REVIEW - SOPHIA

​REVIEW SESSIONS

By Rodley Lina

Multiple Choice

A type of variation that involves 3 or more quantities that may vary directly.

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Multiple Choice

Determine if there is a constant of variation. If so, explain what it represents.

The equation y = 24 x represents the number of bottles of water y in x packages.

• The constant of variation is 24. This means that there are 24 bottles of water in each package.

• There is no constant of variation. The number of bottles varies per package.

Multiple Choice

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k? 

• 121
• 4
• 100
• 6

Multiple Choice

Suppose y varies jointly as x & z. 
If y = -180 when z = 15
and x = -3,
then find y when x = 7 and z = -5.

• -140
• 140
• -4
• 4

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3
• Yes; 3
• Yes; 5
• No

Multiple Choice

This graph represents what kind of variation?

• Direct variation

• Inverse variation

• Joint variation

• Combined variation

Multiple Choice

If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.

• 126

• 132

• 148

• 154

Multiple Choice

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

• 4

• 5

• 8

• 10

Multiple Choice

If y varies jointly as a and b and inversely as the square root of c, and y = 12 when a = 3, b = 2, and c = 64, find y when a = 5, b = 2, and c = 25.

• 8

• 16

• 24

• 32

Multiple Choice

If x varies directly as y and inversely as z, and x = 10 when y = 5 and z = 3, for what value of z will x = 3 and y = 4?

• 2

• 4

• 6

• 8

Multiple Choice

z varies inversely with x and directly with y. If x = 4, y = 48 and z = -2, find x when z = 8 and y = 96.

• -2

• -1

• 0

• 1

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Simplify  $$\frac{t^9}{t^2}$$  

• $$t^{-7}$$  

• $$t^7$$  

• $$1^7$$  

• $$1^{-7}$$  

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Multiple Choice

√36n⁴

• 6n
• 6n⁴
• 6n²√2
• 6n²

Multiple Choice

Simplify the radical...

