Ratios & Proportional Relationships:

Transcription

1 Middle School Math Study Guide for Robotics Competition Against Time Containers will have a combination of math problems that are seen in common core standards for Grades 6, 7 and 8. Reminder, process of work does not need to be shown, but Note: All answers must be in reduced form and include appropriate units of measurement. Here is an example of how the problems will look like: Problem # 1: Note: answer must be in reduced form and include appropriate units of measurement. Solve the following ratio: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 40 hours? A: Ratios & Proportional Relationships: 1. For every 5 boys on a softball team there is 1 girl. What is the ratio of boys to girls? a. 5:1 2. At the store for every 7 movies sold there were 2 books sold. What is the ratio of books sold to movies sold? a. 2:7 3. A recipe had 4 tablespoons of seasoning to 9 cups of flour. So there is of a tablespoon of seasoning for each cup of flour. 4 a A printer took 7 minutes to print 56 pages. What is the rate of pages per minute? a. 8 minutes 5. Determine the number that correctly fills in the blank in the function machine. 6. A builder could get 6 sheets of sheetrock for $9. If he bought 12 sheets, how much money would he have spent?

2 a. $18 7. Find the ratio and unit rate: 24 pints of juice in 2 containers a. Ratio: 24:2 b. Unit rate: 12 pints per container 8. A book store was selling 5 books for $ Online the you could buy 6 books for $ Which place has a lower unit price? a. book store = $5.45, online = $5.36, Online has a lower unit price. 9. What is 150% of 18? a A recipe called for the ratio of sugar to flour to be 5:1. If you used 35 ounce of sugar, how many ounces of flour would you need to use? a. 7 ounces 11. Reduce the ratio to its lowest form: 50: 35 a. 50: 35 = 10: Every pint is 2 cups. This can be expressed using the equation y 2 = Z, where y is equal to the number of pints and Z is equal to the total number of cups. Using this equation find the total cups in 7 pints a. 14 cups 13. For each pound there are 16 ounces. Write an equation to express the total number of ounces (Z) in (y) pounds. a. y 16 = z 14. Find the equivalent fraction. Write as a mixed number 5/9 2 = x 3 1 5/9 a. 2 = x 15 ; x = Solve: A snail going full speed was taking 1 5 of a minute to move 1 2 of a centimeter. At this rate, how long would it take the snail to travel a centimeter? 2 a. mintue It takes yards of thread to make 2 5 of a sock. How many yards of thread will it take to make an entire sock? a yards 17. Fill in the blank to make an equivalent ratio: 72:64 = 9: a. 72:64 = 9:8 18. Determine if the values in the table are proportional (yes) or not (no). a. Yes 19. A florist used the equation Y=KX to determine how many flowers she'd need for 7 bouquets. She determined she'd need 175 flowers. How many flowers were in each bouquet? a. 25 flowers

3 20. Identify the constant of proportionality. Write your answer as y = kx a. y = 3x 21. Determine the constant of proportionality for each table. Express your answer as y = kx a. For every can of paint you could paint 3 bird houses; therefore, y = 3x 22. Using 50 boxes of nails a carpenter was able to finish 450 bird houses. Write an equation that can be used to express the relationship between the total number of birdhouses completed(t) and the boxes of nails(b) used. a. t = 9 b 23. Determine what the value of A means in the following problem. a. Every piece of chicken costs $ A small bag of flour weighed 13 ounces. A large bag was 5 percent heavier. How much does the large bag weigh? a ounces 25. Find the missing value of the following ratio:? = a Solve the following quotient: = The Number System: a = = = = 13 6 = 2 1 6

