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Correlation of ALEKS objectives, Pie 1, and ALEKS Online Worktext
....An important idea is "order of operations"
...Another basic concept is "using the distributive property and combining like terms"
..This site will help you understand the relationship among sets of numbers
..An important skill set is the ability to solve linear equations
..To help you solve inequalities
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Beginning Algebra |
119 Objectives |
Sample Problem |
Worktext Section |
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I. Real Numbers |
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A. Operations, substitution and evaluation |
arith605: Plotting rational numbers on a number line | ||||||||||||
| arith071: Absolute value of a number | |||||||||||||
| arith104: Operations with absolute value | |||||||||||||
| arith106: Signed fraction addition | |||||||||||||
| arith105: Signed fraction multiplication | |||||||||||||
| arith234: Signed decimal addition | |||||||||||||
| arith047: Evaluating expressions with exponents: Problem type 1 | |||||||||||||
| arith049: Evaluating expressions with exponents: Problem type 2 | |||||||||||||
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alge005: Evaluation of a linear expression in two variables |
Evaluate the
expression |
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alge004: Evaluation of a polynomial in one variable |
Evaluate the
expression |
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| arith600: Exponents and order of operations | |||||||||||||
| arith016: Square root of a perfect square | |||||||||||||
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B. Algebraic symbols |
alge015: Writing an inequality |
Write the
algebraic expression for the sentence |
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alge016: Translating sentences into linear equations |
Write the
algebraic expression for the sentence |
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alge186: Writing a compound inequality |
Write " x is greater than or equal to – 6 and less than – 4" as an algebraic expression. |
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alge602: Writing a mathematical expression |
Write an algebraic
expression to answer the question below. |
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C. Number system |
alge001: Integer and rational numbers |
For each of the two number systems, indicate all the numbers which belong to it. (Problems in ALEKS) |
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alge002: Integer, rational and irrational numbers (real) |
For each of the
four number systems, indicate all the numbers which belong to it.
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D. Properties of real numbers |
alge606: Distributive Property, simple |
Use the
Distributive Property to remove the parentheses from the following
expression: |
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alge604: Distributive Property, advanced |
Use the
Distributive Property to remove the parentheses from the following
expression: |
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alge607: Combining like terms, basic |
Simplify the
following expression: |
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| alge663: Combining like terms, advanced | |||||||||||||
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alge187: Properties of addition |
The properties of
addition are:
For each equation below, indicate the property that justifies the equation by filling in the box with the appropriate number.
6 + (b + 4) = (6
+ b) + 4 [ ] Answer:
6 + (b + 4) = (6
+ b) + 4 [ 2 ] |
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alge188: Properties of real numbers |
For each equation below, indicate the property that justifies the equation by filling in the box with the appropriate number 9 + 3 = 3 + 9 [ ]
5 + 0 = 5 [ ]
Answer: 9 + 3 = 3 + 9 [ 1 ]
5 + 0 = 5 [ 3 ]
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II. Solving Linear Equations |
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A. One occurrence of the variable |
alge010: Additive property of equality: Problem type 2 |
What is the
value of w if |
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alge226: Additive property of equality: Problem type 3 |
If 153 = 242 –
w, |
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alge802:Multiplicative property of equality with fractions |
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alge008:Multiplicative property of equality: Problem type 1 |
Solve for w: 3w = 87 |
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alge012: Multiplicative property of equality: Problem type 2 |
Solve the
following equation for t: |
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alge006: Solving a linear equation: Problem type 1 |
Solve the
following equation for t: |
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alge208: Solving a linear equation: Problem type 2 |
Solve for x:
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alge200: Solving a linear equation: Problem type 3 |
Evaluate the
expression |
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B. Several occurrences of the variable |
alge011: Solving a linear equation with several occurrences of the variable: Problem type 1 |
What is the
value of u if
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alge061: Solving a linear equation with several occurrences of the variable: Problem type 2 |
Solve for x: Write your answer as a fraction in simplest form.