√20a²b⁴

• 2ab²√5

• 4ab²√5

• 5ab²√2

• 2a²b²√5

Multiple Choice

$$\sqrt{48x^7y^3z^4}$$  

• $$4x^3yz^2\sqrt{3xy}$$  

• $$16x^3yz^2\sqrt{3xy}$$  

• $$3x^2yz\sqrt{3xy}$$  

Multiple Choice

$$\sqrt{128a^5b^8}$$  

• $$2a^2b^4\sqrt{2a}$$  

• $$2a^2b^4\sqrt{8a}$$  

• $$8a^2b^4\sqrt{2a}$$  

Multiple Select

$$\sqrt{m^7a^{11}t^5h^9}$$  

• $$m^3a^5t^2h^3\sqrt{math}$$  

• $$m^3a^5t^2h^4\sqrt{math}$$  

• $$m^3a^6t^2h^3\sqrt{math}$$  

• $$math\sqrt{math}$$  

Multiple Choice

∜ $$a^{12}b^7c$$  

• $$a^3b$$  ∜bc

• $$a^3b\ ∜b^3c$$  

• $$a^3b\ ∜b^2c$$  

Multiple Choice

√675

• 225√3
• 15√5
• 3√15
• 15√3

Multiple Choice

What is the missing exponent of the expression $$\sqrt[3]{y^?}=y^4$$  

• 12

• 8

• 4

• 2

Multiple Choice

$$\sqrt[2]{16^2x^2y^2}\ =\ 4xy$$  

• TRUE

• FALSE

Multiple Choice

Which whole number is equal to the expression $$64^{\frac{2}{3}}$$  

• 128

• 64

• 16

Fill in the Blank

What is the missing coefficient of the $$?\ \cdot\sqrt[2]{64x^2}=16x$$  

Multiple Choice

Simplify the expression $$\sqrt[]{288\ x^3y^9}=?$$  

• $$12xy^4\ \sqrt[]{2xy}$$  

• $$2xy\ \sqrt[]{12xy^4}$$  

• $$12xy^4\sqrt[]{xy}$$  

Multiple Choice

The cube root of $$x^{15}=?$$  

• $$x^{15}$$  

• $$x^5$$  

• $$x^3$$  

• $$x$$  

Multiple Choice

$$2\ \sqrt{7}\ -5\ \sqrt{7}$$  

• $$3\sqrt{7}$$  

• $$-3\sqrt{7}$$  

• $$7\sqrt{7}$$  

Multiple Choice

1. You can combine radicals with different indices.

• TRUE

• FALSE

Multiple Choice

• 11√5
• 11√10
• 5√5
• 12√10

Multiple Choice

• 7√3
• Can't Simplify
• 6√15
• 6√3

Multiple Choice

• 17√2
• 9√1
• 9
• 9√2

Multiple Choice

Add:  $$3\sqrt{7}\ -2\sqrt{28}+10\sqrt{4}$$

• $$-\sqrt{7}+10\sqrt{4}$$  

• $$-9\sqrt{11}$$  

• $$20-\sqrt{7}$$  

• Cannot simplify any further

Multiple Choice

Add: $$6\sqrt{24}-24\sqrt{6}$$  

• $$-12\sqrt{6}$$  

• $$-18\sqrt{18}$$  

• $$18\sqrt{6}$$  

• $$12\sqrt{6}$$  

Multiple Choice

(√3)( √15) =

• 3√5

• 5√3

• 2√7

• √17

Multiple Choice

(√5)(√10)

• 50

• 2√5

• 5√2

• 5√10

Multiple Choice

Simplify √75

• 10√2

• 10√3

• 5√2

• 5√3

Multiple Choice

$$\left(\sqrt{3}\right)\left(\sqrt{15}\right)$$   

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

• $$2\sqrt{7}$$  

• $$\sqrt{17}$$  

Multiple Choice

$$\ Simplify:\ \ \ 6\sqrt{2}\cdot5\sqrt{14}$$  

• $$32\sqrt{7}$$  

• $$60\sqrt{7}$$  

• $$2\sqrt{7}$$  

• $$30\sqrt{7}$$  

Multiple Choice

2. Adding and subtracting radical expressions is very much similar to adding and subtracting similar terms of polynomials.

• TRUE

• FALSE

Multiple Choice

3. In the process of multiplying radicals, there are only three cases to be considered: (a) To multiply radicals of the same order. (b) To multiply binomials involving radicals. (c) To multiply radicals of different orders.

• TRUE

• FALSE

Multiple Choice

4. Rationalizing is necessary for the division of radicals.

• TRUE

• FALSE

Multiple Choice

5.

$$\frac{\sqrt{5}}{\sqrt{8}}=\frac{\sqrt{5}}{2\sqrt{10}}$$  

• TRUE

• FALSE

Multiple Choice

$$\sqrt{18}\cdot\sqrt{14}\ is\ equal\ to\ 6\sqrt{7}$$  

• TRUE

• FALSE

Multiple Choice

The product of the square root of two positive integers is equal to the square root of the product of these integers.

• TRUE

• FALSE

Multiple Choice

The process of removing the radical from the numerator is called rationalizing the denominator.

• TRUE

• FALSE

Multiple Choice

To multiply radical expressions with more than one term, use the associative property to remove parenthesis.

• TRUE

• FALSE

Multiple Choice

We add or subtract the indices and retain the radicand when we combine similar radicals.

• TRUE

• FALSE

Multiple Choice

$$2\sqrt{8}\ +\ 3\sqrt{2}$$  

• $$4\sqrt{2}$$  

• $$7\sqrt{2}$$  

• $$5\sqrt{2}$$  

Multiple Choice

$$5\sqrt{6}\ +\ 8\ \sqrt{6}-\ 3\sqrt{6}$$  

• $$10\sqrt{6}$$  

• $$16\sqrt{6}$$  

• $$\sqrt{6}$$  

Multiple Choice

$$_3\sqrt{81}\ +\ _3\sqrt{3}$$  

• $$4_{\ \ 3}\sqrt{3}$$  

• $$3\ _3\sqrt{3}$$  

• $$2\ _3\sqrt{3}$$  

Multiple Choice

$$\sqrt{12}\cdot\ \sqrt{2}$$  

• $$\sqrt{24}$$  

• $$2\sqrt{6}$$  

• $$4\sqrt{6}$$  

Multiple Choice

$$\sqrt{2x^6y^5}\cdot\ \sqrt{2x^2y}$$  

• $$2x^4y^3$$  

• $$4x^8y^6$$  

• $$\sqrt{2x^4y^3}$$  

Multiple Choice

$$2\ \ _3\sqrt{8}\ -3\ _3\sqrt{2}$$  

• $$_3\sqrt{2}$$  

• $$4-_{\ 3}\sqrt{2}$$  

• $$\sqrt{2}$$  

Multiple Select

Like radicals are radicals with the same indices and same radicands.

• TRUE

• FALSE

Multiple Select

$$\sqrt{x\ }\cdot\ \sqrt{y}\ =\ \sqrt{xy}$$  

• TRUE

• FALSE

Multiple Select

$$\sqrt{\frac{a}{b}}=\ \frac{\sqrt{a}}{\sqrt{b}}$$  

• TRUE

• FALSE

Multiple Choice

$$\frac{\sqrt{16x^5}}{\sqrt{2x}}$$  

• $$\sqrt{8x^4}$$  

• $$2x\sqrt{2}$$  

• $$2x^2\sqrt{2}$$  

Multiple Select

To add and subtract radicals, add and subtract like radicals or similar radicals.

