Free Printable General Mathematics Reviewer

1.

Which of the following situation represents a one-to-one function?

a)

The relation pairing a book to its author.

b)

The relation pairing the person to his/her citizenship.

c)

The relation pairing a teacher to their classroom.

d)

The relation pairing a person to their fingerprint.

2.

Which of the following relationships do NOT represent one-to-one function?

a)

Country to its capital city

b)

Car to its license plate number

c)

Students to their subjects

d)

School to its School ID

3.

Which is NOT a one-to-one function?

a)

$f\left(x\right)=x^3$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=e^x$

d)

$f\left(x\right)=2x$

4.

Which of the following statements is FALSE?

a)

A quadratic function is not a one-to-one function.

b)

The inverse of $y=x$ is $y=\frac{1}{x}$

c)

The inverse of $f^{-1}\left(x\right)$ is $f\left(x\right)$

d)

The graph of the inverse function is a reflection of the graph of the original function along $y=x$

5.

Which of the following is the inverse of {(-4, 3), (-5, 2)}?

a)

{( -4, 3), (-5, 2)}

b)

{(3, -4), (-2, 5)}

c)

{(4, -3), (-5, 2)}

d)

{(3, -4), (2, -5)}

6.

The statement "A function has an inverse function if and only if it is one - to - one" is

a)

sometimes true

b)

never true

c)

always true

d)

false

7.

Which of the following is the correct representation of the inverse of the function given the table of values below?

a)

b)

c)

d)

8.

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

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

9.

If 5 is a constant added to f(x) = 3x-2, what will its inverse be equal to?

a)

$f^{-1}\left(x\right)=3x+2$

b)

$f^{-1}\left(x\right)=3x-2$

c)

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

d)

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

10.

Which of the following is the graph of the inverse of the graph below?

a)

b)

c)

d)

11.

Suppose 𝑓(𝑥) is a one-to-one function. What is the range of f^-1(x)?

a)

range of 𝑓(𝑥)

b)

domain of 𝑓(𝑥)

c)

set of real numbers

d)

set of positive integers

12.

Determine the inverse of f(x) = 3x+5.

a)

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

b)

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

c)

$f^{-1}\left(x\right)=\frac{x-5}{3}$

d)

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

13.

Find the inverse of $f\left(x\right)=\frac{2x+3}{x-4}$ .

a)

$f^{-1}\left(x\right)=\frac{4x+3}{x-2}$

b)

$f^{-1}\left(x\right)=\frac{2x+3}{x+4}$

c)

$f^{-1}\left(x\right)=\frac{x-4}{2x+3}$

d)

$f^{-1}\left(x\right)=\frac{3x+2}{x-4}$

14.

If $f\left(x\right)=4x-1$ , what is the inverse function $f^{-1}\left(x\right)$ ?

a)

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

b)

$f^{-1}\left(x\right)=\frac{x+1}{4}$

c)

$f^{-1}\left(x\right)=4x+1$

d)

$f^{-1}\left(x\right)=4x-1$

15.

Which of the following statements is TRUE regarding inverse functions?

a)

The graph of a function and its inverse are identical.

b)

All functions have inverses.

c)

The inverse of a one-to-one function is also one-to-one.

d)

The inverse of a function is always a function.

16.

One of these does not belong to the group, which one and why?

I. $5^{\left(x+1\right)}=3^2$ II. $f\left(x\right)=5^{\left(x+1\right)}$ III. $4^{\left(-3x+5\right)}=16$ IV. $6=3\left(2\right)^{\left(3-x\right)}$

a)

I, because it is the only exponential equation while the rest are all exponential functions.

b)

II, because it is the only exponential function while the rest are all exponential equations.

c)

III, because it is the only exponential function while the rest are all exponential inequalities.

d)

IV, because it is the only exponential equation while the rest are all exponential inequalities.

17.

Which of the following will result in the equation $3^{\left(x+1\right)}\cdot27=9^{\left(x+2\right)}$ ?

a)

$3^{\left(x+1\right)}\cdot3^3=3^{\left(2x+4\right)}$

b)

$3^{\left(3x+3\right)}=3^{\left(2x+4\right)}$

c)

$81^{\left(x+1\right)}=9^{\left(x+2\right)}$

d)

$3^{\left(4x+4\right)}=3^{\left(2x+4\right)}$

18.

Which two alternative solutions will solve the equation $16^{\left(x+2\right)}\cdot4^3=2^{2x}$ ?

I. $4^{\left(2x+2\right)}\cdot4^3=4^x$ II. $4^{\left(2x+4\right)}\cdot4^3=4^x$ III. $4^{\left(2x+4\right)}\cdot2^6=4^x$ IV. $4^{\left(x+2\right)}\cdot2^6=4^x$

a)

I and III

b)

I and IV

c)

II and III

d)

II and IV

19.

Which is being exemplified by $27^{\left(x-2\right)}=9$ ?

a)

Exponential Equation

b)

Exponential Expression

c)

Exponential Function

d)

Exponential Inequality

20.

Which of the following is an exponential inequality?

a)

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

b)

$4^x=2^{\left(2x+1\right)}$

c)

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

d)

$4^x>2^{\left(2x+1\right)}$

21.

The teacher asks Joseph to solve the equation $9^{\left(x-3\right)}=3^{\left(x-2\right)}$ . What is the value of x?

a)

-4

b)

4

c)

2

d)

-2

22.

