SHSAT Math Quiz: Order Of Operations

20 questions · exam conditions

0:00

Order Of OperationsQuestion 1 of 20

Compute $7[3-2(4^{0})]$ .

SHSAT Math Quiz

SHSAT Math Quiz: Order Of Operations

Practice Order Of Operations in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Order Of Operations, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Compute $7[3-2(4^{0})]$ .

7 (correct answer)
21
28
35

Explanation: This question tests your understanding of order of operations (PEMDAS) and exponent rules, particularly what happens when you raise a number to the zero power. Let's work through

7[3-2(4^{0})]

step by step. The key insight is recognizing that any non-zero number raised to the zero power equals 1, so

4^{0} = 1

. Now we can substitute and follow order of operations:

7[3-2(1)] = 7[3-2] = 7[1] = 7

. Looking at the wrong answers: Choice B (21) likely comes from incorrectly treating

4^{0}

as 4, giving you

7[3-2(4)] = 7[3-8] = 7[-5] = -35

, then taking the absolute value or making a sign error. Choice C (28) might result from treating

4^{0}

as 0, yielding

7[3-2(0)] = 7[3-0] = 7[3] = 21

, then making an additional calculation error. Choice D (35) could come from the same

4^{0} = 0

mistake but then incorrectly computing

7 \times 5 = 35

by somehow getting 5 instead of 3. The correct answer is A. Remember that

a^{0} = 1

for any non-zero number

a

- this is one of the most commonly tested exponent rules on the SHSAT. When you see expressions with zero exponents, immediately replace them with 1 before continuing with order of operations. This rule trips up many students, so mastering it will give you an advantage.

Question 2

What is the value of $2^3 \cdot 3^2 - 4(5 + 2^2) + 3 \cdot 2^4 \div 4$ ?

$26$
$36$
$48$ (correct answer)
$56$

Explanation: Following order of operations: First evaluate exponents:

2^3 = 8

3^2 = 9

2^2 = 4

2^4 = 16

. Then parentheses:

(5 + 4) = 9

. Now we have

8 \cdot 9 - 4(9) + 3 \cdot 16 \div 4

. Next, multiplication and division from left to right:

8 \cdot 9 = 72

4(9) = 36

3 \cdot 16 = 48

48 \div 4 = 12

. Finally, addition and subtraction from left to right:

72 - 36 + 12 = 48

. Choice A results from calculation errors in the exponents. Choice B comes from forgetting to add the final term

12

. Choice D results from treating division with lower precedence than addition.

Question 3

What is $\left(\dfrac{6}{3}\right)^{2}+4\times2$ ?

12 (correct answer)
16
20
24

Explanation: This question tests your ability to apply the order of operations (PEMDAS) correctly when evaluating mathematical expressions. When you see an expression with multiple operations, you must follow the proper sequence: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through

\left(\dfrac{6}{3}\right)^{2}+4\times2

step by step: First, handle the parentheses:

\dfrac{6}{3} = 2

Next, apply the exponent:

2^2 = 4

Then perform the multiplication:

4 \times 2 = 8

Finally, add:

4 + 8 = 12

Looking at the wrong answers: Choice B (16) likely comes from incorrectly calculating

2^2 + 4 \times 2

2 + 4 = 6

, then

6^2 + 8 = 36 + 8

, but this shows confusion with order of operations. Choice C (20) might result from adding first:

(2 + 4) \times 2 + 8

, ignoring that exponents come before addition. Choice D (24) could come from treating the entire expression as

(2 + 4) \times 4

, completely misapplying the order of operations. The correct answer is A (12). Strategy tip: When you see complex expressions on the SHSAT, always write out each step of PEMDAS clearly. Don't try to do multiple operations in your head at once—this leads to the exact mistakes that create the wrong answer choices. Work methodically through each operation in the correct order.

Question 4

Find the value of $5+2^{3}\div2$ .

