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Sample Questions for Arithmetic Skills

1. Estimate to the nearest hundred: 31,253−1275

2. Round to the nearest hundredth: 6.4562

3. Find the missing number:

4. Write as a mixed number

5. Combine:

6. Divide:

7. Combine: 1.3 + 1.8 + 2.6 + 7.2 + 0.8

8. Multiply: 0.002× 4.31

9. Divide: 3.186 ÷ 0.03

10. Mr. Carr is installing wall-to-wall carpeting in a room that measuresft. by 9 ft. How much will it
cost Mr. Carr if he purchases carpet priced at $26.00 per square yard?

11. Write as a percentage: 3/8

12. Find 250% of 36

13. In a given university, 720 of the 960 new students will study algebra during their first year. What
percentage of the new students will study algebra during their first year?

14. An investment pays 8% simple interest per year. If the investment earns $84 interest in the first year,
then how much money was originally invested?

15. If Mary wants to finish a 16 kilometer race in no more that 2 hours, then what is the minimum
distance in kilometers that she should run every 15 minutes?

Answers For Sample Arithmetic Questions

Sample Questions for Elementary Algebra Skills

1. Combine Like terms: 13a −15b − a + 2b

2. Multiply: (2x −1)(4x +1)

3. Solve for x: 5(2x − 3) − (x + 3) = 0

4. Find all the factors of

5. Factor out the greatest common factor:

6. Divide:

7. Simplify:

8. Multiply:

9. Simplify:

10. The average of x, y, and z is 80. If two of the numbers are 74 and 78, then what is the other number?

11. Find all the solutions of 4( x + 3) (3x − 2) = 0

12. Find the value of x in the solution of the following system of equations:

13. In which quadrants (I, II, III, and/or IV) will you find ordered pairs for which x > -3 and y<0?

14. Find the values of x for which − x − 3 >12

15. What are all values of x for which

16. Factor:

17. Solve:

20. If Sam walks 650 meters in x minutes then write an algebraic expression which represents the number of
minutes it will take Sam to walk 1500 meters at the same average rate.

Answers For Sample Elementary Algebra Questions

Sample Questions for College Level Mathematics

1. Simplify each fraction:

2. Combine the following polynomial:

3. Express with positive exponents:

4. Today’s fastest modem computers can perform one operation in 1 x 10-8 second. How many operations
can such a computer perform in 1 minute? Answer in scientific notation.

5. Remove the greatest common factor:

6. Solve for the root(s) of the quadratic equation:

7. Simplify the rational expression:

8. Solve and graph on a number line: 4(2 − x)≤3

9. Solve for h:

10. Factor:

11. Find the slope of the line 4x − 3y − 7 = 0

12. Line p has a slope of What is the slope of a line parallel to line p? What is the slope of a line
perpendicular to line p?

13. Find the equation of a line that passes through (−1, 6) and (2, 3).

14. Find the indicated values for a function: f (x) = 3x − 7

a) f (− 2) b) f (4)

15. To the nearest thousandth, how much error can be tolerated in the length of a wire that is supposed to be
2.57 centimeters long? Specifications allow an error of no more than 0.25%

Answers for Sample College-Level Mathematics Questions

operations in one minute

A Brief Review of Math Skills

Topic Procedure Examples
Absolute Value The absolute value of a number is the
distance between that number and zero
on the number line. The absolute
value of any number will be positive
or zero.
Adding signed
numbers with the
same sign
If the signs are the same, add the
absolute values of the numbers. Use
the common sign in the answer
Adding several
signed numbers
with opposite signs
If the signs are different:
1. Find the difference of the larger
absolute value and the smaller.
2. Give the answer the sign of the
number having the larger absolute
Adding several
signed numbers
When adding several signed numbers,
separate them into two groups by
common sign, Find the sum of all the
positives and all the negatives.
Combine these two subtotals by the
method described above.
Subtracting signed
Change the sign of the second number
and then add
(−3) − (−13) = (−3) + (+13) =10
Multiplying and
dividing signed
1. If the two numbers have the same
sign, multiply (or divide). The result
is always positive.
2. If the two numbers have different
signs, multiply (or divide) as indicated.
The result is always negative
Exponent form The base tells you what number is
being multiplied. The exponent tells
you how many times this number is
used as a factor.
Raising a negative
number to a power
When the base is negative, the result is
positive for even exponents, and
negative for odd exponents.
Use the distributive law to remove
a(b + c) = ab + ac
Combining like
Combine terms that have identical
letters and exponents
Order of operations Remember the proper order of
1. Operations inside Parentheses () and
brackets []
2. Exponents
3. Multiplication and Division from
left to right.
4. Addition and Subtraction from left
to right.
Substituting into
variable expressions
1. Replace each letter by the numerical
value given.
2. Follow the order of operations in
evaluating the expression
Using formulas 1. Replace each variable in the
formula by the given values.
2. Evaluate the expression.
3. Label units carefully
Find the area of a circle with radius feet.
Use with approximatley 3.14.

