PreAlgebra Review Winter 2012 Algebra 2 PreAlgebra Includes

Pre-Algebra Review Winter 2012 Algebra 2

Pre-Algebra Includes: • • • Number problems Multiples, factors primes Divisibility and remainders Percentages (%) Ratios, proportions Mean, median, mode Probability Absolute value ( |-7| ) Exponents, roots Series

TIPS • Story Problems: – Read through problems and UNDERLINE or CIRCLE important information • Use your calculator WISELY • Encourage your “inner artist” – The ACT provides a space to “do your figuring here” – That means DRAW! • UNDERSTAND what the questions is asking BEFORE you start to solve. • If all else fails, WORK BACKWARD from the answers provided. • The test is “roughly” organized by order of difficulty

Story Problems – Question 1 • Samantha had 5 more cookies than Arthur. Then Arthur gave her 10 of his cookies. Now how many more cookies does Samantha have than Arthur? A. 35 B. 10 C. 15 D. 20 E. 25

Story Problems – Question 1 • What does the question ask? l l How many _____ cookies does Samantha have than Arthur? We need to know: l l l How many cookies Samantha has How many cookies Arthur has The __________ between them!

Story Problems – Question 1 • Samantha had 5 more cookies than Arthur. Then Arthur gave her 10 of his cookies. Now how many more cookies does Samantha have than Arthur? A. 35 PICK a number for Arthur. Let’s say he has 20 (he must have AT LEAST 10 in B. 10 order to give 10 to Samantha)! C. 15 D. 20 E. 25

Story Problems – Question 1 • Samantha had 5 more cookies than Arthur. Then Arthur gave her 10 of his cookies. Now how many more cookies does Samantha have than Arthur? DO YOUR FIGURING HERE: A. 35 B. 10 C. 15 D. 20 E. 25

Story Problems – Question 1 • Samantha had 5 more cookies than Arthur. Then Arthur gave her 10 of his cookies. Now how many more cookies does Samantha have than Arthur? A. 35 PICK a number for Arthur. Let’s say he has 11 (he must have AT LEAST 10 in B. 10 order to give 10 to Samantha)! C. 15 D. 20 E. 25

Story Problems – Question 2 • Allie has 4 more marbles than Steve gives her 2 of his marbles. How many less marbles does Steve have than Allie? A. 10 B. 8 C. 16 D. 14 E. 2

Averages – Question 3 • The daily profits of a fast food restaurant for a week in July was $432, $354, $213, $571, $761, and $320. What was the average daily profit for the restaurant? A. $441. 83 B. $530. 20 C. $662. 75 D. $1325. 50 E. $2651. 00

Averages – Question 3 • How do you find the average (mean)? l l _______ all of the numbers and ______ by the number of numbers Example: l Find the average: 5, 4, 6, 8, 10

Averages – Question 3 • The daily profits of a fast food restaurant for a week in July was $432, $354, $213, $571, $761, and $320. What was the average daily profit for the restaurant? Do your figuring here: A. $441. 83 B. $530. 20 C. $662. 75 D. $1325. 50 E. $2651. 00

Averages – Question 4 • James scores the following percentages on his Algebra 2 tests: 100, 90, 60, 70, 50. What is his test score average? A. 93% B. 74% C. 62% D. 185% E. 80%

Probability – Question 5 • Joey has 4 blue pants and 3 black pants. In a rush to get to work, Joey randomly grabs a pair of pants from the closet. What is the probability he will pick a blue pair of pants? A. B. C. D. E.

Probability – Question 5 • What is the question asking? l Probability (likelihood/chances) that Joey picks a pair of blue pants. l Probability = l For this question: Probability =

Probability – Question 5 • Joey has 4 blue pants and 3 black pants. In a rush to get to work, Joey randomly grabs a pair of pants from the closet. What is the probability he will pick a blue pair of pants? A. B. C. D. E. Do your figuring here # of blue pants: # of pants total:

Probability – Question 6 • Brendan has a box of 5 black marbles and 3 red marbles. If he reaches in and grabs a marble without looking, what is the probability that he will choose a red marble? A. B. C. D. E.

