These questions seem pretty basic to me. So I'm skeptical about having these questions in SAT.

Take a look through some practice tests. Tests 5, 6, 7, and 8 were all used as actual SAT tests, and they should have multiple of these "solve for a variable" questions per math section. A lot of SAT questions do indeed seem basic once you get to know them, and that's because they are. They can just seem intimidating to some test-takers because they haven't seen the equation before, or don't know what to do with so many letters and variables instead of a numerical expression.

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SAT

Course: SAT > Unit 6

Lesson 4: Passport to Advanced Math: lessons by skill

Solving quadratic equations | Lesson
Interpreting nonlinear expressions | Lesson
Quadratic and exponential word problems | Lesson
Manipulating quadratic and exponential expressions | Lesson
Radicals and rational exponents | Lesson
Radical and rational equations | Lesson
Operations with rational expressions | Lesson
Operations with polynomials | Lesson
Polynomial factors and graphs | Lesson
Graphing quadratic functions | Lesson
Graphing exponential functions | Lesson
Linear and quadratic systems | Lesson
Structure in expressions | Lesson
Isolating quantities | Lesson
Function Notation | Lesson

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Passport to Advanced Math: lessons by skill

Isolating quantities | Lesson

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What is "Isolating quantities" and how frequently do these questions appear on the test?

Many real-world scenarios can be described using equations and formulas with multiple variables. For example, the formula for the area,

A

A, of a rectangle with length

\ell

ell and width

w

w is

A=\ell w

A, equals, ell, w. In this form, area (

A

A) is isolated: it is alone on one side of the equation.

If we wanted to find the equivalent equation, but with

\ell

ell isolated, we could divide both sides of the equation by

w

w, giving us

\ell =\dfrac{A}{w}

ell, equals, start fraction, A, divided by, w, end fraction.

On your official SAT, you'll likely see 0 to 2 questions that test your ability to isolate a variable in an equation with two or more variables.

You can learn anything. Let's do this!

How do I isolate quantities?

Manipulating formulas: temperature

Khan Academy video wrapper

Manipulating formulas: temperature

See video transcript

Like solving equations, but with more variables

Isolating quantities is similar to solving equations. However, instead of ending up with a variable equal to a constant, we end up with a variable equal to an expression containing other variables. In fact, if you've rewritten a linear equation like

x+y=1

x, plus, y, equals, 1 in slope-intercept form, then you've already isolated

y

y by rearranging a linear equation!

[Show me more!]

The most important thing to remember is that the rearranged equation will remain equivalent to the original equation only if we always treat both sides equally: whenever we do something to one side, we must do the exact same thing to the other side.

To isolate a quantity in an equation or formula:

Write down the original equation. If needed, translate the word problem or given context into an equation.
Perform the same operation on both sides of the equation to begin isolating the desired quantity.
Repeat Step 2 until the desired quantity is isolated.

Let's look at some examples!

A physics student uses the formula

E_\text{k}=\dfrac{1}{2}mv^2

E, start subscript, start text, k, end text, end subscript, equals, start fraction, 1, divided by, 2, end fraction, m, v, squared to calculate the kinetic energy in joules,

E_\text{k}

E, start subscript, start text, k, end text, end subscript, of an object with a mass of

m

m kilograms traveling at a speed of

v

v meters per second. What is

v

v in terms of

E_\text{k}

E, start subscript, start text, k, end text, end subscript and

m

m ?

[Show me!]

The distance

d

d traveled by an object moving at constant velocity is found by multiplying the velocity

v

v of the subject by time

t

t. Write an equation that gives the time

t

t in terms of

d

d and

v

[Show me!]

Try it!

try: identify the steps to isolate a variable

V=\pi r^2 h

V, equals, pi, r, squared, h

The equation above shows the volume

V

V of a right cylinder with radius

r

r and height

h

To rewrite the equation to isolate

r

r, we must first isolate

r^2

r, squared. To do so, we

both sides of the equation by

\pi h

pi, h.

Next, to isolate

r

r, we

both sides of the equation.

Which of the following correctly expresses

r

r ?

Choose 1 answer:

(Choice A)
r, equals, left parenthesis, V, pi, h, right parenthesis, squared
(Choice B)
r, equals, square root of, V, pi, h, end square root
(Choice C)
r, equals, left parenthesis, start fraction, V, divided by, pi, h, end fraction, right parenthesis, squared
(Choice D)
r, equals, square root of, start fraction, V, divided by, pi, h, end fraction, end square root

Your turn!

practice: isolate a quantity in one step

Giselle uses the formula

I=Prt

I, equals, P, r, t to calculate

I

I, the simple interest in dollars, she collects from a loan of

P

P dollars at an interest rate of

r

r per month over a period of

t

t months. Which of the following expresses

P

P in terms of the other variables?

Choose 1 answer:

(Choice A)
P, equals, I, r, t
(Choice B)
P, equals, I, minus, r, t
(Choice C)
P, equals, start fraction, I, divided by, r, t, end fraction
(Choice D)
P, equals, start fraction, r, t, divided by, I, end fraction

practice: write an equation, then isolate a quantity

The perimeter

P

P of a rectangle is found by multiplying the sum of the rectangle's length

l

l and width

w

w by

2

2. Which of the following equations gives the width

w

w in terms of

P

P and

l

l ?

Choose 1 answer:

(Choice A)
w, equals, P, minus, l
(Choice B)
w, equals, P, minus, start fraction, l, divided by, 2, end fraction
(Choice C)
w, equals, start fraction, P, divided by, 2, end fraction, minus, l
(Choice D)
w, equals, start fraction, P, minus, l, divided by, 2, end fraction

practice: isolate a quantity with exponents

F=\dfrac{Gm_1m_2}{d^2}

F, equals, start fraction, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, d, squared, end fraction

The equation above shows the

F

F, the gravitational force between two objects, in terms of

G

G, the gravitational constant,

m_1

m, start subscript, 1, end subscript and

m_2

m, start subscript, 2, end subscript, the masses of the two objects, and

d

d, the distance between the two objects. Which of the following correctly expresses

d

d in terms of

F

G

m_1

m, start subscript, 1, end subscript, and

m_2

m, start subscript, 2, end subscript ?

Choose 1 answer:

(Choice A)
d, equals, start fraction, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, F, end fraction
(Choice B)
d, equals, square root of, F, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, end square root
(Choice C)
d, equals, square root of, start fraction, F, divided by, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, end fraction, end square root
(Choice D)
d, equals, square root of, start fraction, G, m, start subscript, 1, end subscript, m, start subscript, 2, end subscript, divided by, F, end fraction, end square root

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fahadbinislampcc
Posted a year ago. Direct link to fahadbinislampcc's post “These questions seem pret...”
These questions seem pretty basic to me.
So I'm skeptical about having these questions in SAT.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- Hecretary Bird
  Posted a year ago. Direct link to Hecretary Bird's post “Take a look through some ...”
  Take a look through some practice tests. Tests 5, 6, 7, and 8 were all used as actual SAT tests, and they should have multiple of these "solve for a variable" questions per math section. A lot of SAT questions do indeed seem basic once you get to know them, and that's because they are. They can just seem intimidating to some test-takers because they haven't seen the equation before, or don't know what to do with so many letters and variables instead of a numerical expression.
  Button navigates to signup page
  (12 votes)