GMAT QUANT 5

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(1/2)(b)(h)

Area of a triangle

A triangle with two equal sides and two equal angles is...

An isosceles triangle

(b)(h)

(f) Area of a parallelogram

(π)(r2)

(f) Area of a circle

(2)(π)(r)

(f) Circumference of a circle

(l)(w)(h)

(f) Volume of a rectangular solid

(f) Volume of a cube

(π)(r2)(h)

(f) Volume of a cylinder

180(n-2) n=number of sides

(f) Sum of interior angles of a polygon

Even exponents always result in...

A positive integer

An exponential expression with a base of 1 =

1

An exponential expression with a base of -1 =

-1 if the exponent is odd, 1 if the exponent is even

When the base of an exponential expression is a positive proper fraction, the value of the expression __________ as the exponent increases

decreases

When the base of an exponential expression is a positive decimal between 0 and 1, the value of the expression _________ as the exponent increases

decreases

(ab)ⁿ

aⁿbⁿ

(a+b)ⁿ ≠

aⁿ + bⁿ

aⁿ + bⁿ ≠

(a+b)ⁿ

nᵃnᵇ =

nᵃᶧᵇ

nᵃᶧᵇ =

nᵃnᵇ

When multiplying two exponential terms with the same base...

Combine exponents by adding

When can you combine exponents via addition?

When you are multiplying exponential terms with the same base

nᵃ/nᵇ =

nᵃ⁻ᵇ

nᵃ⁻ᵇ =

nᵃ/nᵇ

When dividing two exponential terms with the same base...

Combine exponents by subtracting

When can you combine exponents via subtraction?

When you are dividing exponential terms with the same base

(nᵃ)ᵇ =

nᵃᵇ

When raising a power to a power...

Combine exponents by multiplying

When can you combine exponents via multiplication?

When you are raising one power by another power

nˉᵃ =

1/nᵃ

1/nᵃ =

nˉᵃ

(n/m)ˉᵃ =

(m/n)ᵃ = mᵃ/nᵃ

(m/n)ᵃ = mᵃ/nᵃ =

(n/m)ˉᵃ

A negative exponent implies...

The reciprocal of the base

Any base raised to the first power is...

The base

What exponent is always implied on a number?

1

Any nonzero base raised to the power of 0 is...

1

0⁰ =

Indeterminate

0⁰ ≠

1

For fractional exponents, the base number is raised to the _______ and taken to the root of the ________.

raise: numerator, root: denominator

nᵃʹᵇ =

ᵇ√(nᵃ) = (ᵇ√n)ᵃ

ᵇ√(nᵃ) =

(ᵇ√n)ᵃ = nᵃ/ᵇ

(ᵇ√n)ᵃ =

nᵃʹᵇ = ᵇ√(nᵃ)

(xᵃ)(xᵇ) =

xᵃ+ᵇ

xᵃ+ᵇ =

(xᵃ)(xᵇ)

(c⁴)(c⁵) =

c⁹

(3⁴)(3⁵) =

3⁹

5(5ⁿ) =

5ⁿ+¹

(aⁿ)(bⁿ) =

(ab)ⁿ

(ab)ⁿ =

(aⁿ)(bⁿ)

(2⁴)(3⁴) = (simplify)

6⁴

12⁵ = (simplify)

(4⁵)(3⁵) = (2¹⁰)(3⁵)

2⁵/2¹¹ = (simplify)

1/2ˉ⁶ = 2⁶

x¹⁰/x⁶ =

x⁴

(a/b)ⁿ =

aⁿ/bⁿ

aⁿ/bⁿ =

(a/b)ⁿ

(10/2)⁶ = (simplify)

10⁶/2⁶ = 5⁶

3⁵/9⁵ = (simplify)

