June 10, Dear Students and Parents,

Transcription

1 June 10, 2015 Dear Students and Parents, Hello and welcome from the Beaumont Math Department! My name is Mr. Hass-Hill and will I teach all of Beaumont s College Prep Algebra I and Honors Algebra I courses during the school year. I look forward to meeting you and helping you build your confidence and capability in mathematics. In order for you to be as successful as possible this coming year and so you can keep all your hardearned math knowledge from slipping away during the summer, I have prepared a required summer review packet for you to complete before you start school this fall. I believe all the material in the packet should be familiar to you from your work in middle school. If any topic is new to you, don t despair (being persistent and resourceful is very important in math)! Reread the examples and description at the beginning of the section. Ask friends, family members, or others for help. Or look for a video or examples on-line. On the reverse side of this letter I ve listed some of the most useful math websites I know that could be useful to you. Please do your best to neatly complete all the questions. Follow the directions carefully and only use a calculator in sections where it is allowed. Write all your answers on the packet and attach any extra pages needed to complete your work. This packet is a required assignment that will be part of your grade, and it is due on Tuesday, August 25, The material in the packet will be reviewed and will be the basis for a quiz within the first several days of school. Please don t wait until the last couple of days of summer to start this review. If you have questions about the completion of the packet, please me at shasshill@beaumontschool.org. I will be checking my regularly throughout the summer and will be happy to help. Enjoy the rest of the summer and I ll see you in August! Sincerely, Mr. Steve Hass-Hill Beaumont School

2 Useful Math Websites: Khanacademy.org Purplemath.com Mathisfun.com Kutasoftware.com/free.html Mathbitsnotebook.com Patrickjmt.com Coolmath.com Virtualnerd.com Regentsprep.org Math.com (choose the appropriate section from the menu on the left of the page) Freemathhelp.com Xpmath.com (for math games and practice) Math-play.com

3 Summer Math Packet 2015 For Students Entering College Prep Algebra I or Honors Algebra I This packet is due on Tuesday, August 25, Read each section, follow the directions carefully (including whether or not a calculator is allowed), and answer each question as indicated. Show your answer in the space provided. You should show your work for all questions. If more workspace is needed than is available in this packet, attach additional pages, clearly indicating the problem number corresponding to the work. 1

4 Section 1: Place Value and Rounding Do not use a calculator for this section Example: 1,234, millions 2 hundred thousands 3 ten thousands 4 thousands 5 hundreds 6 tens 7 ones 8 tenths 9 hundredths 0 thousandths Example: Write the place value of the underlined digit: 3,427, Answer: 4 tenths or 0.4 Example: Round 23,561 to the nearest thousand Answer: 24,000 Reminder: If the number to the right of the place value is 5 or greater, round up. Write the place value of the underlined digit 1.1 6,665, ,366, ,368, ,488, ,737, ,943, Round to the given place value ,095 to the nearest hundred to the nearest tenth to the nearest thousandth ,323,585 to the nearest ten thousand ,561 to the nearest thousand to the nearest hundredth 2

5 Section 2: Comparing and Ordering Numbers Do not use a calculator for this section Examples: Reminders: Read the problem from left to right < means less than > means greater than You might change fractions to decimals before you compare You might want to use a number line to make good comparisons Fill in the blank with the correct symbol (<, >, or =) Write the following numbers in order from least to greatest

6 Section 3: Simplifying Fractions Do not use a calculator for this section Examples: Simplfy The greatest common factor of and is Dividing the numerator and denominator by gives the answer of Simplfy The greatest common factor of and is Dividing the numerator and denominator by gives the answer of Reminders: A fraction is the same thing as division. That is, the division problem is equal to the fraction. Or the fraction is equal to the division problem. The greatest common factor is the largest whole number that divides evenly into two other numbers Unless specified otherwise, leave results as improper fractions instead of mixed numbers (that is, leave a fraction as instead of ). Simplify the following fractions

7 Section 4: Fraction Computations Do not use a calculator for this section Examples: Reminders: When adding or subtracting, find the common denominator. Multiplication can always be indicated either by a dot (like ) or by parentheses. So. When multiplying, multiply numerators by each other and denominators by each other. Simplify the result either by cancelling before multiplying or by reducing the fraction you get as your result. When dividing, multiply the first fraction by the reciprocal of the second fraction (that is, flip the second fraction). Change mixed numbers into improper fractions first, if necessary. Add the following fractions. Make sure your final answer is written in simplest form Subtract the following fractions. Make sure your final answer is written in simplest form Multiply the following fractions. Make sure your final answer is written in simplest form Divide the following fractions. Make sure your final answer is written in simplest form