9 (correct answer)
8
11
13

Explanation: When you encounter an expression with multiple operations like this one, you need to follow the order of operations (PEMDAS/BODMAS). This means handling Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through

5+2^{3}\div2

step by step. First, calculate the exponent:

2^3 = 2 \times 2 \times 2 = 8

. Now the expression becomes

5 + 8 \div 2

. Next, perform the division:

8 \div 2 = 4

. Finally, add:

5 + 4 = 9

. Looking at the wrong answers reveals common order of operations mistakes. Choice B (8) likely comes from calculating

2^3 = 8

and then incorrectly thinking this is the final answer, or from doing

5 + 2 = 7

, then

7^3 \div 2

, which shows misunderstanding of how exponents work in the order of operations. Choice C (11) probably results from adding first:

5 + 2 = 7

, then cubing to get

7^3 = 343

, then dividing by 2 to get approximately 171.5, or more likely from doing

5 + 2^3 = 5 + 8 = 13

, then subtracting 2 instead of dividing. Choice D (13) comes from ignoring the division entirely and just calculating

5 + 2^3 = 5 + 8 = 13

. Remember: exponents come before addition, and division comes before addition. When you see mixed operations, always write out PEMDAS and work through each step methodically. Don't rush—order of operations errors are among the most common mistakes on standardized math tests.

Question 5

What is the value of $\dfrac12\,(8-3)^{2}-7$ ?

5.5 (correct answer)
12.5
18.5
-5.5

Explanation: This problem tests your ability to follow the order of operations (PEMDAS/BODMAS) when evaluating expressions with parentheses, exponents, multiplication, and subtraction. Let's work through

\frac{1}{2}(8-3)^2-7

step by step. First, handle what's inside the parentheses:

8-3=5

. Next, apply the exponent:

5^2=25

. Then multiply by

\frac{1}{2}

\frac{1}{2} \times 25 = 12.5

. Finally, subtract 7:

12.5-7=5.5

. Looking at the wrong answers reveals common mistakes. Choice B (12.5) represents stopping too early—you've correctly calculated

\frac{1}{2}(8-3)^2

but forgot to subtract the 7 at the end. Choice C (18.5) likely comes from incorrectly adding 7 instead of subtracting it:

12.5+7=18.5

. Choice D (-5.5) could result from a sign error where you calculated

7-12.5

instead of

12.5-7

, essentially reversing the subtraction. The correct answer is A) 5.5. Strategy tip: On order of operations problems, work methodically through PEMDAS and resist the urge to rush. Many wrong answers on the SHSAT are designed to catch students who skip steps or make sign errors. Always double-check your final arithmetic, especially when subtracting at the end of a multi-step calculation.

Question 6

What is the value of $2^{3} + (4 - 1)^{2}$ ?

11
17 (correct answer)
23
27

Explanation: This question tests your ability to apply the order of operations (PEMDAS) while evaluating expressions with exponents and parentheses. When you see an expression like this, work systematically through each operation in the correct order: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's evaluate

2^{3} + (4 - 1)^{2}

step by step: First, handle the parentheses:

(4 - 1) = 3

Next, evaluate the exponents:

2^{3} = 8

and

3^{2} = 9

Finally, add:

8 + 9 = 17

Looking at the wrong answers: Choice A (11) likely comes from calculating

2^{3} + (4 - 1) = 8 + 3 = 11

— forgetting to square the result in parentheses. Choice C (23) might result from incorrectly calculating

2^{3} = 8

but then doing

8 + (4 - 1)^{3} = 8 + 27 = 35

or making other computational errors. Choice D (27) could come from calculating

(4 - 1)^{3} = 27

instead of

(4 - 1)^{2} = 9

, then subtracting

2^{3}

instead of adding it. The correct answer is B (17). Study tip: When evaluating expressions with multiple operations, write out each step clearly. Don't try to do everything in your head — small errors in order of operations or arithmetic can easily lead you to a tempting wrong answer that appears among the choices.

Question 7

Find the value of $|5-2\times4|-3$ .

0 (correct answer)
3
5
-3

Explanation: This question tests your understanding of order of operations and absolute value. When you see expressions with multiple operations and absolute value bars, you must carefully follow the correct sequence of calculations. Let's work through

|5-2\times4|-3

step by step. First, handle what's inside the absolute value bars using order of operations (PEMDAS). Within

|5-2\times4|

, multiplication comes before subtraction, so:

2\times4 = 8

, giving us

|5-8| = |-3|

. The absolute value of

-3

3

. Finally, subtract:

3-3 = 0

. Now let's examine why each answer choice might be tempting. Choice A (0) is correct based on our calculation above. Choice B (3) represents stopping after finding

|5-2\times4| = 3

but forgetting to subtract the final 3. Choice C (5) likely comes from incorrectly doing subtraction before multiplication inside the absolute value bars, calculating

|5-2|\times4-3 = 3\times4-3 = 9

, though this doesn't directly give 5. Choice D (-3) results from forgetting to apply the absolute value, calculating

5-2\times4-3 = 5-8-3 = -6

, or making other order of operations errors. The key strategy here is to work methodically: handle parentheses and absolute value bars as grouping symbols, apply order of operations within them, then continue from left to right. Always double-check that you've applied absolute value correctly—it always produces a non-negative result.