(3/9)⁵ = (1/3)⁵ = 3ˉ⁵

aᵐⁿ =

(aᵐ)ⁿ = (aⁿ)ᵐ

(3⁴)⁵ =

(3⁵)⁴ = 3²⁰

xˉᵃ =

1/xᵃ

1/xᵃ =

xˉᵃ

(3/2)ˉ² =

(2/3)² = 4/9

2xˉ⁴ =

2/x⁴

27⁴ʹ³ =

³√(27⁴) = (³√27)⁴ = 3⁴ = 81

³√x¹⁵ =

x¹⁵ʹ³ = x⁵

aⁿ + aⁿ + aⁿ =

3aⁿ

3⁴ + 3⁴ + 3⁴ = (simplify)

3(3⁴) = 3⁵

3ⁿ + 3ⁿ + 3ⁿ =

3(3ⁿ) = 3ⁿ⁺¹

You can simplify exponential expressions that are linked by...

multiplication or division

You can not simplify exponential expressions that are linked by...

addition or subtraction

You can simplify exponential expressions linked by multiplication/division if...

they have an exponent or base in common

(x+y)² =

x² + 2xy + y²

(x-y)² =

x² - 2xy + y²

(d) Root

Radical, Opposite of an exponent

When taking the even root of a number, only use the...

nonnegative root

Odd roots have the _____ of the base

sign

Describe the numerator and denominator of a fractional exponent

numerator = power raised, denominator = root taken

You can find the root of a number by...

Breaking the number down into prime factors

You can simplity roots by combining/separating in...

multiplication or division

(d) Imperfect square

Square root of the the number is not an integer

How do you estimate the roots of imperfect squares?

Find the two closest perfect squares. If there is a coefficient, transfer it to under the root before searching for the two closest perfect squares

(ⁿ√x) / (ⁿ√y) =

ⁿ√(x/y)

(√10) / (√5) =

√2

(³√16) / ³(√2) =

³√8 = 2

(ⁿ√x)(ⁿ√y) =

ⁿ√(xy)

(√10)(√5) =

√50

(³√24)(³√9) =

³√216 = 6

ᵇ√xᵃ =

(ᵇ√x)ᵃ = ᵇ(√xᵃ) = xᵃʹᵇ

25³ʹ² = (solve)

(√25)³ = 5³ = 125

49ˉ¹ʹ² = (solve)

1/√49 = 1/7

⁵√x¹⁵ =

x¹⁵ʹ⁵ = x³

√(x+y) =

Cannot be simplified

√x + √y =

Cannot be simplified

√(x-y) =

Cannot be simplified

√x - √y =

Cannot be simplified

1² = (solve)

1

1.4² ≈ (solve)

2

1.7²≈ (solve)

3

2.25²≈ (solve)

5

2² = (solve)

4

3² = (solve)

9

4² = (solve)

16

5² = (solve)

25

6² = (solve)

36

7² = (solve)

49

8² = (solve)

64

9² = (solve)

81

10² = (solve)

100

11² = (solve)

121

12² = (solve)

144

13² = (solve)

169

14² = (solve)

196

15² = (solve)

225

16² = (solve)

256

20² = (solve)

400

25² = (solve)

625

30² = (solve)

900

√1 = (solve)

1

√2 ≈ (solve)

1.4

√3 ≈ (solve)

1.7

√5 ≈ (solve)

2.25

√4 = (solve)

2

√9 = (solve)

3

√16 = (solve)

4

√25 = (solve)

5

√36 = (solve)

6

√49 = (solve)

7

√64 = (solve)

8

√81 = (solve)

9

√100 = (solve)

10

√121 = (solve)

11

√144 = (solve)

12

√169 = (solve)

13

√225 = (solve)

15

√256 = (solve)

16

√400 = (solve)

20

√625 = (solve)

25

√900 = (solve)

30

1³ = (solve)

1

2³ = (solve)

8

3³ = (solve)

27

4³ = (solve)

64

5³ = (solve)

125

³√1 = (solve)

1

³√8 = (solve)

2

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