]{x}$

b)

$y=x^3$

c)

$y=\left|x\right|$

d)

$y=\sqrt[3]{x}$

e)

None of the choices

66.

What are the x-intercepts for the graph of $y=\sqrt[]{2x^2-8x-24}$ ?

a)

2, $-6$

b)

$-4$ , 3

c)

$-6$ , 4

d)

0

e)

None of the choices

67.

Which of the following are the solutions for this equation?

$\sqrt[3]{x^2}-\sqrt[3]{x}-6=0$

a)

2, $-3$

b)

$-2,\ 3$

c)

$-8,\ 27$

d)

$8,\ -27$

e)

None of the choices

68.

he radius of a right circular cylinder of height h and volume V is given by $r=\sqrt[]{\frac{V}{\pi\ h}}$

Using this formula to solve for h in terms of r and V, what is the value of h?

a)

$\frac{\pi\ r^2}{V}$

b)

$\frac{V}{\pi\ r^2}$

c)

$\frac{\left(\pi\ r\right)^2}{V}$

d)

$\frac{V}{\pi\ r^{ }}$

e)

None of the choices

69.

Which of the following are the signs of $f\left(x\right)=\frac{x-2}{\sqrt[]{x^2+4}}$ ?

a)

For $x\ne\pm2,\ f\left(x\right)>0$

b)

For $x\ne\pm2,\ f\left(x\right)>0$

c)

For $x<2,\ f\left(x\right)<0;$

for $x>2,\ f\left(x\right)\ >0$

d)

For $x<-2,\ f\left(x\right)<0;$

for $x>-2,\ f\left(x\right)>0$

e)

None of the choices

70.

Which of the following intervals represents the domain of this function?

$f\left(x\right)=\frac{x^2}{\sqrt[]{1-x^2}}$

a)

$\left(1,\ \infty\right)$

b)

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

c)

$\left(-\infty,\ -1\right)$ and $\left(1,\ \ \infty\right)$

d)

$\left(-1,\ 1\right)$

e)

None of the choices

71.

Which of the following is/are CORRECT?

I. $x\ \sqrt[]{x^2+1}=\sqrt[]{x^3+x}$

II. $\left(x\right)^{-\frac{1}{5}}\ +\ \left(x\right)^{\frac{3}{5}}\ =\ \left(x\right)^{-\frac{1}{5}}\left(1\ +\ x^{\frac{2}{5}}\right)$

III. $\left(x^2-3\right)^{\frac{1}{3}}\ \left(x^2-3\right)^{\frac{2}{3}}\ =\ \left(x^2-3\right)^{\frac{2}{9}}$

a)

Only I

b)

Only II

c)

Only III

d)

Only I & II

e)

None of the choices

72.

Let $f\left(x\right)\ =\ \frac{1}{x^2\ -\ 1}$ and $g\left(x\right)\ =\ \sqrt[]{x}$ .

What is $\frac{f}{g}\left(4\right)$ ?

a)

$\frac{12}{15}$

b)

$\frac{15}{12}$

c)

$\frac{1}{30}$

d)

30

e)

None of the choices

73.

Simplify: $x^{\frac{1}{3}}\ +\ \left(x-8\right)\left(\frac{1}{3}\right)\left(x^{-\frac{2}{3}}\right)$

a)

$\frac{x^{\frac{1}{3}}+x-8}{3x^{\frac{2}{3}}}$

b)

$\frac{3x^{\frac{1}{3}}+x-8}{x^{\frac{2}{3}}}$

c)

$\frac{x-8}{3\ \sqrt[3]{x}}$

d)

$\frac{4x-8}{3\ \sqrt[3]{x^2}}$

e)

None of the choices

74.

Let $f\left(x\right)=\sqrt[]{x^3\ +\ 1}$ and $g\left(x\right)=2x-3$

What is $f\left(g\left(2\right)\right)$ ?

a)

$\sqrt[]{2}$

b)

1

c)

3

d)

25

e)

None of the choices

75.