Question 8

Compute $9-4^{2}\div8$ .

7 (correct answer)
2
1
25

Explanation: When you encounter expressions with multiple operations, order of operations (PEMDAS/BODMAS) is crucial. You must perform operations in the correct sequence: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Let's work through

9-4^{2}\div8

step by step. First, handle the exponent:

4^2 = 16

. The expression becomes

9-16\div8

. Next, perform the division:

16\div8 = 2

. Finally, subtract:

9-2 = 7

. Looking at the answer choices, (A) 7 is correct because we followed the proper order of operations. Choice (B) 2 likely comes from incorrectly doing

9-4 = 5

, then

5^2 = 25

, then

25\div8 = 3.125

, which doesn't match, or from some other order mix-up. Choice (C) 1 might result from calculating

4^2\div8 = 16\div8 = 2

, then mistakenly doing

9\div2 - 7 = 1

or similar errors. Choice (D) 25 comes from the common mistake of ignoring order of operations entirely and working left to right:

9-4 = 5

, then

5^2 = 25

, completely forgetting about the division by 8. Strategy tip: Always write out each step when working with order of operations. Don't try to do multiple steps mentally—exponents and division/multiplication before addition/subtraction. This systematic approach prevents the costly mistakes that create these attractive wrong answers on the SHSAT.

Question 9

Refer to the table to answer the question. What is the value of $2x^{2}-yz$ when the given values are used?

28 (correct answer)
18
8
-10

Explanation: From the table,

x=3,\;y=-2,\;z=5

. First square

x

x^{2}=9

. Multiply:

2\times9=18

. Next,

yz=(-2)(5)=-10

. Subtract:

18-(-10)=18+10=28

. B: Stops after calculating

2x^2

without subtracting

yz

. C: Incorrectly computes

18-10=8

instead of

18-(-10)

. D: Only calculates

yz=-10

without the rest of the expression.

Question 10

What is the value of $4 + 3[2^2 + 5(3 - 1)] - 6$ ?

$38$
$52$
$46$
$40$ (correct answer)

Explanation: When you encounter a complex expression with multiple operations, the order of operations (PEMDAS) is your roadmap. Work systematically: Parentheses first, then Exponents, then Multiplication and Division from left to right, finally Addition and Subtraction from left to right. Let's break down

4 + 3[2^2 + 5(3 - 1)] - 6

step by step: First, handle the innermost parentheses:

(3 - 1) = 2

Now we have:

4 + 3[2^2 + 5(2)] - 6

Next, the exponent:

2^2 = 4

This gives us:

4 + 3[4 + 5(2)] - 6

Continue with multiplication inside the brackets:

5(2) = 10

So:

4 + 3[4 + 10] - 6

Simplify inside the brackets:

4 + 10 = 14

Now:

4 + 3[14] - 6

Multiply:

3[14] = 42

Finally:

4 + 42 - 6 = 40

The answer is D)

40

. Here's why the other choices are wrong: A)

38

likely comes from incorrectly calculating

4 + 42 - 8

(perhaps misreading the final 6). B)

52

probably results from adding instead of subtracting at the end:

4 + 42 + 6

. C)

46

comes from forgetting to subtract 6 entirely:

4 + 42

. Strategy tip: Write out each step when working with order of operations. Don't try to skip steps mentally—small arithmetic errors in complex expressions are easy to make but costly on the SHSAT.

Question 11

What is the value of $6 + 3 \times 4 - 5$ ?

13 (correct answer)
17
23
9

Explanation: When you encounter an expression with multiple operations like this one, you need to follow the order of operations (PEMDAS/BODMAS). This means you perform multiplication and division before addition and subtraction, working from left to right. Let's work through

6 + 3 \times 4 - 5

step by step. First, identify that you have addition, multiplication, and subtraction. According to order of operations, you must do the multiplication first:

3 \times 4 = 12

. Now your expression becomes

6 + 12 - 5

. Next, work from left to right with the remaining operations:

6 + 12 = 18

, then

18 - 5 = 13

. The answer is 13, which is choice A. Let's see where the wrong answers come from. Choice B (17) likely results from incorrectly doing