• TRUE

• FALSE

Multiple Choice

$$\sqrt{\frac{1}{2}}$$  

• $$\frac{1}{\sqrt{2}}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$\frac{\sqrt{2}}{4}$$  

Multiple Choice

$$\sqrt{9x^5yz^3}\cdot\ \sqrt{2xyz}$$  

• $$3x^3yz^2\ \sqrt{2}$$  

• $$18x^6y^2z^4$$  

• $$9x^3yz^2\ \sqrt{2}$$  

Multiple Choice

$$\frac{\sqrt{9xy}}{\sqrt{2x}}$$  

• $$\frac{x\sqrt{18y}}{2x}$$  

• $$\frac{\sqrt{18x^2y}}{2x}$$  

• $$\frac{3\sqrt{2y}}{2}$$  

Multiple Choice

√72

• 7√9
• 4√6
• 6√2
• 3√4

Multiple Choice

Simplify the following radical: 2√24

• 4√6
• 2√6
• 24√2
• 4√4

Multiple Choice

5√80

• 20√5
• 4√5
• 5√20
• 4√5

Multiple Choice

Simplify:

• 1/5

• 20/100

• 2/10

• 1/√25

Multiple Choice

Simplify

• 9
• √9
• 3√9
• can't simplify

Multiple Choice

√16

• 4
• 8
• 16
• 64

Multiple Choice

Simplify:
√200

• 10√2
• 2√10
• 50√2
• 2√50

Multiple Choice

Simplify:
√45

• 9√5
• 3√5
• 5√9
• 3√15

Multiple Choice

Simplify:
√96

• 16√6
• 6√16
• 9√6
• 4√6

Multiple Choice

√125

• 5√5
• 25√5
• 5√25
• 5√2

Multiple Choice

Simplify √60

• 2√15
• 12
• 4√15
• 3√5

Multiple Choice

In simplest radical form,
√80 is equivalent to

• 16√5
• 2√20
• 4√5
• 8√5

Multiple Choice

Simplify the following radical: √150

• 5√15
• 5√2
• 5√6
• 15√5

Multiple Choice

-4√1000

• -400
• -40
• -400√100
• -40√100

Multiple Choice

$$\left(x^{2s}\right)^3$$  

Simplify

• $$x^{2s+3}$$  

• $$x^{5s}$$  

• $$x^{6s}$$  

• $$\frac{1}{x^{6s}}$$  

Multiple Choice

$$3^x\cdot2^x$$  

Simplify

• $$6^x$$  

• $$5^{2x}$$  

• $$5^x$$  

• $$6^{2x}$$  

Multiple Choice

$$\frac{2^c}{4}$$  

Write as a single power of 2.

• $$2^{-2c}$$  

• $$\frac{1}{2^{c+2}}$$  

• $$2^{c+2}$$  

• $$2^{c-2}$$  

Fill in the Blank

$$\left(2018^{2018}\right)^0$$  

Find the value of

Multiple Choice

$$\sqrt{5^3}$$  

Rewrite using a fraction as an exponent.

• $$5^{\frac{3}{2}}$$  

• $$5^{\frac{3}{1}}$$  

• $$5^{\frac{2}{3}}$$  

• $$5^{\frac{1}{3}}$$  

Multiple Choice

$$\left(\frac{6}{7}\right)^{-2}$$  

Evaluate

• $$\frac{36}{49}$$  

• $$\frac{49}{36}$$  

• $$\frac{14}{12}$$  

• $$\frac{12}{14}$$  

Multiple Choice

$$\left(2x\right)^5\cdot\left(3x\right)^2$$  

Write without brackets:

• $$288x^{10}$$  

• $$288x^7$$  

• $$90x^{10}$$  

• $$90x^7$$  

Multiple Choice

$$r^2\cdot r^5\cdot r^4$$  

Simplify

• $$r^{40}$$  

• $$3r^{11}$$  

• $$r^{11}$$  

• $$3r^{40}$$  

Multiple Choice

$$\frac{w^7}{w^p\cdot w^3}$$  

Simplify

• $$w^{p-4}$$  

• $$w^{4-p}$$  

• $$w^{10+p}$$  

• $$w^{p-10}$$  

Multiple Choice

(2ab)³

• 2³a³b³
• 2ab³
• 6a³b³
• 6ab

Multiple Choice

Simplify:
(x³)(x²)

• x⁵
• x⁶
• x
• x^1.5

Multiple Choice

• -6c⁵
• -6c
• 6c
• -6c⁶

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷
• -18x⁷
• 18x¹⁰
• 3x⁷

Multiple Choice

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

• 5⁷
• 5⁶
• 7⁵
• 5

Multiple Choice

• 4⁹
• 4⁴⁴
• 4²¹
• 4¹⁵

Multiple Choice

How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?