8 Section 5: Converting Among Fractions, Decimals, and Percents You may use a calculator for this section Examples: Convert Convert Convert to a decimal: to a percent: to a fraction: Reminders: From a decimal to a percent: Multiply by 100 (or move the decimal two places to the right). From a percent to a decimal: Divide by 100 (or move the decimal two places to the left. Percents are always out of 100. Convert these fractions to decimals. Round to the nearest hundredth if necessary Convert these decimals to fractions. Write your final answer in simplest form Convert these decimals to percents Convert these percents to decimals. Round to the nearest hundredth if necessary Convert these fractions to percents. Round to the nearest hundredth if necessary Convert these percents to fractions

9 Section 6: Integer Operations Do not use a calculator for this section Examples: Reminders: When adding numbers with like signs, add the digits and keep the sign. When combining numbers with different signs, subtract the smaller digit from the larger and use the sign that went with the larger digit. When multiplying or dividing, if the signs are the same, the result is positive; if the signs are different, the result is negative. Simplify the given expression

10 Section 7: Powers and Exponents You may use a calculator for this section Examples: Write Write as a product (a multiplication) as a power Calculate Reminders: In the expression, is called the base and is called the exponent. The whole expression is called a power. When expanding a power into a product (a multiplication problem), the base is multiplied by itself the number of times shown as the exponent. When writing a product as a power, the number being multiplied by itself becomes the base, and the number of times it is multiplied by itself becomes the exponent. To calculate a power, use the ^ key on your calculator (if it has one) or treat the power as a product and enter the multiplication problem on your calculator. Write the given power as a product Write the given product as a power Calculate the given power

11 Section 8: Order of Operations Do not use a calculator for this section Examples: Reminders: Some of you probably use the mnemonic PEMDAS (for parentheses, exponents, multiplication, division, addition, subtraction ) to remember the order. Instead, we will use: 1. Grouping symbols (), [], {} 2. Exponents and radicals (such as square roots) 3. Multiply or divide from left to right 4. Add or subtract from left to right The reason we ll use that instead of PEMDAS is that multiplication and division have the same priority, as do addition and subtraction. It is not true that multiplication always comes before division or additional always comes before subtraction. Simplify the given expression

12 Section 9: Graphing Do not use a calculator for this section Examples: Plot the following points and indicate which quadrant each is in or which axis each is on A B C D E A Point A is in Quadrant I C D B Point B is in Quadrant IV Point C is in Quadrant II Point D is on the -axis E Point E is on the -axis Identify the ordered pair for each labeled point and indicate which quadrant each is in or which axis each is on A Point A is at and is on the -axis D Point B is at and is in Quadrant III E Point C is at and is in Quadrant IV C Point D is at and is in Quadrant II B Point E is at and is on the -axis Reminders: The coordinate plane is divided into four regions by the -axis (which is horizontal) and the -axis (which is vertical). The axes intersect at the origin. The four regions are called quadrants and are labeled using Roman numerals I, II, III, and IV. (Reminders continue on the next page) 10

13 The location of a point on the coordinate plane is indicated by an ordered pair, written in the form. If the first coordinate (or -coordinate) in the ordered pair is positive, it indicates the point is right of the origin; if it is negative, the point is left of the origin. If the second coordinate (or -coordinate) in the ordered pair is positive, it indicates the point is above the origin; if it is negative, the point is below the origin. Plot the following points and indicate which Quadrant each is in or which axis each is on. Quadrant/axis Point A: Point B: Point C: Point D: Point E: Point F: Point G: Point H: Point J: 11

14 Identify the ordered pair for each labeled point and indicate which Quadrant each is in or which axis each is on. A Quadrant/axis G Point A: H J D F B Point B: Point C: Point D: Point E: Point F: E C Point G: Point H: Point J: 12

15 Section 10: Evaluating Expressions Do not use a calculator for this section Examples: Evaluate the following expressions when Evaluate this expression when and Reminders: To evaluate something means to find its value. To evaluate an expression, replace any variables with their given values then use order of operations to calculate the numeric answer. Evaluate the following expressions given that,, and