Is the result of multiplying 2 positive numbers positive or negative? Is the result of multiplying 2 negative numbers positive or negative?

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1 Write down all the work necessary for the problem, this is a part of your class notes that you can use to study from. You will not be able to use notes on quizzes or tests. DO NOT simply write it and toss it away. 1. Basic Arithmetic: A) Solve each of the following equations without using a calculator. 1) ) ) (-12) - (-24) 4) ) ) 6 B) Translate # 1-6 above into English sentences. 1) 2) 3) 4) 5) 6) Is the result of multiplying 2 positive numbers positive or negative? Is the result of multiplying 2 negative numbers positive or negative? Is the result of multiplying 1 positive numbers and 1 negative number positive or negative?

2 2. Order of Operation What is the order of operation? Write in complete sentences below. Calculate each of the following expression: (Show your work!)

3 3. Evaluating 1-variable equations x x x x ( 4) x

4 4. Distributive property, and combining like terms Use distributive Property to simplify each expression, SHOW YOUR WORK! 1) (3x + 4) ( 2x -2) 2) (5x + 1) ( 3x) 3) (4x - 2) ( 3x + 5) 4) (-2x - 1) ( 3+ 5) 5) (3x y) ( x) 6) ( 2x + y) ( 3x - 4)

5 5. Simplifying fractions Simplify each of the following Fractions(SHOW YOUR WORK!)

6 6. Multiplying and dividing fractions What happens to the fraction when multiplying fractions? What happens to the fractions when dividing fractions? Simplify each expression(show your work) Multiply each pair of fractions: 2 3, , , 21 8 Divide each pair of fractions (the first fraction goes first): 12, , 2 6 7, 9 8 5

7 7. Evaluating complex fractions How does complex fractions relate to multiplying and dividing fractions? Simplify each complex fractions: Solving inequalities Solve and graph each inequalities: 3x > 12 < > 3x 12 < > 2.5x 3.5 < 13.5 < >

8 9. Ratio and rates Identifying ratios Students were asked in a survey whether they eat school lunch or not. The data can be represented with the table below: Responses - number of students yes - 15 no - 85 more than 3 times a week - 56 less than 3 times a week - 44 total number of students surveyed Question 1) What is the ratio of students eating school lunch to the students not eating school lunch? Question 2) What is the ratio of students eating school lunch more than 3 times a week to the number of students eating school lunch less than 3 time a week? Question 4) Student A saw the ratio 100: 85, what is the student comparing from the survey? Question 5) Student B saw the ratio 44: 56, what is Student B comparing?

9 10. Proportional relationship For every 1 of a math problem completed, 3 you are distracted for 6 minutes. How many minutes will it take to complete 12 homework problems? Represent the number of minutes as m. Write the proportional relationship here: Solve the proportion here:

10 11. Taxes, mark-ups, and discounts Scenario1: Costco s giant teddy bear takes $27.52 to make, and it is given a Mark-up of 175% How much does Costco s giant teddy bear cost after calculating mark-up? That same Costco s giant teddy bear is now being sold at Costco for. They are having a sale of 21% on Costco s giant teddy bear. How much will customers pay before taxes? Tax is 9.15% How much do customers pay after taxes? Did Costco earn any profit from selling the phone case at a discounted price? How much did they make? or How much did they lose?

11 12. Simple interest, and compound interest Calculate the Simple interest, and compound interest given the following: a) Compound interest: Simple interest: Principal $672 Principal $672 Interest rate 13.75% Interest rate 13.75% Number of years: 5 Number of years: 5 Number of compounds each year: semi-annually Balance after 1 years Balance after 2 years Balance after 3 years Balance after 4 years Interest earned over 4 years? Balance after 1 years: Balance after 2 years: Balance after 3 years: Balance after 4 years: Interest earned over 4 years?