6 + 3 = 9

, then

9 \times 4 = 36

, then

36 - 5 = 31

— wait, that's not 17 either. Actually, B probably comes from

6 + 3 \times 4 = 6 + 12 = 18

, then forgetting to subtract 5, giving you

18 - 1 = 17

through a calculation error. Choice C (23) results from working strictly left to right without following order of operations:

6 + 3 = 9

, then

9 \times 4 = 36

, then

36 - 5 = 31

— actually, this suggests 23 might come from

6 \times 4 - 1 = 23

through misreading. Choice D (9) comes from

6 + 4 - 5 = 5

if you somehow skip the 3 entirely. Remember: multiplication and division always come before addition and subtraction. When you see mixed operations, circle the multiplication and division first, solve those, then work left to right with what remains.

Question 12

What is the value of $\dfrac{3(4+5)}{2}-1$ ?

12.5 (correct answer)
13.5
26
35

Explanation: This question tests your understanding of the order of operations (PEMDAS/BODMAS) - the sequence you must follow when evaluating mathematical expressions with multiple operations. When you see an expression like this, work systematically through the order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's evaluate

\dfrac{3(4+5)}{2}-1

step by step: First, handle the parentheses:

(4+5) = 9

Next, perform the multiplication and division from left to right:

3 \times 9 = 27

, then

\dfrac{27}{2} = 13.5

Finally, subtract:

13.5 - 1 = 12.5

Looking at the wrong answers: Choice B (13.5) represents stopping after the division step and forgetting to subtract 1 - a common error when students lose track of the final operation. Choice C (26) likely comes from incorrectly calculating

3(4+5) = 3 \times 9 = 27

, then subtracting 1 to get 26, but forgetting to divide by 2. Choice D (35) appears to result from adding instead of following proper order:

3 + 4 + 5 + 2 - 1 = 13

, or some other computational error. The correct answer is A (12.5). Strategy tip: Always write out each step of the order of operations, especially on standardized tests. Many wrong answer choices are specifically designed to catch students who skip steps or work too quickly through the calculation sequence.

Question 13

Compute $7 - [3 + 2(5 - 1)]$ .

-4 (correct answer)
4
8
-8

Explanation: This question tests your understanding of order of operations (PEMDAS/BODMAS), specifically how to handle nested brackets and multiple operations in sequence. When you see an expression with brackets inside brackets, work from the innermost parentheses outward. Start with

(5 - 1) = 4

. Next, handle the multiplication:

2(4) = 8

. Now the expression becomes

7 - [3 + 8]

. Simplify inside the brackets:

3 + 8 = 11

. Finally, compute

7 - 11 = -4

. Let's examine why each answer choice might appear: A) -4 is correct, following proper order of operations as shown above. B) 4 likely results from incorrectly computing the final subtraction. You might have calculated

11 - 7 = 4

instead of

7 - 11 = -4

, essentially flipping the subtraction order. C) 8 probably comes from stopping too early in your calculations. After finding

2(5-1) = 8

, you might have forgotten to complete the remaining operations with the 3 and the outer subtraction. D) -8 could result from a sign error during the middle steps, perhaps incorrectly treating the addition inside the brackets as subtraction, giving you

7 - [3 - 8] = 7 - (-5) = 12

, though this doesn't directly lead to -8, this represents the type of sign confusion that creates incorrect negative results. Strategy tip: When dealing with nested operations, write out each step clearly and double-check your signs. The most common errors on SHSAT order of operations questions involve sign mistakes and rushing through the sequential steps.

Question 14

Find the value of $(-3)^{2}-4(2-5)$ .

21 (correct answer)
13
-3
-21

Explanation: This question tests your understanding of order of operations and working with negative numbers and exponents. When you see an expression with multiple operations, you need to follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) carefully. Let's work through

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

step by step. First, handle what's in parentheses:

(2-5) = -3

. Next, evaluate the exponent:

(-3)^{2} = (-3) \times (-3) = 9

. Notice that the negative sign is inside the parentheses, so it gets squared too, making the result positive. Now we have

9 - 4(-3)

. Next comes multiplication:

4(-3) = -12

. Finally, subtract:

9 - (-12) = 9 + 12 = 21

. The correct answer is A) 21. Let's examine why the other answers are wrong. B) 13 likely results from incorrectly calculating

(-3)^2

-9

instead of

9

, giving you

-9 - 4(-3) = -9 + 12 = 3

, or making an error in the final arithmetic. C) -3 could come from multiple errors, such as treating

(-3)^2

-9

and then computing

-9 - 4(-3) = -9 - 12 = -21

, then making a sign error. D) -21 results from the common mistake of treating

(-3)^2

-9

, giving you

-9 - 4(-3) = -9 + 12 = 3

, or calculating

9 - 4(-3)

9 - 12 = -3

. Remember:

(-3)^2

means the negative number squared, which is positive, while

-3^2

would mean the negative of three squared.

