Question 1

Use the rule for order of operations to simplify the expression as much as possible. $1+4(9-5)$
A) $31$
B) $32$
C) $20$
D) $17$
E) $40$

Accepted Answer

First, solve the expression inside the parentheses: $9 - 5 = 4$. Then multiply by 4: $4 \times 4 = 16$. Finally, add 1: $1 + 16 = 17$.

Question 2

Use the rule for order of operations to simplify the expression as much as possible. $12-4(3 \cdot 2-11)$
A) $37$
B) $32$
C) $59$
D) $216$
E) $40$

Accepted Answer

First, we must perform the operation inside the parentheses, which is $3\cdot2-11=-5$. Now we have $12-4(-5)$, which simplifies to $12+20=32$. Remember that when you have a negative sign in front of parentheses, you must distribute the negative sign to every term inside the parentheses using the distributive property.

Question 3

Use the rule for order of operations to simplify the expression as much as possible. $(4+3)^{2}$
A) $49$
B) $25$
C) $17$
D) $14$.
E) $14$

Accepted Answer

First, perform the operation inside the parentheses, which is $4+3=7$. Then, raise the result to the power of 2, which is $7^2=49$.

Question 4

Use the rule for order of operations to simplify the expression as much as possible. $2^{5}+6^{2} \div 2^{2}-3^{2}$
A) $32$
B) $7$
C) $26$
D) $1$
E) $55$

Accepted Answer

The answer of Use the rule for order of operations...

Question 5

Use the rule for order of operations to simplify the expression as much as possible. $8+4(2 \cdot 5-3)+4$
A) $28$
B) $40$
C) $121$
D) $36$
E) $49$

Accepted Answer

The answer of Use the rule for order of operations...

Question 6

Use the rule for order of operations to simplify the expression as much as possible. $6(1+5)$
A) $31$
B) $35$
C) $12$
D) $36$
E) $11$

Accepted Answer

According to the rule for order of operations, we must first simplify what is inside the parentheses, then perform any multiplication or division before addition or subtraction. Therefore, we have:

\begin{align*}
6(1+5)&=6(6)&&	ext{\small Parentheses}\
&=36 &&	ext{\small Multiplication}
\end{align*}

Thus, the answer is D.

Question 7

For the sentence below, write an equivalent expression in symbols. The product of $7$ and y is less than or equal to the sum of y and $6$ .
A) $7 y \leq y+6$
B) $7-y \geq y+1$
C) $7 y \leq 6 y$
D) $7 y \leq x+6$
E) $7 y \geq y+6$

Accepted Answer

"The product of 7 and y" can be written as 7y. "Is less than or equal to" can be written as ≤. "The sum of y and 6" can be written as y + 6. Therefore, the equivalent expression in symbols is 7y ≤ y + 6, which is choice A.

Question 8

Use the rule for order of operations to simplify the expression as much as possible. $2 \cdot 9+8 \cdot 3$
A) $78$
B) $42$
C) $77$
D) $102$
E) $29$

Accepted Answer

Following the order of operations (PEMDAS/BODMAS), we first perform the multiplication and then the addition: $2 \cdot 9 = 18$ and $8 \cdot 3 = 24$. Adding these results together gives $18 + 24 = 42$.

Question 9

Use the rule for order of operations to simplify the expression as much as possible. $(9+3)(9-3)$
A) $27$
B) $90$
C) $105$
D) $72$
E) $33$

Accepted Answer

Using the order of operations (PEMDAS), we first simplify within the parentheses:
(9+3)(9-3) = 12*6
Then we perform the multiplication: 
12*6 = 72
Therefore, the answer is D.

Question 10

Use the rule for order of operations to simplify the expression as much as possible. $3 \cdot 10^{2}+2 \cdot 10+6$
A) $326$
B) $86$
C) $3,066$
D) $9,026$
E) $926$

Accepted Answer

Following the order of operations (PEMDAS/BODMAS), first calculate the exponents: $10^{2} = 100$. Then multiply: $3 \cdot 100 = 300$ and $2 \cdot 10 = 20$. Finally, add all the results together: $300 + 20 + 6 = 326$.

Question 11

For the sentence below, write an equivalent expression in symbols. The sum of x and $3$ is $15$ .
A) $x+15=3$
B) $x=18$
C) $x=3+15$
D) $3 x=15$
E) $x+3=15$

Accepted Answer

The phrase "the sum of" suggests addition, so we want to express this as an equation with "x + 3." "Is" means "equals," so we have x + 3 = 15.

Question 12

Expand and multiply. $6^{2}$
A) $64$
B) $25$
C) $12$
D) $8$
E) $36$

Accepted Answer

$6^{2}$ means $6 \times 6$, which equals $36$.

Question 13

Find the next number in the sequence.
2, 2, 4, 6, 10, . . . (A Fibonacci-like sequence.)
A) 22
B) 15
C) 12
D) 53
E) none of these

Accepted Answer

The answer of Find the next number in the sequence.
2,...

Question 14

Find the next number in the sequence. $1,4,9,16,25,36$ (The sequence of squares.)
A) $40$
B) $98$
C) $61$
D) $64$
E) $49$

Accepted Answer

The answer of Find the next number in the sequence....

Question 15

For the sentence below, write an equivalent expression in symbols. The quotient of x and $9$ is equal to the sum of x and $8$ .
A) $\frac{x}{9}=x+8$
B) $\frac{X}{9}=\frac{X}{8}$
C) $9 x=x+8$
D) $\frac{x}{9}=8 x$
E) $\frac{x+8}{9}=\frac{x}{9}$

Accepted Answer

"The quotient of x and 9" can be written as $\frac{x}{9}$. "Is equal to" can be represented by the equal sign (=). "The sum of x and 8" can be written as $x+8$. Therefore, the equivalent expression in symbols is $\frac{x}{9}=x+8$.