12 13. Probability Finding Probability: a) What is probability? Use the letters from THIS IS THE FINALS REVIEW to find the probability of each of the following b) p(letter T) c) p(letter H) d) p(vowel) e) p(letter K) Odds a) What is odds? Use the letters from THIS IS THE FINALS REVIEW to find the odds of each of the following b) the odds of letter C c) the odds of letter S d) the odds of consonant e) the odds of letter Y e) What is the difference between independent events and dependent events? f) 5 cards are pulled from a deck of 52 cards with replacement. Are the 5 picks independent events or dependent events? g) A 6-sided Dice and a 8-sided dice are tossed. Are the two tosses independent events or dependent events? How many results are there in total? (show your work) h) License Place are generated at random. Driver A has the license plate: 4ABC543, and driver B has the license plate 3THE946. Are the generation of the two license plate independent events or dependent events? Explain your thoughts.

13 Theoretical Probability: A coin is known to be rigged with 55% chance of landing on tail. Assuming the coin is flipped 2 times independently. a) Draw a tree diagram (on a separate sheet of paper) to represent the sample space, and label the probability of each outcome. b) Calculate the probability of each of the following using the tree diagram: p(hh) p(tt) p(ht) p(th) c) Calculating probability using the information above: p(at least 1 H) p(at least 1 T) p(no T) p(exactly 2 T) 14. Experimental probabilities: A medical laboratory had done research on a possible medication that can prevent the formation of scars after surgery. They have tested the medication on 712 patients. 53 of the patients did not get a scar after using the medication. a) What is the effectiveness of the medication? b) Do you think this medication will be made available for other patients? c) Why do you think so? d) At what percentage of effectiveness will you be willing to make this medication available for patients? Our friend Kate and Danielle decided to play a game of cards to see who can pull a higher card 50 times with replacement. The result is Kate winning 45 out of 50 times, and Danielle winning 5 out of 50 times. e) What s the probability of Kate winning? f) What s the probability of Danielle winning? g) Do you think the game was fair? Why do you think so?

14 15. Statistics Find the mean, mode, and the 5-point summary for the following list of data. Data for the meaningful words: 2, 3, 4, 7, 7, 7, 8, 8, 8,, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14,14, 14, 15, 5, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20 Total number of data : Min Q1 median Q3 Max data points. Mean Median Mode Create a Histogram, and Box plot for the data given.

15 16. Area of 2-D objects a) Given a Triangle with the base of 3cm, and height of 7 cm. Find the area of the triangle. b) Given a circle with a radius of 7.5in. Find the area of the circle. 17. Volume of 3-D objects a) Given a Cylinder with radius of 5m, and a height of 4 m. Find the volume of the cylinder. b) Given a rectangular pyramid with base area 75cm 2, and a height of 12cm. Find the volume of the rectangular pyramid. 18. Surface area of 3-D objects a) Given a cube with the length of 5 meters. Calculate the surface area of the cube. b) Given a trapezoid with base 1 5 in, base 2 7 in, and height of 2 in. Find the area of the trapezoid. The height of the trapezoidal prism is 9 in. Find the surface area of the trapezoid prism.

16 19. Calculating angle measurements Identify the following set of angles as complementary angles, supplementary angles or neither. 1) measure a 11, and measure b 17: 2) measure a 122, and measure b 58: 3) measure a 90, and measure b 180: 7) Given 2 angles are supplementary angles, measure a 12. Find b. 4 Equation to represent this situation: Measure b Sketch the diagram to the right. 8) Given 2 angles are complementary angles, measure a Find b. Equation to represent this situation: Measure b Sketch the diagram to the right. 9) Given 2 angles are supplementary angles, measure a Find b. Equation to represent this situation: Measure b Sketch the diagram to the right.

17 Practice problem Set 2(Identify the Transversal, corresponding angles, and alternate interior angles): Identify the transversal for each of the following, THEN identify the corresponding angles, and alternate interior angles. 1) Label the 4 pairs of corresponding angles: Pair 1:, Pair 2:, Pair 3:, Pair 4:, Identify 2 pairs of alternate interior angles using the diagram: Pair 1:, Pair 2:, Identify each pair of vertical angles. Vertical angles(first pair):, Vertical angles(second pair):, Vertical angles(third pair):, Vertical angles(fourth pair):, Find the measure of 2, 3, 4, 5, 6, 7, 8 Given

Illinois Math Assessment Framework, Grade 7. correlated to

Illinois Math Assessment Framework, Grade 7 correlated to Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write