Question 15

Compute $\dfrac{(4+2)^{2}}{3}$ .

12 (correct answer)
24
36
6

Explanation: This question tests your understanding of order of operations (PEMDAS/BODMAS) and careful arithmetic computation. When evaluating

\dfrac{(4+2)^{2}}{3}

, you must follow the correct sequence: parentheses first, then exponents, then division. Start by computing what's inside the parentheses:

(4+2) = 6

. Next, apply the exponent:

6^{2} = 36

. Finally, divide by 3:

\dfrac{36}{3} = 12

. Looking at the wrong answers reveals common computational errors. Choice B (24) likely comes from incorrectly computing

6^{2} = 24

instead of 36, or from making an arithmetic mistake in the final division. Choice C (36) represents stopping after finding

6^{2} = 36

but forgetting to complete the division by 3. This is a classic "incomplete calculation" trap. Choice D (6) suggests either computing just the parentheses

(4+2) = 6

and stopping there, or making multiple errors that coincidentally yield 6. The correct answer is A (12), which follows from the complete and accurate calculation:

\dfrac{(4+2)^{2}}{3} = \dfrac{6^{2}}{3} = \dfrac{36}{3} = 12

. Strategy tip: On order of operations problems, write out each step clearly and don't skip ahead mentally. Many students make errors by trying to do too much at once. Also, when you see answer choices that represent intermediate steps in your calculation (like 6 and 36 here), that's a signal to double-check that you've completed the entire problem.

Question 16

Evaluate $\dfrac{(2+3)(4-1)}{2^{2}}$ .

3.75 (correct answer)
6
7.5
12

Explanation: When you see a complex fraction with multiple operations, always follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Start by evaluating what's inside the parentheses:

(2+3) = 5

and

(4-1) = 3

. Next, handle the exponent in the denominator:

2^2 = 4

. Now your expression becomes

\frac{5 \times 3}{4} = \frac{15}{4}

. To convert this improper fraction to a decimal, divide:

15 ÷ 4 = 3.75

. So the answer is A) 3.75. Let's see where the wrong answers come from. Choice B) 6 likely results from incorrectly calculating the denominator as 2 instead of

2^2 = 4

, giving

\frac{15}{2} = 7.5

, then making an arithmetic error. Choice C) 7.5 comes from that same denominator mistake: treating

2^2

as just 2, so

\frac{15}{2} = 7.5

. Choice D) 12 probably comes from multiplying the numerator results without dividing by the denominator at all:

5 \times 3 = 15

, then making a calculation error, or possibly adding instead of multiplying:

(2+3) + (4-1) + 2^2 = 5 + 3 + 4 = 12

. Remember: when you see exponents mixed with other operations, don't rush. Exponents come before multiplication and division in the order of operations, and

2^2

means

2 \times 2 = 4

, not just 2. Double-check your fraction-to-decimal conversion by multiplying back.

Question 17

What is the value of $-2^{3}+3^{2}$ ?

1 (correct answer)
-1
17
-17

Explanation: This question tests your understanding of order of operations and how negative signs interact with exponents—a common source of confusion on standardized tests. Let's work through

-2^{3}+3^{2}

step by step. The key insight is recognizing that

-2^{3}

means "the negative of

2^{3}

," not "negative 2, cubed." According to order of operations, exponents come before multiplication (and applying a negative sign is multiplication by -1). First, calculate the exponents:

2^{3} = 8

and

3^{2} = 9

. Then apply the negative sign:

-2^{3} = -8

. Finally, add:

-8 + 9 = 1

. Looking at the wrong answers: Choice B (-1) likely comes from calculating

-8 + 9

incorrectly or from misunderstanding the order of operations. Choice C (17) suggests someone calculated

(-2)^{3} + 3^{2} = -8 + 9

but then made an error, possibly getting

8 + 9 = 17

by dropping the negative. Choice D (-17) indicates the student correctly found

8 + 9 = 17

but incorrectly applied a negative sign to the final result. The correct answer is A) 1. Study tip: When you see a negative sign before an exponent without parentheses, remember that the exponent applies only to the number, then you apply the negative. If the problem meant "negative 2, cubed," it would be written as

(-2)^{3}

. This distinction frequently appears on the SHSAT, so practice identifying it.

