Algebra Worksheets

Algebra Worksheets
  • Page 1
 1.  
The volume of a sphere is given by the formula V = 43πr3. Find the radius of a sphere whose volume is 141 7 m3?
a.
15 m
b.
17 m
c.
1.7 m
d.
1.5 m


Solution:

V = 43πr3

3V / 4= πr3

3V4π = r3

r3 = 3V4π

r = 3V4π3
[Solve the formula for r.]

r = 3 × 14174 × 2273

r = 3 × 99 × 74 × 22 × 73

r = 2783

r =1.5

The radius of the sphere is 1.5 m.


Correct answer : (4)
 2.  
The kinetic energy, E, of a body moving with a velocity v is given by the equation E = 12mv2, where m is the mass of the body. Find the mass of a body moving with a velocity 40 m/s and having an energy of 3000 N.
a.
4.05 kg
b.
3.75 kg
c.
3.65 kg
d.
6.75 kg


Solution:

E = 12mv2

2E = mv2

2Ev2 = m
[Solve the equation for m.]

m = 2 × 300040 × 40
[Substitute: E = 3000, v = 40.]

m = 2×7540 = 3.75

The mass of the body is 3.75 kg.


Correct answer : (2)
 3.  
Solve the formula V = 1 3πr2h for the variable h. Indicate any restrictions on the values of the variables.
a.
h = 3+r2πV, V ≠ 0
b.
h = 2πrV3, r ≠ 0
c.
h = 3Vπr2, r ≠ 0
d.
h = V3πr2, r ≠ 0


Solution:

V = 1 / 3πr2h

3V = πr2h
[Multiply both sides by 3.]

3Vπr2 = h
[Divide both sides by πr2.]

h = 3Vπr2
[Symmetry property.]

The solution is h = 3Vπr2, r ≠ 0
[If r = 0, denominator becomes zero. Division by zero is undefined.]


Correct answer : (3)
 4.  
Solve the formula p = 2(l + b) for b.
a.
b = p2 + l
b.
b = 2p
c.
b = 2pl
d.
b = p2 - l


Solution:

p = 2(l + b)

p2 = l + b
[Divide both sides by 2.]

p2 - l = b
[Subtract l from both sides.]

b = p2 - l
[Symmetry property.]


Correct answer : (4)
 5.  
Solve the formula v = u + at for a. Indicate any restrictions on the values of the variables.
a.
a = v + ut, t ≠ 0
b.
a = v - ut, t ≠ 0
c.
a = (v + u)t, v ≠ 0
d.
a = u + vt, t ≠ 0


Solution:

v = u + at

v - u = at
[Subtract u from both sides.]

v - ut = a
[Divide both sides by t.]

a = v - ut
[Symmetry property.]

The solution is a = v - ut, t ≠ 0
[The solution must exclude values of a variable that make the denominator zero.]


Correct answer : (2)
 6.  
Solve 1f = 1u + 1v for u.
a.
u = f-vfv
b.
u = -1f - 1v
c.
u = f+vfv
d.
u = fvv-f


Solution:

1f = 1u + 1v

1f - 1v = 1u
[Subtract 1v from both sides.]

v-ffv = 1u
[Simplify.]

fvv-f = u


Correct answer : (4)
 7.  
Solve s = 2πr(r + h) for h and indicate any restrictions on the values of the variables.
a.
h = 4s, s ≠ 0
b.
h = s + 2πrr, r ≠ 0
c.
h = 2πrs
d.
h = s2πr - r, r ≠ 0


Solution:

s = 2πr(r + h)

s2πr = r + h
[Divide both sides by 2πr.]

s2πr - r = h
[Subtract r from both sides.]

h = s2πr - r, r ≠ 0
[Symmetry property.]


Correct answer : (4)
 8.  
Solve P = 100I RT for I.
a.
I = 100PRT
b.
I = 100PRT
c.
I = PRT100
d.
I = 100 + PRT


Solution:

P = 100I / RT

PRT = 100I
[Multiply RT on both sides.]

PRT100 = I
[Divide both sides by 100.]

I = PRT100
[Symmetry property.]


Correct answer : (3)
 9.  
Solve V = π(R - s)h for s.
a.
s = R + Vπh
b.
s = R + Vπh
c.
s = R - Vπh
d.
s = R - V2πh2


Solution:

V = π(R - s)h

Vπh = R - s
[Divide both sides by πh.]

Vπh - R = - s
[Subtract R from both sides.]

R - Vπh = s
[Multiply both sides by -1.]

s = R - Vπh


Correct answer : (3)
 10.  
Solve y = mx + c for m.
a.
m = xc + y
b.
m = x(y + c)
c.
m = y - cx
d.
m = y + cx


Solution:

y = mx + c

y - c = mx
[Subtract c from both sides.]

y - cx = m
[Divide both sides by x.]


Correct answer : (3)

More Algebra Worksheets
Algebraic Expressions Worksheets Solving Compound Sentences with Inequalities Worksheet
Solving Inequalities (using Addition and Subtraction) Worksheet Solving Inequalities (using Multiplication and Division) Worksheet
One Step Equations Worksheets Solving Inequalities Using Addition or Subtraction Worksheet
Solving Inequalities Using Multiplication or Division Worksheet Solving Inequalities with Addition and Subtraction Worksheet
Solve Equation Worksheet Solve Equations with Variables on both Sides Worksheet
Solve Linear Equation Worksheet Solve Multi Step Equations Worksheet
Solve Quadratic Equation Worksheet Solve Quadratic Equations by Finding Square Roots Worksheet
Solve System of Equations Worksheet Solve the Equation by Completing the Square Worksheet
Solving a Quadratic Equation by Completing the Square Worksheet Solving Addition and Subtraction Equations Worksheet
Solving Equations in Quadratic Form Worksheet Solving Equations Using Addition and Subtraction Worksheet
Solving Equations with One Variable Worksheet Solving Equations with Variables on both Sides Worksheet
Solving Equations Worksheet Solving Linear Equations Worksheet
Solving Linear Systems (using Linear Combinations) Worksheet Solving Linear Systems (using Substitution Method) Worksheet
Solving Linear Systems by Elimination Worksheet Solving Linear Systems by Linear Combinations Worksheet
Solving Linear Systems by Substitution Worksheet Solving Multi Step Equations Worksheet
*AP and SAT are registered trademarks of the College Board.