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SAT II Math I : Mathematical Relationships

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

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All SAT II Math I Resources

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Example Questions

Example Question #1 : Mathematical Relationships

Evaluate the expression.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

Possible Answers:

Correct answer:

Explanation:

Follow the correct order of operations: parenthenses, exponents, multiplication, division, addition, subtraction.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

First, evaluate any terms in parenthesis.

$(7)^2+(\frac{8}{2})+6\div 2$

$7^2+4+6\div 2$

Next, evaluate the exponent.

$\small 49+4+6\div2$

Divide.

$\small 49+4+3$

Finally, add.

$\small 49+4+3=56$

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Example Question #2 : Mathematical Relationships

Evalute the expression:

$\left (\frac{3*2}{6}\right)+8^2-4*6+5$

Possible Answers:

$\small 64$

$\small 366$

$\small 21$

Correct answer:

Explanation:

Follow the correct order of operations: parentheses, exponents, multiplication, division, addition, subtraction. (This is typically abbreviated as PEMDAS. Note that both multiplication and division, and addition and subtraction, are equal to each other in terms of rank, so when both are present, solving the equation proceeds from left to right).

First, simplify anything in parentheses.

$\left(\frac{6}{6}\right)+8^2-4*6+5$

$\small 1+8^2-4*6+5$

Next, simplify any terms with exponents.

$\small 1+64-4*6+5$

Now, perform multiplication.

$\small 1+64-24+5$

Since all we are left with is addition and subtraction, we perform simplification from left to right.

$\small \small 65-24+5 = 41+5=46$

Thus, our answer is:

$\small \small 46$

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Example Question #3 : Mathematical Relationships

Add in modulo 7:

5 + 4 + 6 + 2

Possible Answers:

Correct answer:

Explanation:

In modulo 7 arithmetic, a number is congruent to the remainder of its division by 7.

Therefore, since 5 + 4 + 6 + 2 = 17 and $17 \div 7 = 2 \textrm{ R }3$ ,

$5 + 4 + 6 + 2 \equiv 3 \mod 7$ ,

and the correct response is 3.

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Example Question #1 : Elementary Operations

Add: 100+1.01+0.01+0.00001

Possible Answers:

101.02002

101.12001

101.02001

101.11001

101.01001

Correct answer:

101.02001

Explanation:

To solve 100+1.01+0.01+0.00001 , make sure the digits are aligned with the correct placeholder. It is also possible to add term by term.

100+1.01= 101.01

101.01+0.01= 101.02

101.02+ 0.00001=101.02001

The correct answer is: 101.02001

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Example Question #5 : Mathematical Relationships

Evaluate: $(2+1)^3-(3*4)-7+3+(24\div 6)$ .

Possible Answers:

Correct answer:

Explanation:

Step 1: Recall PEMDAS...

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Step 2: Perform the evaluation in separate pieces...

(2+1)^3=3^3=27

(3*4)=12

-7+3=-4

$(24\div 6)=4$

Step 3: Replace the values and keep the signs..

27-12+4-4

Step 4: Evaluate:

(27-12)+(4-4)=15+0=15

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Example Question #1 : Elementary Operations

Find the sum of the numbers: 13+14+88+12+54

Possible Answers:

121

181

201

193

191

Correct answer:

181

Explanation:

Add all the ones digits.

3+4+8+2+4 = 21

Add the tens digits with the two as the carryover.

1+1+8+1+5+(2) = 18

Combine this value with the ones digit of the first number.

The answer is: 181

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Example Question #7 : Mathematical Relationships

Evaluate: 134+189+879

Possible Answers:

1092

1302

1212

1202

1112

Correct answer:

1202

Explanation:

Add the ones digits.

4+9+9 = 22

Add the tens digits with the tens digit of the previous number as carryover.

3+8+7+(2) = 20

Repeat the process with the hundreds digits.

1+1+8+(2) = 12

Combine this number with the ones digits of the previous calculations.

The answer is: 1202

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Example Question #1 : Mathematical Relationships

How many elements are in a set that has exactly 128 subsets?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

A set with elements has $2 ^{N}$ subsets.

Solve:

$2 ^{N} = 128$

$\ln 2 ^{N} = \ln 128$

$N \ln 2 = \ln 128$

$N = \frac{\ln 128}{\ln 2} = \frac{4.8520 }{0.6931} = 7$

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Example Question #4 : Mathematical Relationships

Rewrite as a single logarithmic expression:

$\ln x - 2 \ln (x + 2)$

Possible Answers:

$\ln \frac{x}{x^{2} +4x + 4}$

$\ln \frac{1}{x +4}$

$\ln \left (-x^{2} -3x -4 \right )$

$\ln \frac{x}{2x + 4}$

$\ln \frac{1}{x^{2} +3x +4}$

Correct answer:

$\ln \frac{x}{x^{2} +4x + 4}$

Explanation:

Using the properties of logarithms

$n \ln a = \ln a^{n}$ and $\ln a - \ln b = \ln \frac{a}{b}$ ,

we simplify as follows:

$\ln x - 2 \ln (x + 2)$

$= \ln x - \ln (x + 2)^{2}$

$= \ln x - \ln (x^{2} +4x + 4)$

$= \ln \frac{x}{x^{2} +4x + 4}$

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Example Question #1 : Exponents And Logarithms

Solve: $log_{3}27$

Possible Answers:

$\frac{1}{9}$

Correct answer:

Explanation:

In order to solve this problem, covert 27 to the correct base and power.

$log_{3}27 = log_{3}\: 3^3$

Since log_xx^n = n , the correct answer is .

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SAT II Math I : Mathematical Relationships

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

All SAT II Math I Resources

Example Questions

Example Question #1 : Mathematical Relationships

Example Question #2 : Mathematical Relationships

Example Question #3 : Mathematical Relationships

Example Question #1 : Elementary Operations

Example Question #5 : Mathematical Relationships

Example Question #1 : Elementary Operations

Example Question #7 : Mathematical Relationships

Example Question #1 : Mathematical Relationships

Example Question #4 : Mathematical Relationships

Example Question #1 : Exponents And Logarithms

All SAT II Math I Resources

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