Math Placement Test
MA102 - Introductory Algebra II
This course is the second in a series, which leads to Intermediate and College Algebra. Admission requires an Academic or Placement Test, or completion of MA101 with a grade of "C" or better. MA102 is worth four credits towards graduation.
MA102 assumes that students have a good understanding of basic mathematical and algebraic skills and their applications, polynomials, and first degree factoring. It involves a study of real number systems, variable expressions and solving equations.
Listed below is the material which you are expected to understand. It is essentially the material covered in the MA101 course.
Chapter 1
A. To use inequality symbols with integers
B. To use opposites and absolute value
C. To add integers
D. To subtract integers
E. To multiply integers
F. To divide integers
G. To write a rational number in simplest form as a decimal
H. To convert between percents, fractions, and decimals
I. To add or subtract rational numbers
J. To multiply or divide rational numbers
K. To evaluate exponential expressions
L. To use the Order of Operations Agreement to simplify expressions
A sample of each of these objectives follows:
A. To use inequality symbols with integers
Which elements of the set {-1, 3, -5, 7, 0] are greater than 1? Ans = 3, 7
B. To use opposites and absolute value
What is the additive inverse of -7? What is the absolute value of |-5|? Ans = 7, 5
C. To add integers
31 + (-17) + 4 + (-9) = ? Ans = 9
D. To subtract integers
31 - (-17) - 4 - (-9) = ? Ans = 53
E. To multiply integers
(-2) x 4 x (-3) x 3 x (-1) = ? Ans = -72
F. To divide integers
Ans -2 Ans G. To write a rational number in simplest form as a decimal
H. To convert between percents, fractions and decimals
I. To add or subtract rational numbers
Ans 1 12 8 J. To multiply or divide rational numbers
3 ÷ 9 = ? x 2.61 = - 8.9523 = 8.95 K. To evaluate exponential expressions
L. To use the Order of Operations Agreement to simplify expressions
> -> (> -> )> +> (> => ?> > Ans = 31 > 48
Chapter 2
A. To evaluate a variable expression
B. To simplify a variable expression using the Properties of Addition
C. To simplify a variable expression using the Properties of Multiplication
D. To simplify a variable expression using the Distributive Property
E. To simplify general variable expressions
F. To translate a verbal expression into a variable expression, given the variable
G. To translate a verbal expression into a variable expression and then simplify
A sample of each of these objectives follows:
A. To evaluate a variable expression
Evaluate 2(x2 + y2) - 3(x - y2) when x = 3, and y = -2. Ans: 29
B. To simplify a variable expression using the Properties of Addition
Simplify 3a + 2b - 2a - 3b + 5a. Ans: 6a - b
C. To simplify a variable expression using the Properties of Multiplication
Simplify (3m2)(2m)3(m). Ans: 24m6;D. To simplify a variable expression using the Distributive Property
Simplify 3p2(2p2 - 3p + 2). Ans: 6p4 - 9p3 + 6p2E. To simplify general variable expressions
Simplify 2x[3x2 - 2(-x3 + x - 1)]. Ans: 4x4 + 6x3 - 4x + 4F. To translate a verbal expression into a variable expression, given the variable
Translate "the quotient of 15 less than h and 5" into a variable expression. Ans (h - 15) ÷ 5G. To translate a verbal expression into a variable expression and then simplify
Translate "a number added to the product of 3 and the square of the number" into a verbal expression then simplify. Ans: 3n2 + n
Chapter 3
A. To determine whether a given number is a solution of an equation
B. To solve an equation of the form x + a = b
C. To solve an equation of the form ax = b
D. To solve application problems using the basic percent equation
E. To solve an equation of the form ax + b = c
F. To solve an equation of the form ax + b = cx + d
G. To solve an equation using parentheses
H. To solve integer problems
I. To translate a sentence into an equation and solve
J. To solve perimeter problems
K. To solve problems involving angles formed by intersecting lines
L. To solve problems using the angles of a triangle
M. To solve value mixture problems
N. To solve percent mixture problems
O. To solve uniform motion problems
A sample of each of these objectives follows:
A. To determine whether a given number is a solution of an equation
Is 2 a solution of 4x4 = 6x3 - 4x + 24. Ans: yes
B. To solve an equation of the form x + a = b
Solve
2 = y - 1 5 3 6 6 C. To solve an equation of the form ax = b
Solve
= 6 -9 D. To solve application problems using the basic percent equation
16 is 80% of what number? Ans: 20
E. To solve an equation of the form ax + b = c
Solve
2 x - 3 = 1 3 6 F. To solve an equation of the form ax + b = cx + d
Solve 3k - 3 = 2k + 3, Ans k = 6
G. To solve an equation using parentheses
Solve 3[2k - 3(2 - 4k) = 21k + 3, Ans k = 1
H. To solve integer problems
Find three consecutive integers whose sum is negative 9. Ans -2, -3, -4
I. To translate a sentence into an equation and solve
The cost of electricity is $0.08 for the first 300 kWh and $0.06 for each kWh after that. During a typical winter month, a family pays $288.66 for their electrical bill. How much electricity did they use? Ans: 4711 kWh
J. To solve perimeter problems
Problems involving perimeters of triangles, rectangles, and squares
K. To solve problems involving angles formed by intersecting lines
Various problems using supplementary angles, complimentary angles, vertical angles, adjacent angles alternate angles, interior angles, exterior angles and corresponding angles.