4 2. Solve the following: =, =, , = a = 37.8 b = 14.6 c = d = Rewrite the expression as a multiple of a sum of two numbers with no common factor: a = (2 2) + (2 2 5) = (2 2) (1 + 5) = 4 (1 + 5) 4. Find the Greatest Common Factor (GFC) of the following two numbers: 21, 12 a. Factors of 21 are 1, 3, 7, 21, Factors of 12 are 1, 2, 3, 4, 6, 12 Therefore, GCF is 3 5. Find the Least Common Multiple (LCM) of the following two numbers: 4, 6 a. Multiples of 4 are 4, 8, 12, 16, 20, 24, 28 Multiples of 6 are 6, 12, 18, 24, 30, 36, 42 Therefore, LCM is What number is the opposite of -(-29)? a Which number is less? -27 or -36? a Starting at (0,0) if you were to go 3 units right and 8 units up what coordinates would you end up at? What quadrant would you be in? a. (3,8) and it will be in the first quadrant 9. Use >, <, or = to compare the following: 31 30, 61 5, a. 31 < 30 b. 61 > Which Letter best shows -112? a. A 11. Find the distance between the two points. a Solve the following problem: ( 26) 39 =, ( 5) + ( 12) =, a. -65 b Determine the value of the variable 75 F = 0 a. F = Convert the following subtraction expression to an addition expression: a ( 2) 15. Solve: 92 + ( 77) =, 52 + ( 89.02) = a. 15 b

5 16. Solve: 45 ( 9) =, 6 ( 2) = a. 5 b Solve for the missing number:? 2 = 5 a Find the missing number: 7 = 9 a. 63 Expressions and Equations: 1. What is 8 to the power of two? a. 8 2 = 8 x 8 = Determine which letter best represents the expression: Find 11 more than Y A) 11 + Y B) Y + 11 a. B 3. Evaluate the following expression: (3 7) a = = = = 29 5 = Apply the distributive property to produce an equivalent expression: 21v + 24, 9(9 + 8r) a. 3(7v + 8) b r 5. Determine which option(s) the variable 'e' could be. If none of the options could be the variable write 'none'. 10e + 3 < 92 A)10, B) 4, C) 6, D) 2 a. B, C, D 6. Write the number sentence as an equation / inequality: x is less than or equal to -91, 57 is greater than x a. x 91 b. 57 > x 7. Use the number line to express the inequality. x 9 a. 8. Expand the following expression: 2 9 ( 1 2b ) a. 2 18b 2 27

6 9. Factor the following expression completely: 4 24c a. ( ) 6 4c Rewrite the following expression in its simplest form: ( ) ( 8 + 7) 45T 9T a T 11. Simplify the expressions shown: 4(7 + 10) 2v + 4v a v 12. Solve the following problem. Round your answer to the nearest hundredth: % =?, What is 6% of 24.77? a b Solve the following problem a Solve for x. 3x 2 = 10 a. x = Find the slope. 6x 6y = 6 a. Slope = 1 Geometry: 1. Find the area of the triangle. Units are not to scale. a. Area: ft 2 2. Determine the number of smaller fractional pieces that can be made from the larger piece. a Find the volume of each rectangular prism. The prism unit is measured in cm (not to scale). a. 39 cm 3

7 4. Find the surface area of the figure. a sq. unit 5. Determine the actual width, height and area of the following scale rectangle. Round the area to the nearest whole number. a. Height = 15.5 ft Width = 13.5 ft Area = 209 ft 2 6. Determine if the statement is possible (P) or impossible (I). A triangle with the angles: 88, 16 and 65 a. I (impossible) 7. Find the area and circumference of the circle. The circle is not to scale. a sq. units 8. Find the circumference of the circle. The circle is not to scale. a sq. units 9. Find the value of 'A' in the set of complementary angles. a. A = The complementary angle of 59 is. a Find the value of angle 'A' and angle 'B'. a. A = 61 B = 119

8 12. Find the value of 'a' and 'b'. Angle XQR is 180. a. a = 8 b = Find the value of 'A' in the set of supplementary angles. a. A = 141 Statistics & Probability: 1. Find the average of the pair of numbers. 54 & 11 a Find the 1st, 2nd (median) and 3rd quartile of the set of numbers. 7, 4, 5, 2, 7, 7, 2 a. 2, 2, 4, 5, 7, 7, 7 therefore the 1 st median is 2, the 2 nd median is 5 and 3 rd quartile is 7 3. Using the set of numbers find the mean (rounded to the nearest tenth), median, mode and range. 89, 76, 85, 76, 77, 84 a. Mean: = 81.2 Median: 80.5 Mode: 76 Range: = Use the scenario to identify populations and samplings. A beverage company wanted to see if people in the United States liked their new logo. Which choice best represents a population? A) A selection of logo artists. B) Every person in the United States. C) A selection of shoppers from different states. D) 3,800 children age 5 15 a. B. Every person in the United States.