Percentages – Question 7 • A pair of shoes costs $42. 40. If the shoes go on sale for 25% off the current price, what will the sale price be of the shoes? A. $21. 20 B. $25. 40 C. $10. 60 D. $31. 80 E. $32. 40

Percentages – Question 7 • Percent OUT OF 100 • 25% off means you still pay ___% * 75% = = ______ • ____ x Current price = What you pay!

Percentages – Question 7 • A pair of shoes costs $42. 40. If the shoes go on sale for 25% off the current price, what will the sale price be of the shoes? • 25% off $42. 40 means you pay A. $21. 20 100% - 25% = 75% B. $25. 40 • 75% as a decimal = ____ C. $10. 60 • _____ x 42. 40 = ______ D. $31. 80 E. $32. 40

Percentages – Question 8 • A gallon of milk costs $3. 99. If you have a coupon for 30% off of the milk, what will the new price of the milk be? A. $2. 73 B. $2. 79 C. $2. 99 D. $1. 20 E. $2. 80

Percentages – Question 10 • The cost of pumpkin pie increased by 20% because of a lack of pumpkins in Michigan. If pumpkin pie used to cost $8, how much would it cost for pumpkin pie with the new increase? A. $6. 40 B. $8. 20 C. $9. 60 D. $9. 20 E. $8. 60

Ratios/Proportions – Question 11 • Air force one is 30 feet and 8 inches long, with a wingspan of 68 feet. If you are making a scale model of this airplane, what should the length of the model’s wingspan be in feet? A. 5 • Looking for WINGSPAN, so what number do we use? • 1/12 of the wingspan means MULTIPLY! B. 5 • USE THE CALCULATOR! C. 5 • (1/12) 68 = 5. 666667 D. 4 • We need it in FRACTION FORM! E. • MATH 1: Frac ENTER

Ratios/Proportions – Question 12 • You want to make a scale model of a car. The car is 8 feet wide and 14 feet long. How long would the model car be (in feet)? A. B. C. D. E.

Ratios/Proportions – Question 13 • Melissa has a basket of blue, white and red roses in a ratio of 2: 4: 5. The basket contains a total of 88 roses. How many white roses are in the basket? A. 16 B. 32 C. 40 D. 20 E. 28

Ratios/Proportions – Question 13 • Ratio is a fraction: • Example: – 1: 3: 2 - the “whole” would be 1+3+2 = 6 • READING ratios: – The ratio of cats to dogs is 4: 5, the numbers are in the same order as the words. • 4 cats and 5 dogs 9 animals TOTAL • Fraction of cats = • Fraction of dogs =

Ratios/Proportions – Question 13 • Melissa has a basket of blue, white and red roses in a ratio of 2: 4: 5. The basket contains a total of 88 roses. How many white roses are in the basket? A. 16 What is the fraction of WHITE roses? B. 32 = C. 40 D. 20 This means OF the 88 roses are white. E. 28 Multiply USE CALC!

Ratios/Proportions – Question 14 • Billy has a bag of large, small and medium sized oranges in a ratio of 1: 4: 2. The bag contains 28 oranges total. How many medium sized oranges are there? A. 8 B. 16 C. 4 D. 20 E. 18

Number Lines – Question 15 On the real number line below, numbers increase in value from left to right. C is positive. The value of B must be: C A. B. C. D. E. Positive Negative Less than C Between 0 and C Equal to 0 B

Number Lines – Question 15 • Negative 0 Positive

Number Lines – Question 15 On the real number line below, numbers increase in value from left to right. C is positive. The value of B must be: C A. B. C. D. E. Positive Negative Less than C Between 0 and C Equal to 0 B

Exponents – Questions 16 -17 • (2 x 2 r 3 y 4)2 • 3 x 2 + 4 x 3 y – 4 x 2 – 10 x 3 y + 6 y