Intermediate Algebra Math Review Sheets
1. Solve each formula for the specified variable
I =prt for t
for b
for d
2. Applications
The bus fare in a city is $1.25. People who use the bus have the option of
purchasing a monthly coupon book for $21.00. With the coupon book, the fare is
reduced to $0.50. Determine the number o times in a month the bus must be used
so that the total monthly cost without the coupon book is the same as the total
monthly cost with the coupon book.
Including 8% sales tax, an inn charges $162 per night. Find the inn’s nightly
cost
before the tax is added.
3. Determine whether each relation is a function. Give the domain and the range
for
each relation.
{(3,10), (4, 10), (5, 10)}
{(13, 14), (15, 16), (13, 17)}
4. Find the indicated function value given 
5. Use the vertical line test to identify if each graph is a function or not.
6. Find the domain of the given function. State the domain
in both set builder and
interval notation
Set builder:
Interval:
7. Given
Find each of the following
What is the domain of
8. Determine the coefficient of each term, the degree of
each term, the degree of the
polynomial, the leading term, and the leading coefficient of the polynomial.
| Term | Coefficient | Degree |
9. Perform the indicated operation (add, subtract or multiply):
10. Factor
11. Solve for x
12. Find the domain of the given rational function. State
the domain in both set builder
and interval notaion.
set Builder:
Interval:
13. Simplify:
14. Multiply
15. Divide
16.Add then simplify
17. Subtract then simplify
18. Simplify
19.Use long division to divide
20. Use synthetic division to divide
21. Solve
22. Solve for R
3. Application
Working alone, two people can clean their house in 3 hours and 6 hours
respectively. They have agreed to clean together so that they can finish in time
to
watch a TV program that begins in 1 ½ hours. How long will it take them to
clean the house together? Can they finish before the program starts?
24. Find the indicated root, or state that the expression is not a real number
25. Find the indicated function values for the function
If the
function value is not a real number and does not exist, so state.
26. Find the domain of the given function. State in set
builder and interval notation.
Set Builder:
Interval:
27. Simplify each expression. Assume that each variable
can represent any real number,
include absolute value bars where necessary.
28. Use radical notation to rewrite each expression. Simplify if possible.
29.Rewrite each expression with rational exponents
30.Use properties of rational exponents to simplify each expression
31. Use rational exponents to simplify each expression. If
rational exponents appear
after simplifying, write the answer in radical notation.
32. Use the product rule to multiply
33. Simplify by factoring. Assume that all variables in
radicand represent positive real
numbers
34.Multiply and simplify. Assume that all variables in
radicand represent positive real
numbers
35. Add or subtract as indicated. Assume that all
variables in radicand represent positive
real numbers
36.Simplify by using the quotient rule.
37. Divide and simplify
38. Multiply. If possible, simplify any radical expressions that appear in the product.
39. Rationalize the denominator and simplify
40. Solve the radical equation
41. Perform the indicated operation. Write the result in the form a + bi
42. Simplify each expression
43. Solve by the square room property.
44. Complete the square for the given binomial. Then
factor the resulting perfect square
trinomial.
45. Solve by completing the square
46. Solve by using the quadratic formula
47.Compute the discriminant. Then determine the number and
type of solutions for the
given equation
48. Solve each equation by the method of your choice.
49. Use the vertex and intercepts to sketch the graph of
each quadratic function. Give
the equation for the parabola’s axis of symmetry.
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50. Application
A model rocket is launched upward from a platform 30 feet above the ground.
he quadratic function 
models the rocket’s
height above
e ground, s(t), in feet, t seconds after it was launched. After how many seconds
does the rocket reach its maximum height? What is the maximum height?
