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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Exponents

(x^3y^6z)(x^2yz^3)=

Possible Answers:

x^6y^6z^3

x^5y^7z^4

x^3y^6z^3

x^2y^7z^3

x^5y^7z^3

Correct answer:

x^5y^7z^4

Explanation:

(x³y⁶z)(x²yz³)

The paraentheses are irrelevant. Rearrange to combine like terms.

x³x²y⁶y¹z¹z³

When you multiply variables with exponents, simply add the exponents together.

x³⁺²y⁶⁺¹z¹⁺³

x⁵y⁷z⁴

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Example Question #14 : Exponents

If an original bacteria colony contains six organisms, and triples every hour, how many organisms are there after 7 hours?

Possible Answers:

4374

13,122

39,366

107,008

Correct answer:

13,122

Explanation:

To find the answer we can apply the equation of population $P=6\cdot 3^{n}$ where is the number of hours.

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Example Question #15 : Exponents

Simplify: $2a^{2}b(ab^{2} - a^{2}b)$

Possible Answers:

$2a^{3}b^{3} - 2a^{4}b^{2}$

$2ab^{2} - 2a^{2}b$

$2a^{3}b^{3} + a^{2}b^{2}$

$ab^{2} - a^{2}b$

$2a^{2}b + 2a^{4}b^{2}$

Correct answer:

$2a^{3}b^{3} - 2a^{4}b^{2}$

Explanation:

Use the distributive property: $a(b+c)=ab+ac$ . When we multiply variables with exponents, we keep the same base and add the exponents: $a^{m}a^{n} = a^{m+n}$

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Example Question #16 : Exponents

Simplify:

$(6x^{2})^{2}\times y^{2} + xyz =$

Possible Answers:

$36x^{5}y^{3}z$

$6x^{4}y^{2}z + xyz$

$36x^{4}y^{2}+xyz$

$\textbf{cannot be simplified}$

$36x^{4}y^{2}$

Correct answer:

$36x^{4}y^{2}+xyz$

Explanation:

$(6x^{2})^{2} = 6^{2}x^{4} = 36x^{4}$

$36x^{4}\times y^{2} = 36x^{4}y^{2}$

We cannot combine $36x^{4}y^{2}$ with $xyz$ , so $(6x^{2})^{2}\times y^{2} + xyz =36x^{4}y^{2}+xyz$ .

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Example Question #17 : Exponents

If c^2=15 , then what is the value of c^4 ?

Possible Answers:

$\sqrt{15}$

125

110

225

Correct answer:

225

Explanation:

c⁴ is equal to (c²)(c²).

We know c² = 15. Plugging in this value gives us c⁴ = (15)(15) = 225.

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Example Question #20 : Exponents

If and are nonzero numbers such that a^2 = b^3 , which of the following is equivalent to a^6 ?

Possible Answers:

b^9

$b^{11}$

b^7

b^8

b^6

Correct answer:

b^9

Explanation:

For this problem, we need to make use of the property of exponents, which states that (x^y)^z = x^y^z.

We are given a² but are asked to find a⁶.

Let's raise both sides of the equation to the third power, so that we will end up with a⁶ on the left side.

(a²)³ = (b³)³

Now, according to the property of exponents mentioned before, we can multiply the exponents.

a^(2*3) = b^(3*3)

a⁶ = b⁹

The answer is b⁹.

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Example Question #2201 : Sat Mathematics

If and are positive integers and $2^{2a}(2^{2b})=16$ , what is the value of a +b ?

Possible Answers:

Correct answer:

Explanation:

The question tells us that 2^2a ( 2^2b)= 16.

We can rewrite 16 as 2⁴, giving us 2^2a ( 2^2b)= 2⁴.

When terms with the same base are multipled, their exponents can be added:

2^{(2a +2b)}= 2⁴

Since the base is the same on both sides of the equation, we can equate the exponents:

2a +2b = 4

2(a + b) = 4

a + b = 2

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Example Question #1561 : Gre Quantitative Reasoning

(b * b⁴* b⁷)^1/2/(b³ * b^x) = b⁵

If b is not negative then x = ?

Possible Answers:

–1

–2

Correct answer:

–2

Explanation:

Simplifying the equation gives b⁶/(b^3+x) = b⁵.

In order to satisfy this case, x must be equal to –2.

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Example Question #1562 : Gre Quantitative Reasoning

If〖7/8〗ⁿ= √(〖7/8〗⁵),then what is the value of n?

Possible Answers:

²/₅

√5

¹/₅

⁵/₂

Correct answer:

⁵/₂

Explanation:

7/8 is being raised to the 5th power and to the ¹/₂ power at the same time. We multiply these to find n.

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Example Question #1563 : Gre Quantitative Reasoning

Simplify: (x³ * 2x⁴ * 5y + 4y² + 3y²)/y

Possible Answers:

10x⁷ + 7y³

10x⁷ + 7y

None of the other answers

10x¹¹ + 7y³

10x⁷y + 7y²

Correct answer:

10x⁷ + 7y

Explanation:

Let's do each of these separately:

x³ * 2x⁴ * 5y = 2 * 5 * x³* x⁴* y = 10 * x⁷ * y = 10x⁷y

4y² + 3y² = 7y²

Now, rewrite what we have so far:

(10x⁷y + 7y²)/y

There are several options for reducing this. Remember that when we divide, we can "distribute" the denominator through to each member. That means we can rewrite this as:

(10x⁷y)/y + (7y²)/y

Subtract the y exponents values in each term to get:

10x⁷ + 7y

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #13 : Exponents

Example Question #14 : Exponents

Example Question #15 : Exponents

Example Question #16 : Exponents

Example Question #17 : Exponents

Example Question #20 : Exponents

Example Question #2201 : Sat Mathematics

Example Question #1561 : Gre Quantitative Reasoning

Example Question #1562 : Gre Quantitative Reasoning

Example Question #1563 : Gre Quantitative Reasoning

All SAT Math Resources

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