[PDF] Accuplacer Math Test Review - UAS.pdf | Plain Text

1 ACCUPLACER MATH TEST REVIEW The following pages are a comprehensive tool used to maneuver the ACCUPLACER UAS Math portion. This tests your mathematical capabilities and designates a class that you would re- ceive the most benefit from. The ACCUPLACER test will consist of multiple choice questions. Scratch paper is allowed during testing, but nothing else is. Good luck! Phone: (907) 747 -7717 Email: sitka.ssc@uas.alaska.edu ARIT HMETIC · ELEMENTARY ALGEBRA · COLLEGE ALGEBRA

2 ARITHMETIC REVIEW This test measures your ability to perform basic arithmetic operations and to solve problems that involve fundamental arithme tic concepts. There are 17 questions on the Arithmetic tests, divided into three types:  Operations with whole numbers and fractions  Operations with decimals and percents  Applications and problem solving Order of Operations Solving problems with several operations requires doing each step in the correct order. Step by Step Example 1: 7 x 14—(12+18) Start with what is in the parentheses: 12+18=30 Solve multiplications and divisions from left to right: 7x14=98 Rewrite the problem to include what work you’ve done: 98– (30)= 68 Step by Step Example 2: 2(6-4) 2 +10 Start with the parentheses: (6 -4)=2 Evaluate the exponential expression now: 2 2 =2x2=4 Rewrite the problem so it’s clearer: 2x4+10 Solve the multiplication first and then the addition: 8+10=18 Fractions: Divide & Conquer Welcome to Fractions 101 Fractions scare most people. We use them in recipes (3/4 cup of flour), shopping (1/2 off), and construction tools (9/16 wren ch). They are very uncomplicated once you get the hang of them. Fractions are a way of saying that out of this many, only a portion are left . Rules for Order of Operations 1. Do all calculations within parentheses ( ), brackets [ ], or braces { } before operations outside. 2. Evaluate all exponential expressions. 3. Do all multiplications and divisions in order from left to right. 4. Do all additions and subtractions in order from left to right. Identify the numerator and the denominator: 3 4 Denominator Numerator Imagine you were eating a pizza with 8 slices total and you had already finished 3 slices. What fraction of the total pizza was left to eat? How many pieces of pizza were there to begin with? 8 slices How many did you already eat? 3 slices How many are left? 5 slices How would that be written as a fraction? Out of 8 total pieces, you have eaten three. That would be written as: 3 8 Any number divided by zero is undefined . 6 = UNDEFINED 0 Zero divided by any number = 0. 0 = 0 7 Any number divided by itself equals 1. 12 = 1 12

3 Add & Subtract Fractions What happens if the fractions have different denominators? Like if one pizza had 12 slices and the other pizza had 8? We can combine those too, but we have to find the Least Common Denominator (LCD) first. Least Common Denominator refers to the smallest number that has all of the denominators as factors. Step by Step Example: 1 + 3 = 3 4 We want to add together these 2 fractions. First, we need to make sure the denominators (the bottom numbers) are the same. The smallest number that has both 3 and 4 as factors is 12. Before we add, we must change both of the fractions to represent the change in the denominator. The numerator (top number) must reflect the change in the denominator. In order to get 12 as the LCD, what do you need to multiply 3 by? 4 Look at the second fraction. What do you need to multiply 4 by to get to 12? 3 So now we have our new fraction, which has common denominators, which means it is ready to add together. What is 4+9? 13 1 x 4 = 4 3 x 4 = 12 3 x 3 = 9 4 x 3 = 12 4 + 9 = 13 12 12 12 Mixed Numbers Vs. Improper Fractions 12/5 is the same as 2 2/5. Here’s how: 12 5 2 5 2 12÷5=2 Remainder 2 2 x 5 +2= Another Example: Follow along in these examples of both adding and subtracting fractions. REDUCED Here are 2 examples of ques- tions you would see on the ACCUPLACER test: ANSWERS: C, C

4 Multiply & Divide Fractions Most people find that multiplying and dividing fractions is easier than adding and subtracting them because you do not need to find a common denominator. To multiply, multiply the numerators to- gether and the denominators together and then reduce if necessary. Dividing fractions has an extra step. First, flip the second fraction on its head: Then, proceed as you would for multiplying fractions. 2 x 6 = 5 7 2x6=12 5x7=35 12 35 2 ÷ 1 3 5 5 1 2 x 5 = 10 3 1 3 Here are 2 examples of ques- tions you would see on the ACCUPLACER test: ANSWERS: B, B

5 Decimals +/ - When you add or subtract decimals, line the decimals points up. x When you multiply, first multiply as you would with whole numbers. Then count the number of places to the right of te decimal in each number and counting from the right of the answer, move the decimal that number of place to the left. ÷To divide , make the divisor into a whole number by moving the decimal to the right. Then move the decimal the same amount of places in the dividend. Here are 4 examples of ques- tions you would see on the ACCUPLACER test: ANSWERS: B,A,C,A