The area of the circleis approximately
50.24 square feet.
Removing grouping
1. Remove innermost grouping
symbols first.
2. Continue until all grouping
symbols are removed.
3. Combine like elements.
Solving equations
without parentheses
or fractions
1. On each side of the equation,
collect like terms if possible.
2. Add or subtract terms on both sides
of the equation in order to get all
terms with the variable on one side of
the equation.
3. Add or subtract a value on both
sides of the equation to get all terms
not containing the variable on the
other side of the equation.
4. Divide both sides of the equations
by the coefficient of the variable.
5. If possible, simplify solution.
6. Check your solution by substituting
the obtained value into the original
Solve for X:

Check: Is x = −3 a solution

Solving equations
with parentheses
and/or fractions
1. Remove any parentheses.
2. Simplify, if possible.
3. If fractions exist, multiply all terms
on both sides by the lowest common
denominator of all the fractions.
4. Now follow the remaining steps of
solving an equation without
parentheses or fractions.

*Remember to check your solution (see
previous example)
Solving formulas 1. Remove any parentheses and
simplify if possible.
2. If fractions exist, multiply all terms
on both sides by the LCD, which may
be a variable.
3. Add or subtract terms on both sides
of the equation in order to get all
terms containing the desired variable
on one side of the equation and all
other terms on the opposite side of the
4. Divide both sides of the equation by
the coefficient of the desired variable.
This decision may involve other
5. Simplify, if possible.
6. Check your solution by substituting
the obtained expression into the
original equation.
Solve for z:

Solving Inequalities 1. Follow the steps for solving a first-degree
equation up until the division
2. If you divide both sides of the
inequality by a positive number, the
direction of the inequality is not
3. If you divide both sides of the
inequality by a negative number, the
direction of the inequality is reversed.

1. Multiply the numerical
2. Add the exponents of a given base.

Dividing monomials

1. Divide or reduce the fraction
created by the quotient of the
numerical coefficients.
2. Subtract the exponents of a given

Exponent of zero
Raising a power to a

1. Raise the numerical coefficient to
the power outside the parentheses.
2. Multiply the exponent outside the
parentheses by the exponent inside the

Negative exponents If x ≠ 0 and y ≠ 0, then

Write with positive exponents

Scientific notation A number is written in scientific
notation if it is the form:
where 1 ≤ a <10 and n is an integer
Add polynomials To add two polynomials, we add the
respective like term
To subtract polynomials, change all
signs of the second polynomial and
add the result to the first polynomial:
(a) − (b) = (a) + (−b)
Multiplying a
monomial by a
Use the distributive property:

Multiplying two
1. The product of the sum and
difference of the same two values
yields the difference of their squares.

2. The square of a binomial yields a
trinomial: the square of the first, plus
twice the product of first and second,
plus the square of the second.

3. Use FOIL for other binomial
multiplication. The middle terms can
often be combined, giving a trinomial

Multiplying two
To multiply two polynomials,
multiply each term of one by each
term of the other. This method is
similar to the multiplication of many-digit
Multiply three or
more polynomials
1. Multiply any two polynomials.
2. Multiply the result by any
remaining polynomials.
Dividing a
polynomial by a
1. Divide each term of the polynomial
by the monomial.
2. When dividing variables use the

Dividing a
polynomial by a
1. Place the terms of the polynomial
and binomial in the descending order.
Insert a 0 for any missing term.
2. Divide the first term of the
polynomial by the first term of the
3. Multiply the partial answer by the
binomial, and subtract the results from
the first two terms of the polynomial.
Bring down the next term to obtain a
new polynomial.
4. Divide the new polynomial by the
binomial using the process described
in step 2.
5. Continue dividing, multiplying,
and subtracting until the reminder is at
a lower power than the variable in the
first term of the binomial divisor.