Let $f\left(x\right)=\sqrt[3]{x}$ and $g\left(x\right)=\frac{1}{x^3-1}$

What is $g\left(f\left(x\right)\right)$ ?

a)

$\frac{1}{\sqrt[3]{x^3-1}}$

b)

$\frac{1}{\sqrt[3]{x-1}}$

c)

$\sqrt[3]{x^3-1}$

d)

$\frac{1}{x-1}$

e)

None of the choices

76.

Which of the following is a one-to-one function of x?

a)

$y=x^4$

b)

$y=\frac{1}{x}$

c)

$y=\left|x\right|$

d)

$x=y^2$

e)

None of the choices

77.

Which of the following is the inverse of $y=f(x)=3x+2$ ?

a)

$y=2x+3$

b)

$y=\frac{1}{3}x-\frac{2}{3}$

c)

$y=2+3x$

d)

$y=\frac{1}{3}x\ +\ 2$

e)

None of the choices

78.

If $f\left(x\right)=\frac{2x}{x-3}$ , then what is $f^{-1}\left(x\right)$ ?

a)

$\frac{x-3}{2x}$

b)

$\frac{x-2}{3x}$

c)

$\frac{3x}{x-2}$

d)

$\frac{xy-3x}{2}$

e)

None of the choices

79.

If $k=j+m$ and $k+j+m=12$ ,

then which of the following is CORRECT?

a)

k = 3

b)

k = 6

c)

k = 12 + j + m

d)

k = 12 – j + m

e)

None of the choices

80.

What is the complete factorization of $32−8x^2$ ?

a)

$−8(x+2)(x−2)$

b)

$8(x+2)(x−2)$

c)

$−8(x+2)^2$

d)

$8(x−2)^2$

e)

None of the choices

81.

Which of the following is/are TRUE for the function $y=f\left(x\right)=b^x\ ;\ b>0\ and\ b\ne1$ ?

I. The domain consists of all real numbers x.

II. The range consists of all positive numbers y.

III. It is a one-to-one function.

a)

Only I

b)

Only II

c)

Only III

d)

I, I, & III

e)

None of the choices

82.

Solve for x:

$b^{\ x^2-2x}\ =\ 1$

a)

x = 0, x = 2

b)

x = 1, x = 3

c)

x = 1

d)

x = 0

e)

None of the choices

83.

For which of the following is the point $(-1,\ \ \frac{1}{4})$ on the graph of the function?

a)

$y=f\left(x\right)=-\log_2\left(x-1\right)$

b)

$y=f\left(x\right)=\log_2\left(x-1\right)$

c)

$y=f\left(x\right)=2^{x-1}$

d)

$y=f\left(x\right)=-2^{x-1}$

e)

None of the choices

84.

What is the domain of the function $y=f(x)=\log_2(x+3)$ ?

a)

$x<3$

b)

$x\ge3$

c)

$x<-3$

d)

$x\ge-3$

e)

None of the choices

85.

Solve for x:

$\log_3x+\log_3(2x+51)=4$

a)

$\frac{3}{2}$

b)

$-27$

c)

$\frac{47}{3}$

d)

10

e)

None of the choices

86.

Solve for b:

$\log_b\ \frac{1}{64}\ =\ -\frac{3}{2}$

a)

$\frac{1}{16}$

b)

8

c)

16

d)

512

e)

None of the choices

87.

Which of the following is/are TRUE?

I. $\left(\log_b\ x\right)^2\ =\ 2\log_b\ x$

II. $\log_b\ A\ +\ \log_b\ B\ =\ \log_b\ \left(A\ +\ B\right)$

III. $\log_b\ A\ -\ \log_b\ B\ =\ \frac{\log_b\ A}{\log_b\ B}$

a)

Only I

b)

Only II

c)

Only III

d)

I, Il, & Il

e)

None of the choices

88.

Which of the following is/are TRUE for the function $y=f(x)=e^x$ ?

I. The domain consists of all real numbers x.

II. The curve is concave up.

Ill. It is a one-to-one function.

a)

Only I

b)

Only II

c)

Only III

d)

I, Il, & Ill

e)

None of the choices

89.