6 Rounding Numbers Rules for Rounding 1. Locate the digit in that place. 2. Consider the next digit to the right. 3. If the digit to the right is 5 or higher, round up. If the digit to the right is 4 or lower, round down. 4. Change all digits to the right of the rounding location to zeros. Round to the nearest hundred. 12, 762.10 The number to the right of the 7, which is in the hundreds place, is 6. Since it is 6>5, round seven to the next highest number, which is 8. The new number is: 12,800.00 Here are 2 examples of ques- tions you would see on the ACCUPLACER test: Tom is going on a trip. His plane ticket costs $1,596, his hotel cost is $532, and his meals cost $379. Rounding to the nearest hundred, how much did his total trip cost? A. $2507 C. $3000 B. $2510 D. $2500 The answer to this multiplication problem will be clos- est to which of these whole numbers? 5.03 x .92 A. 45 C. 6 B. 5 D. 7 ANSWERS: D, B Percents 50% = .50 = 1/2 8% = .08 = 2/25 To change a number from a percent to a decimal, move the decimal point two places to the left and rewrite without the % symbol. To change a number from a decimal to a percent, move the decimal point two places to the right and add the % symbol. Here are 2 examples of ques- tions you would see on the ACCUPLACER test:

7 Percents Percents are used often in everyday life. We can find percents in stores, marking down a price (20% off!), determining the amount of interest someone will pay on a loan (8% interest rate), tax rates (6% sales tax rate in Sitka). When converting a percent to its fraction form, it will always have a denominator of 100. Changing Decimals to Percents and Back Again If changing a decimal to a percent, make sure you move the decimal point two places to the right and add the percent sign. .42 = 42% .08 = 8% 1.23 = 123% To change from a percent to a decimal, move the decimal point two places to the left and drop the percent sign. 60% = .6 .9% = .009 200% = 2.0 Fractions to Percents and Back Again Divide the denominator of the fraction into the top number and move the point 2 places to the right. Or you can multiply the fraction by 100%. OR T o get a perc en t back to a fraction , write the p erce nt as a fraction with 100 a s t he d en om i- n at or an d t hen r ed uce the fraction to lo west term s. S te p b y Ste p E xam ple : 72% 72% = 72 ÷ 4 = 18 100 4 25 Wor king w ith Pe rc e n ts S te p b y Ste p E xam ple 1: Wh at is 40% of $3, 200 ? Ste p b y Ste p E xam ple 2: 11 i s wh at perce nt of 99 ? Bre ak dow n t he p ro ble m fro m Engli sh t o M ath. Wh at=x (w hat w e’re sol vin g f or) Is = = 40% =.4 =2 /5 (what eve r yo u’re mos t co mfo rta ble with ) Of = mu ltiplie d Re writ e t he p ro ble m usin g t he sub stitu tion word s. x= .40 x 3200 Solv e: .40x3 200= $1 ,280 1 = 11% 9 Bre ak dow n t he p ro ble m fro m Engli sh t o M ath a nd r ew rit e it . 11= y x 99 ‘Y ’ is the u nkn ow n v ar iab le w e’re sol vin g fo r. We w ant to get y b y it se lf , so we n eed to get rid of 99. Divide b oth sides b y 99. Y is n ow b y it se lf , s o reduce the frac tion 11/99 a nd y ou h av e 1/9. Divide t he d en om inat or by t he n um era to r to get the n um ber in to a p erce nta ge . 11 =y 99 H ere are 4 e xam ples of qu es- ti ons yo u w ould see on t he A CCU PLACE R t es t: 1. 4. 3. 2. AN SW ER S: 1 .D 2.C 3.C 4.B

8 Applications Much of the ACCUPLACER Arithmetic Test involves problem solving and critical thinking. You take the basic concepts and apply them to math applications. Step by Step Example 1: Find the area of a square whose sides measure 4cm. What do we know about squares? A square has 4 equal sides, so if 1 side of our square is 4cm long, the other 3 will be too. What do we know about finding the area? Base x Height. So take the base length (4cm) times the height (4cm). 4x4=16cm 2 4cm 2 lbs = 24 lbs 3 weeks ? weeks Step by Step Example 2: A dieter lost 2 pounds in 3 weeks. If he continues to lose weight at this rate, how many weeks will it take him to lose 24 pounds? Set this up as a simple ratio: Cross multiply to make a new equation. Divide both sides to get x by itself. At the rate of 2 pounds every 3 weeks, it will take him 36 weeks to lose 24 pounds. 2X = 72 X = 72/2 = 36 3 .04 x .27 = Step by Step Example 3: 3.04 x .27 = 304 x27 2128 6080 .8208 Move the decimal four spaces to accommodate the four spaces from the two numbers multiplied together. Step by Step Example 4: 4 1/3 + 2 3/5 = First, change the mixed numbers into improper fractions. 13/3 + 13/5 Next, find a common denominator. 3x5=15 65/15 + 39/15 Add the numerators together. 104/15 And change it back into a mixed number. 90 14/15 The World Almanac lists all 4 -year colleges in the United States with enrollments of 600 or more. This list is 13 pages long, with an average of 89 colleges on a page. 1. Which figure best estimates the number of 4 year colleges listed? a. 157 b. 8000 c. 54000 d. 50 e. 1000 2. Estimate the minimum number of students enrolled at the colleges listed. a. 54,000 b. 9000 c. 600,000 d. 5,400,000 e. 6,600,000 3. If you could compare the actual number of students attending 4 -year colleges to your estimate for question 2, your estimate would turn out to be: a. much higher b. a little higher c. much lower d. a little lower e exactly right.