Integers

1. When both integers have the same signs keep the sign and add. When the signs are different, disregard the signs, subtract the numbers, and keep the sign of the larger number.

2. Change the sign of the number being subtracted. Then add using the preceding rules.

3. Multiply as you would whole numbers. The product is positive if there are an even number of negative factors. The product is negative if there are an odd number of negative factors.

4. Forget the signs and divide. The quotient is positive if both integers have the same sign. The quotient is negative if the integers have different signs.

Formulas

Using a formula is like evaluating an expression. Just replace the variables with values. Here are some important formulas to know. The area of a figure if the amount of space it occupies in two dimensions. The perimeter of a figure is the distance around the figure. Use 3.14 for , b —- base, h — height, s — side, l — length, w — width, r — radius, d — diameter.

Figure	Area	Perimeter/Circumference
Triangle	1/2bh	s1 + s + s3
Square	s^2	4s
Rectangle	lw	2l + 2w
Parallelogram	bh	2s + 2h
Trapezoid	1/2h(b1 + b2)	b1 + b2 + s1 + s2
Circle	r^2	2r or d

Figure	Volume
Cube	s^3
Rectangular Prism	lwh
Sphere	4/3r^3

Equations

The whole idea of solving equations is to isolate the variable on one side of the equal sign. The value of the variable is what’s on the other side of the equal sign. Substitute your answer into the original equation to check your solution. Solving two-step equations add or subtract before you multiply or divide: 3x – 6 = 24.

READING AND INTERPRETING GRAPHS

Examples of the four main types of graphs are shown below. The Pictograph uses symbols to stand for numbers. The Bar Graph represents information by the length of a bar. The graph below shows the rain­fall during two months in each of five towns. The Line Graph plots information against two axes. The Circle Graph represents an entire amount. In the graph below, each wedge-shaped piece of the graph represents the percent of tax money spent on different town services.

POST-READING ACTIVITIES

Say what you’ve learned from the texts about:

1) the special strategies for answering the mathematics multiple-choice items;

2) the concepts and topics do you need to know to pass mathematics part of the LAST;

3) the review sections of the mathematics part of the LAST.

Vocabulary practice

Ex. 1. Make sure you understand and can explain the following terms and notions:

Mathematics, Algebra, Geometry, Statistics, Probability, problem, mode, mean, product, expression, operation, factor.

Ex. 2. Translate the LAST test objectives (SUBAREA I: 01-03) followed by focus statements that provide examples of the range, type, and level of content that may appear on the test (for a list of test objectives, see APPENDIX B).

Ex. 3. Complete the following sentences with the appropriate word.

1. … are used to represent numbers between 0 and 1.

2. Descriptive … are used to explain or describe a set of numbers.

3. … numbers such as 1^st, 2^nd, 9^th, and 18^th tell about order.

4. The … is the number that occurs most often.

5. The negative whole numbers and the positive whole numbers are called … .

Ex. 4. Select the term that seems odd.

1. sequence — equivalence — series — succession

2. common fraction — simple fraction — vulgar fraction — complex fraction

3. digit — number — decimal — numeral

4. median — medial — mode — middle

5. ratio — progression — fraction — proportion

Ex. 5. Supply the sentences with required words; if necessary change their grammatical forms.

perimeter variable volume square area formula

1. Using a … is like evaluating an expression.

2. Just replace the … with values.

3. The … of a figure if the amount of space it occupies in two dimensions.

4. The ... of a figure is the distance around the figure.

5. The … of a figure if the amount of space it occupies in three dimensions.

Ex. 6. Replace each italicized word or phrase with the correct word.

1. When both integers have the same signs keep the sign and subtract.

2. Write any mixed number as an proper fraction.

3. The events are dependent when the outcome of one event does not affect the probability of the other event.

4. The product is negative if there are an even number of negative factors.

5. The quotient is positive if both integers have the different sign.

REVIEW QUESTIONS

1. Are the LAST test objectives of Subarea I: Scientific and Mathematical Processes significant?

2. What skills, concepts and topics do you need to know to pass mathematics part of the LAST?

3. What special test strategies should you remember to use while taking the mathematics portion of the LAST?

4. Does the phrase “Please Excuse My Dear Aunt Sally” help you to focus your thinking about Mathematics?

5. What review sections of the mathematics part of the LAST do you need to reread or study thoroughly?

6. How will you use knowledge of Mathematics as you teach and go about your everyday life?

7. What examples of solving real-world problems do the LAST focus statements of the Subarea I - Scientific and Mathematical Processes provide?

8. Why do you need to sharpen your skills of reading and interpreting charts, graphs and maps to pass the LAST? What types of graphs will you certainly encounter on the tests?

MATHEMATICS PRACTICE ITEMS

These Mathematics items will help you practice the concepts in this review section. The items you encounter on the real LAST may have a different emphasis and may be more complete. See APPENDIX D.

APPENDIX D