Answer:
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alge013: Solving a linear equation with several occurrences of the variable: Problem type 3 |
Solve the
following equation for x : |
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alge209: Solving a linear equation with several occurrences of the variable: Problem type 4 |
Solve the
following equation for x: |
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alge179: Solving a linear equation with several occurrences of the variable: Problem type 5 |
Solve for u:
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| alge810: Introduction to algebraic symbol manipulations | |||||||||||||
| alge 160: Algebraic symbol manipulation |
The surface area S of a right prism is given by
S = 2 B + Ph, |
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C. Inequalities |
alge019: Solving a linear inequality: Problem type 1 |
Solve the inequality t – 5 < 20 for t |
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alge020: Solving a linear inequality: Problem type 2 |
Solve the
inequality |
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alge021: Solving a linear inequality: Problem type 3 |
Solve the
inequality |
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alge207: Solving a linear inequality: Problem type 4 |
Solve the
inequality
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alge017: Graphing a linear inequality on the number line |
Graph
x
>
4 on the number line.
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alge166: Graphing a compound linear inequality on the number line |
Graph the portion
of the number line containing all points for which |
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D. Applications |
alge014: Solving a word problem using a linear equation: Problem type 1 |
A total of 328
tickets were sold for the school play. The number of student tickets
sold is three times the number of adult tickets sold. How many
student tickets were sold? |
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alge219: Solving a word problem using a linear equation: Problem type 2 |
A small publishing
company is planning to produce a new self-help book. The company
needs to spend $79,744 for one-time fixed costs such as editing,
typesetting, cover design, and so on. Variable costs, including
printing and marketing, are $8.25 per book. The publisher will sell
the finished product to the bookstores at a wholesale price of
$24.25 per book. How many books must the publisher print and sell so
that the costs for production will equal the revenue from sales? Answer: Let x represent the number of books to be printed and sold. The production cost is $79,744 (for one-time fixed costs) plus $8.25 times x (the variable costs for x books). In other words, Production costs (in dollars) = 79744 + 8.25 x. The revenue from the sales of x books is $24.25 times x. Therefore, Revenue from sales (in dollars) = 24.25x. Since the production costs should be equal to the revenue from sales, we have Production costs
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| alge173: Solving a word problem using a linear equation: Problem type 3 |
Two discounted bouquets of flowers were sold for $43.34. If the discount on each bouquet of flowers was $9.28, what was the price of each bouquet of flowers before discount? (Suppose that each bouquet of flowers has the same price). |
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alge704: Solving a word problem using a linear equation: Problem type 4 |
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alge022: Word problem with linear inequalities |
The sum of two
numbers is less than 12. The second number is 6 more than the first.
What are the possible values for the first of the two numbers? |
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mstat014: Random samples and prediction
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In a magazine survey, 150 randomly selected students from several middle schools throughout the United States are asked whether they have access to a computer at home and if they have a personal e-mail account. The responses of the students are summarized in the following table:
(a) What
percentage of the students surveyed have an e-mail account?
What percentage of
the students surveyed have no computer access at home?
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| arith232: Simple interest | |||||||||||||
| arith074: Word problem on percentage: Problem type 1 | |||||||||||||
| arith031: Word problem on percentage: Problem type 2 | |||||||||||||
| stat803: Find the value for a new score that will yield a given mean | |||||||||||||
| geom300: Perimeter of square or rectangle | |||||||||||||
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geom078: Sides of polygons having the same perimeter |
A wire is first
bent into the shape of a square with side 12 cm. The wire is then
bent into the shape of an equilateral triangle. What is the length
of a side of the triangle? Answer: The wire is first bent into the following square. The perimeter P of the square gives us the length of the wire. The length of the wire is thus P = (4)(12) = 48 cm.
Afterward, the wire
is bent into an equilateral triangle. Thus, the perimeter of the
equilateral triangle is also 48cm.
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| geom019: Area of a square or rectangle | |||||||||||||
| geom217: Finding the side length of a rectangle given its perimeter or area |