Which of the following is equal to $\log_5\ 85$ ?

a)

$\frac{\log_{10}\ 5}{\log_{10}\ 85}$

b)

$\frac{\log_{10}\ 85}{\log_{10}\ 5}$

c)

$\frac{\log_5\ 10}{\log_5\ 85}$

d)

$\frac{\log_5\ 85}{\log_5\ 10}$

e)

None of the choices

90.

Solve for x: $e^{\ln\left(2-x\right)}\ =\ 2x$

a)

$e^2$

b)

$\ln2$

c)

$\frac{3}{2}$

d)

$\frac{2}{3}$

e)

None of the choices

91.

Which of the following is/are TRUE for the function $y=f(x)=\ln x$ ?

I. The domain consists of all real numbers x.

II. The range consists of all y > 0.

III. The curve is concave down.

a)

Only I

b)

Only II

c)

Only III

d)

I, II, & III

e)

None of the choices

92.

Solve for x: $\ln\left(x+1\right)-1=\ln x$

a)

$e-1$

b)

$\frac{1}{e-1}$

c)

1

d)

e

e)

None of the choices

93.

Solve for x: $9^{x-1}\ =4$

a)

$\frac{\ln4}{\ln9}+1$

b)

$\frac{\ln5}{\ln9}$

c)

$\ln4-\ln9+1$

d)

$\frac{\ln9}{\ln5}+1$

e)

None of the choices

94.

As n becomes larger and larger,

what value does the expression $\left(1+\frac{r}{n}\right)^n$ approach?

a)

$e^r$

b)

$e^n$

c)

e

d)

1

e)

None of the choices

95.

Which of the following reflections is appropriate to obtain the graph of $y=\frac{1}{2^x}$ ?

a)

$y=2^x$ in the x-axis

b)

$y=2^{-x}$ in the x-axis

c)

$y=2^x$ in the y-axis

d)

$y=2^{-x}$ in the y-axis

e)

None of the choices

96.

To show the graph of $y=\log_2\ 4x$ ,

which of the following translations of $y=\log_2\ x$ is

correct?

a)

Two units down

b)

Two units up

c)

Multiply the ordinates by 4

d)

Four units to the right

e)

None of the choices

97.

What is the relationship between the graphs of $y=8^x$ and $y=\log_8\ x$ ?

a)

They are reflections of each other in the x-axis.

b)

They are reflections of each other in the y-axis.

c)

They are reflections of each other in the line y = x.

d)

There is no reflective relationship to each other.

e)

None of the choices

98.

A radioactive substance decays according to the formula $y=Ae^{kx}$ , where the initial amount A = 40 grams.

If after 8 years 30 grams remain, then the amount y remaining after x years is given by _____.

a)

$y=30e^{\frac{\left(x\ln0.75\right)}{8}}$

b)

$y=40e^{\frac{\left(x\ln0.75\right)}{8}}$

c)

$y=40e^{\frac{\left(x\ln1.3\right)}{8}}$

d)

$y=40e^{\frac{\left(x\ln0.75\right)}{\ln8}}$

e)

None of the choices

99.

A 3000 investment earns interest at the annual rate of 8.4% compounded monthly.

After 5 years the total amount of the investment, $A_5$ , is given by _____.

a)

$A_5=3000(1.084)^{60}$

b)

$A_5=3000(1.084)^5$

c)

$A_5=3000(1.007)^{60}$

d)

$A_5=3000(1.007)^{12}$

e)

None of the choices

100.

If $Q=\frac{\left(\sqrt[5]{409}\right)\left(0.0058\right)}{7.29}$ ,

then what is the equivalent of $\log_bQ$ ?

a)

$\frac{1}{5}\left(\log_b\ 409\ +\ \log_b\ 0.0058\right)\ -\ \log7.29$

b)

$5\log_b\ 409\ +\ \log_b\ 0.0058\ -\ \log_b\ 7.29$

c)

$\frac{\frac{1}{5}\log_b\ 409\ +\ \log_b\ 0.0058}{\log_b\ 7.29}$

d)

$\frac{1}{5}\log_b\ 409\ +\ \log_b\ 0.0058\ -\ \log_b\ 7.29$

e)

None of the choices

Basic and Advanced Algebra

Total questions: 100

Worksheet time: 2hrs 52mins

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