Question 18

What is the value of $\dfrac{9-3}{2}+4(1.5)$ ?

9 (correct answer)
6
4.5
12

Explanation: This problem tests your ability to apply the order of operations (PEMDAS) correctly when evaluating expressions with multiple operations. Let's work through

\dfrac{9-3}{2}+4(1.5)

step by step. First, handle what's inside the parentheses and fraction bar:

9-3=6

, so we have

\dfrac{6}{2}+4(1.5)

. Next, perform division and multiplication from left to right:

\dfrac{6}{2}=3

and

4(1.5)=6

. Finally, add the results:

3+6=9

. Looking at the wrong answers: Choice B (6) likely comes from only calculating one part of the expression, such as just

\dfrac{9-3}{2}=3

and

4(1.5)=6

, then choosing the larger value instead of adding them. Choice C (4.5) might result from incorrectly calculating

4(1.5)

4+1.5

instead of

4 \times 1.5

, giving

3+1.5=4.5

. Choice D (12) could come from multiplying the two parts instead of adding them:

3 \times 4=12

, or from incorrectly computing

\dfrac{9-3}{2}+4(1.5)

\dfrac{9-3}{2+4}(1.5)

. The correct answer is A (9). Study tip: When evaluating expressions with multiple operations, write out each step clearly and double-check that you're following PEMDAS correctly. The most common errors on these problems come from rushing through the order of operations or making small arithmetic mistakes.

Question 19

Compute $\dfrac{2+4}{3}\times(7-2^{2})$ .

6 (correct answer)
4
3
9

Explanation: When you encounter an expression with multiple operations like this, success depends on following the correct order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Let's work through

\dfrac{2+4}{3}\times(7-2^{2})

step by step. First, handle what's inside parentheses and the fraction's numerator. In the numerator:

2+4=6

. In the second parentheses, you need the exponent first:

2^{2}=4

, then

7-4=3

. So now you have

\dfrac{6}{3}\times 3

. Next, perform the division:

\dfrac{6}{3}=2

. Finally, multiply:

2\times 3=6

. Looking at the answer choices, (A) 6 is correct. The wrong answers likely come from order of operations errors. (B) 4 might result from calculating

2^{2}=4

and stopping there, or from incorrectly combining terms. (C) 3 could come from evaluating just the second parentheses

(7-2^{2})=3

or making an arithmetic mistake in the final steps. (D) 9 might result from adding instead of multiplying the final terms, giving

2+3+4=9

, or from other calculation errors. The key strategy here is to slow down and carefully apply PEMDAS. Many students rush through order of operations problems and make careless mistakes. Write out each step clearly, and double-check that you're handling exponents before subtraction and completing all operations inside parentheses before moving to multiplication.

Question 20

Find the value of $\sqrt{25}+\dfrac{3^{2}}{3}$ .

8 (correct answer)
10
6
5

Explanation: This question tests your ability to evaluate expressions involving square roots and exponents. When you see mixed operations like this, handle each part separately before combining them. Let's break down

\sqrt{25}+\dfrac{3^{2}}{3}

step by step. First, evaluate

\sqrt{25}

. Since

5 \times 5 = 25

, we have

\sqrt{25} = 5

. Next, simplify

\dfrac{3^{2}}{3}

. Calculate the numerator:

3^{2} = 3 \times 3 = 9

. So we have

\dfrac{9}{3} = 3

. Now add the results:

5 + 3 = 8

. The answer is A) 8. Let's examine why the other choices are incorrect. Choice B) 10 likely comes from incorrectly calculating

\sqrt{25} = 10

or making an arithmetic error in the addition. Choice C) 6 might result from computing

\dfrac{3^{2}}{3} = \dfrac{9}{3} = 3

correctly but then miscalculating

\sqrt{25} = 1

or making an addition mistake. Choice D) 5 occurs when you correctly find

\sqrt{25} = 5

but then either forget to add the second term entirely or incorrectly assume

\dfrac{3^{2}}{3} = 0

. Strategy tip: For multi-part expressions, work through each component methodically before combining. Double-check basic computations like perfect squares (

\sqrt{25} = 5

\sqrt{16} = 4

, etc.) and remember that

\dfrac{a^{n}}{a} = a^{n-1}

, so

\dfrac{3^{2}}{3} = 3^{1} = 3