Question 16

In 1993 the government standardized the way in which nutrition information was presented on the labels of most packaged food products. The figure shows a standardized food label from a package of cookies that I ate at lunch the day I was writing the problems for this problem set. Use the information in the figure to answer the following question.  If the calories category stands for calories per serving, how many calories did I consume by eating the whole package of cookies?
A) $1,050 \text { calories }$
B) $420 \text { calories }$
C) $390 \text { calories }$
D) $210 \text { calories }$
E) $391 \text { calories }$

Accepted Answer

The answer of In 1993 the government standardized the way...

Question 17

Expand and multiply. $3^{2}$
A) $8$
B) $6$
C) $5$
D) $9$
E) $4$

Accepted Answer

To expand means to write out the power in its full form, so $3^{2}$ becomes $3 \times 3$, which equals 9. Therefore, the correct answer is D) 9.

Question 18

The following bar chart gives the number of calories burned by a 150-pound person during 1 hour of various exercises. Use the bar char to determine the number of calories burned during 1 hour of skiing. 
A) $272 \text { calories }$
B) $545 \text { calories }$
C) $267 \text { calories }$
D) $546 \text { calories }$
E) $\text { none of these }$

Accepted Answer

The answer of The following bar chart gives the number...

Question 19

Use the rule for order of operations to simplify the expression as much as possible. $6+5 \cdot 9$
A) $20$
B) $50$
C) $51$
D) $99$
E) $59$

Accepted Answer

According to the rule of order of operations, we must perform the multiplication before the addition. Therefore, we have:

$6+5 \cdot 9 = 6 + 45 = 51$

Thus, the correct answer is choice (C).

Question 20

Use the rule for order of operations to simplify the expression as much as possible. $8+8 \div 2+6$
A) $14$
B) $18$
C) $24$
D) $22$
E) $2$

Accepted Answer

According to the order of operations (PEMDAS/BODMAS), division is performed before addition. So, $8 \div 2 = 4$. Then, add the remaining numbers: $8 + 4 + 6 = 18$.

Quiz 1: The Basics

Use the rule for order of operations to simplify the expression as much as possible. $1+4(9-5)$

Use the rule for order of operations to simplify the expression as much as possible. $12-4(3 \cdot 2-11)$

Use the rule for order of operations to simplify the expression as much as possible. $(4+3) ^{2}$

Use the rule for order of operations to simplify the expression as much as possible. $2^{5}+6^{2} \div 2^{2}-3^{2}$

Use the rule for order of operations to simplify the expression as much as possible. $8+4(2 \cdot 5-3) +4$

Use the rule for order of operations to simplify the expression as much as possible. $6(1+5)$

For the sentence below, write an equivalent expression in symbols. The product of $7$ and y is less than or equal to the sum of y and $6$ .

Use the rule for order of operations to simplify the expression as much as possible. $2 \cdot 9+8 \cdot 3$

Use the rule for order of operations to simplify the expression as much as possible. $(9+3) (9-3)$

Use the rule for order of operations to simplify the expression as much as possible. $3 \cdot 10^{2}+2 \cdot 10+6$

For the sentence below, write an equivalent expression in symbols. The sum of x and $3$ is $15$ .

Expand and multiply. $6^{2}$

Find the next number in the sequence. 2, 2, 4, 6, 10, . . . (A Fibonacci-like sequence.)

Find the next number in the sequence. $1,4,9,16,25,36$ (The sequence of squares.)

For the sentence below, write an equivalent expression in symbols. The quotient of x and $9$ is equal to the sum of x and $8$ .

Expand and multiply. $3^{2}$

Use the rule for order of operations to simplify the expression as much as possible. $6+5 \cdot 9$

Use the rule for order of operations to simplify the expression as much as possible. $8+8 \div 2+6$

Quiz 1: The Basics

Use the rule for order of operations to simplify the expression as much as possible. 1+4(9−5) 1+4(9-5) 1+4(9−5)

Use the rule for order of operations to simplify the expression as much as possible. 12−4(3⋅2−11) 12-4(3 \cdot 2-11) 12−4(3⋅2−11)

Use the rule for order of operations to simplify the expression as much as possible. (4+3) 2(4+3) ^{2}(4+3) 2

Use the rule for order of operations to simplify the expression as much as possible. 25+62÷22−322^{5}+6^{2} \div 2^{2}-3^{2}25+62÷22−32

Use the rule for order of operations to simplify the expression as much as possible. 8+4(2⋅5−3) +48+4(2 \cdot 5-3) +48+4(2⋅5−3) +4

Use the rule for order of operations to simplify the expression as much as possible. 6(1+5) 6(1+5) 6(1+5)

For the sentence below, write an equivalent expression in symbols. The product of 777 and y is less than or equal to the sum of y and 666 .

Use the rule for order of operations to simplify the expression as much as possible. 2⋅9+8⋅32 \cdot 9+8 \cdot 32⋅9+8⋅3

Use the rule for order of operations to simplify the expression as much as possible. (9+3) (9−3) (9+3) (9-3) (9+3) (9−3)

Use the rule for order of operations to simplify the expression as much as possible. 3⋅102+2⋅10+63 \cdot 10^{2}+2 \cdot 10+63⋅102+2⋅10+6

For the sentence below, write an equivalent expression in symbols. The sum of x and 333 is 151515 .

Expand and multiply. 626^{2}62