What should be considered in solving an exponential equation?

a)

Bases on both sides must be the same.

b)

Bases on both sides must be simplified.

c)

Exponents on both sides must be the same.

d)

Exponents on both sides must be simplified.

23.

What is the value of x in the equation $8^x=16^{\left(x+5\right)}$ ?

a)

20

b)

-10

c)

10

d)

-20

24.

Solve for the exponential equation $3^x=3^2$ ?

a)

2

b)

4

c)

6

d)

8

25.

A certain type of bacteria doubles its population every 15 minutes. If a sample of this bacteria is kept in ideal conditions and continues to double, how long will it take for the population to become eight times its original size?

a)

15 mins

b)

30 mins

c)

45 mins

d)

60 mins

26.

For an exponential function $f\left(x\right)=b^x$ , which can be a value of b?

a)

-1

b)

0

c)

1

d)

2

27.

A certain type of microorganism divides into two every 10 minutes. If you start with one microorganism, how many microorganisms will there be after 1 hour?

a)

32

b)

64

c)

128

d)

256

28.

What is the solution to $2^{\left(x+3\right)}\ge4^{\left(x-1\right)}$ ?

a)

$x\ge5$

b)

$x>5$

c)

$x\le5$

d)

$x<5$

29.

Solve for x: $\left(\frac{1}{3}\right)^{\left(2x-2\right)}<\left(\frac{1}{27}\right)^{\left(x+1\right)}$

a)

$x>-5$

b)

$x<-5$

c)

$x>5$

d)

$x<5$

30.

A company has 800 job applicants. During each round of interviews, half of the remaining applicants are eliminated. How many rounds of interviews are needed to reduce the number of applicants to 100?

a)

2

b)

3

c)

4

d)

5

31.

The solution to $\log_39x^2-\log_3x=4$ is x=9. 1. Which law of logarithms was used to solve it?

a)

Power Law

b)

Product Law

c)

Quotient Law

d)

Change of Base Formula

32.

Which of the following uses the laws /properties of logarithms to simplify $\log_7x^2+\log_7x$ ?

a)

$\log_7x$

b)

$\log_7x^3$

c)

$-\log_7x$

d)

$-\log_7x^2$

33.

John simplified $\log_416+2\log_28$ without using a calculator. Which laws were used?

A. C.

a)

Product Law then Power Law

b)

Power Law then Product Law

c)

Quotient Law then Power Law

d)

Power Law then Quotient Law

34.

Express $\log_{25}5=\frac{1}{2}$ into exponential form

a)

$\left(\frac{1}{2}\right)^5=25$

b)

$25^5=\frac{1}{2}$

c)

$\left(\frac{1}{2}\right)^{25}=5$

d)

$25^{\frac{1}{2}}=5$

35.

Which of the following is a logarithmic equation?

a)

$3=\log_7x$

b)

$y=\log_4x$

c)

$y\le\log_2x$

d)

$y\ge\log_524$

36.

What is the exponential form of the function $y=\log_63x$ ?

a)

$6^{3x}=y$

b)

$6^y=3x$

c)

$y^6=3x$

d)

$y^{3x}=6$

37.

If the formula for calculating the population is $P=\log_{10}x$ and x=100, what is the value of P?

a)

3

b)

2

c)

10

d)

1

38.

In the Grade 11 class of Miss Soto, Laura was asked to give an example of a logarithmic function. Which of the following examples should Laura give?

a)

$\log\left(x+3\right)=\log4$

b)

$\log\left(2x-1\right)>3$

c)

$f\left(x\right)=x+4$

d)

$f\left(x\right)=\log_3\left(x+1\right)$

39.

In Miss Alvarez's class, three students were asked to give examples of logarithmic functions, logarithmic equations, and logarithmic inequalities. Sarah cited $f\left(x\right)=\log_2\left(x+6\right)$ , Rachel cited $\log_4\left(x-2\right)\ge1$ , and Luis cited $\log_5\left(3x-4\right)=2$ . Who gave the correct example of a logarithmic equation?

a)

Sarah and Luis

b)

Sarah

c)

Luis

d)

Rachel

40.

Which of the following statement is TRUE?

a)

Common logarithms have base e.

b)

Natural logarithms have base 10.

c)

In the logarithmic form $\log_bx,\ x$ can be negative.

d)

$\log_bx$ can be negative if $0<x<1$ .

41.

Solve for x: $\log_381=x$

a)

3

b)

4

c)

2

d)

5

42.

The perimeter P of a regular hexagon is determined using the function $P\left(x\right)=6x$ , which function can be used to find the length of the side of the pentagon?

a)

$P^{-1}\left(x\right)=\frac{x}{6}$

b)

$P^{-1}\left(x\right)=\frac{6}{x}$

c)

$P^{-1}\left(x\right)=\frac{x+1}{6}$

d)

$P^{-1}\left(x\right)=\frac{6-x}{x}$

43.

What is $\log_327$ ?

a)

3

b)

1

c)

2

d)

5

44.

Solve for x: $\log_4\left(x+2\right)=3$

a)

63

b)

62

c)

61

d)

60

45.

Solve for x: $\log_2\left(x+4\right)=5$

a)

16

b)

25

c)

28

d)

31

General Mathematics Reviewer

Total questions: 45

Worksheet time: 23mins

Similar Resources on Wayground