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SAT II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solving Exponential Equations

$(3)2^{x}=24$

Possible Answers:

x=1

x=0

x=4

x=-2

x=3

Correct answer:

x=3

Explanation:

The first step in thist problem is divide both sides by three: $2^{x}=8$ . Then, recognize that 8 could be rewritten with a base of 2 as well ( 2^3 ). Therefore, your answer is 3.

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Example Question #9 : Solving Exponential Equations

Solve for .

2^x=64

Possible Answers:

Correct answer:

Explanation:

Let's convert to base .

We know the following:

64=2*2*2*2*2*2

Simplify.

2*2*2*2*2*2=2^6

Solve.

x=6

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Example Question #10 : Solving Exponential Equations

Solve for .

3^x=2187

Possible Answers:

Correct answer:

Explanation:

Let's convert 2187 to base .

We know the following:

2187=3*3*3*3*3*3*3

Simplify.

3*3*3*3*3*3*3=3^7

Solve.

x=7 .

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Example Question #11 : Solving Exponential Equations

Solve for .

2^x*2^x=2^6

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents with the same base, we will apply the power rule of exponents:

(a^m)^n=a^m^n

We will simply add the exponents and keep the base the same.

2x=6

x=3

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Example Question #11 : Solving Exponential Functions

Solve for .

$3^7*3^{x+3}=3^{24}$

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents with the same base, we will apply the power rule of exponents:

(a^m)^n=a^m^n

We will simply add the exponents and keep the base the same.

7+x+3=24

Simplify.

10+x=24

Solve.

x=14

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Example Question #13 : Solving Exponential Equations

Solve for .

2^x+2^x=2^7

Possible Answers:

3.5

2.5

Correct answer:

Explanation:

When adding exponents with the same base, we need to see if we can factor out the numbers of the base.

In this case, let's factor out 2^x .

We get the following:

2^x(1+1)=2^x(2)

Since we are now multiplying with the same base, we get the following expression:

$2^{x+1}$

Now we have the same base and we just focus on the exponents.

The equation is now:

x+1=7

Solve.

x=6

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Example Question #14 : Solving Exponential Equations

Solve for .

3^x+3^x+3^x=27^2

Possible Answers:

$\frac{2}{3}$

$\frac{5}{3}$

Correct answer:

Explanation:

First, we need to convert 27^2 to base .

We know 27=3^3 .

Therefore we can write the following expression:

(3^3)^2=3^6 .

Next, when we add exponents of the same base, we need to see if we can factor out terms.

In this case, let's factor out 3^x .

We get the following:

3^x(1+1+1)=3^x(3) .

Since we are now multiplying with the same base, we get the following expression:

$3^{x+1}$ .

Now we have the same base and we just focus on the exponents.

The equation is now:

x+1=6

Solve.

x=5

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Example Question #1 : Graphing Exponential Functions

Give the -intercept of the graph of the equation $f(x) = 2 ^{x- 7} + 4$ .

Possible Answers:

(5,0)

(3.9921875, 0)

(4.0078125, 0)

(9,0)

The graph has no -intercept.

Correct answer:

The graph has no -intercept.

Explanation:

Set f(x) = 0 and solve for

$f(x) = 2 ^{x- 7} + 4$

$2 ^{x- 7} + 4 = 0$

$2 ^{x- 7} = -4$

We need not work further. It is impossible to raise a positive number 2 to any real power to obtain a negative number. Therefore, the equation has no solution, and the graph of has no -intercept.

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Example Question #21 : Solving Exponential Functions

What is/are the asymptote(s) of the graph of the function $g(x) = 0.4 ^{x - 2} + 0.7$ ?

Possible Answers:

y = 0.4

y = 1.1

y = 0.7

x = 2

x = 2 and y = 0.7

Correct answer:

y = 0.7

Explanation:

An exponential function of the form

$g(x) = a^{x- h}+k$

has as its one and only asymptote the horizontal line y = k .

Since we define as

$g(x) = 0.4 ^{x - 2} + 0.7$ ,

then k= 0.7 ,

and the only asymptote is the line of the equation y = 0.7 .

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Example Question #21 : Solving Exponential Functions

Determine whether each function represents exponential decay or growth.

$\newline a) \newline y=(\frac{1}{2})^{x}$

$\newline b) \newline y=0.4(1.1)^x$

Possible Answers:

a) growth

b) decay

a) decay

b) growth

a) growth

b) growth

a) decay

b) decay

Correct answer:

a) decay

b) growth

Explanation:

This is exponential decay since the base, (1/2) , is between and .

This is exponential growth since the base, 1.1 , is greater than .

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All SAT II Math I Resources

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SAT II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Solving Exponential Equations

Example Question #9 : Solving Exponential Equations

Example Question #10 : Solving Exponential Equations

Example Question #11 : Solving Exponential Equations

Example Question #11 : Solving Exponential Functions

Example Question #13 : Solving Exponential Equations

Example Question #14 : Solving Exponential Equations

Example Question #1 : Graphing Exponential Functions

Example Question #21 : Solving Exponential Functions

Example Question #21 : Solving Exponential Functions

All SAT II Math I Resources

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