• 5⁷
• 5⁶
• 7⁵
• 5

Multiple Choice

• 4⁹
• 4⁴⁴
• 4²¹
• 4¹⁵

Multiple Choice

• a⁷
• a¹⁰
• a³
• a^-3

Multiple Choice

Simplify the following expression:
$$\frac{30y^{12}}{15y^2}$$  

• 2y²⁴

• 2¹⁰

• 2y¹⁰

• 2y¹⁴

Multiple Choice

$$\left(3x^4\right)^5$$  

• $$15x^9$$  

• $$243x^{20}$$  

• $$15x^{20}$$  

• $$243x^9$$  

Multiple Choice

$$\left(7x^3\right)^0$$  

• 1

• 7

• $$21x^3$$  

• $$x^{10}$$  

Multiple Choice

$$\frac{x^8}{x^5}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

• $$x^{13}$$  

• $$x^{40}$$  

Multiple Choice

Simplify $$3\left[\left(x^2\right)^3\right]^0$$  

• 0

• 1

• 3

• $$3x^6$$  

Multiple Choice

A single frog can finish 20 flies in 4 days. If 2 frog will feed on 20 flies they can finish it in 2 days. Therefore this represents what type of variation?

• Inverse variation

• Direct variation

• Combined variation

• Joint variation

Multiple Choice

A pair of shoes cost PHP500. If Lily buys 2 pairs of shoes, she will spend PHP1,000. If she buys 3 pairs of shoes, she will spend PHP1,500. Therefore this represents what type of variation?

• Combined variation

• Joint variation

• Inverse variation

• Direct variation

Multiple Choice

This graph represents what kind of variation?

• Joint variation

• Direct variation

• Combined variation

• Inverse variation

Multiple Choice

If c is inversely proportional to d, and c=20 when d=5, find the value of c when d=25.

• 100 & 4

• 200 & 25

• 250 & 15

• 500 & 5

Multiple Choice

This represents what type of variation?

• Combined variation

• Indirect variation

• Joint variation

• Direct variation

Multiple Choice

j varies jointly with l and m. If m=15 when j=150 and l=5, find m when j=45and l=20.

• 4 & 2/3

• 5 & 3/4

• 7 & 8/9

• 2 & 9/8

Multiple Choice

c= kad/b : This represents what kind of variation?

• Direct variation

• Inverse variation

• Combined variation

• Joint variation

Multiple Choice

If e varies directly as f and inversely as g, and e=22 when f=11 and g=5, find the value of g when e=3 and f=6.

• 5 & 10

• 10 & 20

• 15 & 30

• 20 & 45

Multiple Choice

If g is directly proportional to h, and g=12 when h=6, find the value of g when h=17.

• 4 & 36

• 1 & 37

• 2 & 34

• 6 & 38

Multiple Choice

This type of variation states that the two quantities increase at the same time or decrease at the same time.

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Multiple Choice

The cost c varies directly as the number of n pencils is written as

• c = kn

• k = cn

• n = k/c

• c = k/n

Multiple Choice

The speed r of a moving object is inversely proportional to the time t travelled is written as

• r = kt

• r = k/t

• t = kr

• t = r/k

Multiple Choice

Which of the following types of variation states that the decrease of one quantity results to the increase of the other quantity?

• Direct Variation

• Inverse Variaton

• Joint Variation

• Combined Variation

Multiple Choice

If y varies directly as x and y = 24, when x = 3, then what is the value of k?

• 4

• 6

• 8

• 72

Multiple Choice

Which of the following phrases illustrate an inverse variation?

• The area of the wall to the amount of paint used to cover it

• The amount of money raised in a concert to the number of tickets sold

• The time a teacher spends in checking papers to the number of students

• The age of a used car to its resale value

Multiple Choice

If s varies directly as t and inversely as v, then which of the following equations describes the relation among the three variables s, t, and v?

• s = k / tv

• s = kv / t

• 1/s = kt/ v

• s = kt / v

Multiple Choice

Which of the following is the graph of a direct square variation?

• Straight Line

• Quadratic Curve

• Broken Line

• Hyperbola

Multiple Choice

This is a variation where one quantity varies directly to other quantity and inversely to the other quantity.

• Direct Variation

• Inverse Variation

• Joint Variaiton

• Combined Variation