SAT II Math I : Elementary Operations

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

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Example Questions

Example Question #1 : Elementary Operations

Evaluate the expression.

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

Possible Answers:

\(\displaystyle 33\)

\(\displaystyle 29\)

\(\displaystyle 60\)

\(\displaystyle 56\)

Correct answer:

\(\displaystyle 56\)

Explanation:

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

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

First, evaluate any terms in parenthesis.

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

\(\displaystyle 7^2+4+6\div 2\)

Next, evaluate the exponent.

\(\displaystyle \small 49+4+6\div2\)

Divide.

\(\displaystyle \small 49+4+3\)

Finally, add.

\(\displaystyle \small 49+4+3=56\)

Example Question #1 : Elementary Operations

Evalute the expression:

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

Possible Answers:

\(\displaystyle \small 366\)

\(\displaystyle \small 64\)

\(\displaystyle 46\)

\(\displaystyle \small 21\)

Correct answer:

\(\displaystyle 46\)

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.

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

\(\displaystyle \small 1+8^2-4*6+5\)

Next, simplify any terms with exponents.

\(\displaystyle \small 1+64-4*6+5\)

Now, perform multiplication.

\(\displaystyle \small 1+64-24+5\)

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

\(\displaystyle \small \small 65-24+5 = 41+5=46\)

Thus, our answer is:

\(\displaystyle \small \small 46\)

Example Question #2 : Elementary Operations

Add in modulo 7:

\(\displaystyle 5 + 4 + 6 + 2\)

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 3\)

\(\displaystyle 6\)

\(\displaystyle 5\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 3\)

Explanation:

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

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

\(\displaystyle 5 + 4 + 6 + 2 \equiv 3 \mod 7\),

and the correct response is 3.

Example Question #1 : Elementary Operations

Add:  \(\displaystyle 100+1.01+0.01+0.00001\)

Possible Answers:

\(\displaystyle 101.01001\)

\(\displaystyle 101.11001\)

\(\displaystyle 101.02001\)

\(\displaystyle 101.12001\)

\(\displaystyle 101.02002\)

Correct answer:

\(\displaystyle 101.02001\)

Explanation:

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

\(\displaystyle 100+1.01= 101.01\)

\(\displaystyle 101.01+0.01= 101.02\)

\(\displaystyle 101.02+ 0.00001=101.02001\)

The correct answer is: \(\displaystyle 101.02001\)

Example Question #2 : Elementary Operations

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

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 12\)

\(\displaystyle 17\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle 15\)

Explanation:

Step 1: Recall PEMDAS...

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

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

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

\(\displaystyle (3*4)=12\)

\(\displaystyle -7+3=-4\)

\(\displaystyle (24\div 6)=4\)

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

\(\displaystyle 27-12+4-4\)

Step 4: Evaluate:

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

 

Example Question #1 : Elementary Operations

Find the sum of the numbers:  \(\displaystyle 13+14+88+12+54\)

Possible Answers:

\(\displaystyle 121\)

\(\displaystyle 181\)

\(\displaystyle 201\)

\(\displaystyle 193\)

\(\displaystyle 191\)

Correct answer:

\(\displaystyle 181\)

Explanation:

Add all the ones digits.

\(\displaystyle 3+4+8+2+4 = 21\)

Add the tens digits with the two as the carryover.

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

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

The answer is:  \(\displaystyle 181\)

Example Question #1 : Mathematical Relationships

Evaluate:  \(\displaystyle 134+189+879\)

Possible Answers:

\(\displaystyle 1202\)

\(\displaystyle 1212\)

\(\displaystyle 1302\)

\(\displaystyle 1092\)

\(\displaystyle 1112\)

Correct answer:

\(\displaystyle 1202\)

Explanation:

Add the ones digits.

\(\displaystyle 4+9+9 = 22\)

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

\(\displaystyle 3+8+7+(2) = 20\)

Repeat the process with the hundreds digits.

\(\displaystyle 1+1+8+(2) = 12\)

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

The answer is:  \(\displaystyle 1202\)

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