L. To solve problems using the angles of a triangle
Sum of the Angles of a Triangle Theorem (SATT) - and relationship to exterior angles.
M. To solve value mixture problems
An importer buys one type of coffee at $2.00 per pound and a second type at $2.50 per pound. He makes a mixture that sells for $2.10 per pound. How much of each type did he use? Ans: 1 : 4 ratio
N. To solve percent mixture problems
A bottle of acetic acid is 80% pure hydrogen acetate. How much of this bottle is needed to make 4 L of household vinegar which contains 3% hydrogen acetate? Ans: 0.15 L
O. To solve uniform motion problems
One plane leaves Detroit at the same time a plane leaves from Sault Ste Marie. The one from Detroit is travelling at twice the speed of the one from Sault Ste Marie. If the two cities are 300 miles apart, and they pass each other in two thirds of an hour, how fast was each plane travelling? Ans 150 mph and 75 mph
Chapter 4
A. To add polynomials
B. To subtract polynomials
C. To multiply polynomials
D. To simplify powers of polynomials
E. To multiply a polynomial by a monomial
F. To multiply two polynomials
G. To multiply two binomials
H. To multiply binomials that have special products
I. To divide monomials
J. To write a number in scientific notation
K. To divide a polynomial by a monomial
L. To divide polynomials
A sample of each of these objectives follows:
A. To add polynomials
(4x4 + 6x3 + 4x + 4) + (2x4 - 6x - 1) + (x4 - x3 - 3x + 7), Ans: 7x4 + 5x3 - 5x + 11B. To subtract polynomials
(4x4 + 6x3 + 4x + 4) - (2x4 - 6x - 1) - (x4 - x3 - 3x + 7), Ans: x4 + 7x3 - 13x - 2C. To multiply polynomials
Multiply (4p3q4)(3p2q5) , Ans: (12p5q9D. To simplify powers of polynomials
Simplify (4p3q4)3, Ans: 64p9q12E. To multiply a polynomial by a monomial
Simplify - 2x4 (4x4 - 6x3 + 4x - 4), Ans - 8x8 + 12x7 - 8x5 + 8x4
F. To multiply two polynomials
(4x2 - 6x - 4) (x + 4), Ans: 4x3 + 10x2 - 28x - 16
G.To multiply two binomials (use FOIL)
(2m + 3) ( 3m - 4) = 6m2 + m - 12
H. To multiply binomials that have special products
(a + b)2 = a2 + 2ab + b2 , (a + b) (a - b) = a2 - b2I. To divide monomials
(xa )(x)b = xa +b , x a ÷ xb = xa - b , x 0 = 1 , x -n = 1 / x n , (xa)b = xab, (xayb)c = xacybc
J. To write a number in scientific notations
602 000 000 = 6.02 x 108
K. To divide a polynomial by a monomial
(3m3 + 6m2 - 9m) ÷ 3m = m2 + 2m - 3
L. To divide polynomials
(x2 - 5x + 8) ÷ (x - 2) = x - 3 with 2 remainder
Chapter 5
To factor a monomial from a polynomial
To factor by grouping
To factor a trinomial in the form x2 + bx + c
To factor completely
To factor a trinomial of the form ax2 + bx + c by using trial factors
To factor a trinomial of the form ax2 + bx + c by grouping
To factor the difference of two squares and perfect-square trinomials
To factor completely
To solve equations by factoring
To solve application problems
To factor a trinomial of the form ax2 + bx + c by using trial factors
L. To factor a trinomial of the form ax2 + bx + c by grouping
M. To factor the difference of two squares and perfect-square trinomials
N. To factor completely
O. To solve equations by factoring
P. To solve application problems
A sample of each of these objectives follows:
A. To factor a monomial from a polynomial
Factor 8x2 + 12x , Ans 4x ( 2x + 3)B. To factor by grouping
6x2 - 9x - 4xy + 6y = 3x( 2x - 3 ) - 2y ( 2x - 3 ) = (2x - 3 )( 3x - 2y )C. To factor a trinomial in the form x2 + bx + c
x2 - 4x -12 = ( x - 6 )( x + 2 )
D. To factor completely
4x2 - 16x - 48 = 4 ( x - 6 )( x + 2 )
E. To factor a trinomial of the form ax2 + bx + c by using trial factors
3x2 + x - 2 = ( x + 1 )( 3x - 2 )F. To factor a trinomial of the form ax2 + bx + c by grouping
6y2 - 5y - 6 = 6y2 + 4y - 9y - 6 = . . . = ( 2y - 3 )( 3y + 2)G. To factor the difference of two squares and perfect-square trinomials
36a2 - 4b2 = ( 6a + 2b )( 6a - 2b ) , 36a2 - 24ab + 4b2 = ( 6a - 2b )2H. To factor completely
4a2b2 - 12ab2 + 9b2 = b2(2a - 3 )2I. To solve equations by factoring
a ( a - 5 ) = 0 , Solution: a = 0 or a = 5
PLACEMENT TEST
Our purpose in having you write a placement test is to attempt to put you in the highest level math course that you can comfortably handle. If you feel you understand the above objectives and examples quite well, then click on the MA102 Test button below to write the MA102 Placement Test.
To look at the course objectives for any of the other courses, click on the respective course buttons.