SAMPLE PLACEMENT TEST FOR MATHEMATICS

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 value.
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 numbers	Change the sign of the second number and then add	(−3) − (−13) = (−3) + (+13) =10
Multiplying and dividing signed numbers	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.
Removing Parentheses	Use the distributive law to remove parentheses: a(b + c) = ab + ac
Combining like terms	Combine terms that have identical letters and exponents
Order of operations	Remember the proper order of operations: 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 symbols	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 equation.	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 equation. 4. Divide both sides of the equation by the coefficient of the desired variable. This decision may involve other variables. 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 step. 2. If you divide both sides of the inequality by a positive number, the direction of the inequality is not reversed. 3. If you divide both sides of the inequality by a negative number, the direction of the inequality is reversed.
Multiplying monomials	1. Multiply the numerical coefficients. 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 base.
Exponent of zero
Raising a power to a power	1. Raise the numerical coefficient to the power outside the parentheses. 2. Multiply the exponent outside the parentheses by the exponent inside the parentheses.
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
Subtracting polynomials	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 polynomials	Use the distributive property:
Multiplying two binomials	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 answer.
Multiplying two polynomials	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 numbers.
Multiply three or more polynomials	1. Multiply any two polynomials. 2. Multiply the result by any remaining polynomials.
Dividing a polynomial by a monomial	1. Divide each term of the polynomial by the monomial. 2. When dividing variables use the property:
Dividing a polynomial by a binomial	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 binomial. 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.