T. H. Rogers School Summer Math Assignment

Transcription

1 T. H. Rogers School Summer Math Assignment Mastery of all these skills is extremely important in order to develop a solid math foundation. I believe each year builds upon the previous year s skills in math. This packet contains problems that reinforce math skills learned this year and skills that will be needed for next grade. Please complete all the pages from this packet. Completing the problems in the packet will help students be better prepared for math work in the fall. Students should not try to complete the packet in one day. Instead, students should work throughout the packet in small weekly session. Note: (Please do not use a calculator except for the last topic, topic 9) This assignment is due on the first day of school. Name: Parent s Signature: Date: 1

2 Topic 1: Integers Addition Subtraction Multiplication Division Same Signs: Add & Keep Sign (+6) + (+5) +11 ( 8) + ( 2) 10 Keep Change Opposite (+10) ( 8) (+10) + (+8) 18 ( 5) (+10) ( 5) + ( 10) 15 Same signs: Positive product (+3)(+8) +24 ( 3)( 5) +15 Same signs: Positive Quotient (+42) (+6) +7 ( 50) ( 10) +5 Different signs: Subtract & take sign of larger value (+9) + ( 5) +4 ( 20) ( 8) ( 20) + (+8) 12 Different signs: Negative product: (+3)( 2) 6 Different signs: Negative Quotient: (+36) ( 6) 6 ( 6) + (+1) 5 ( 4)(+6) 24 ( 24) (+2) 12 Recall the order of operations: PEMDAS 1. Parentheses or grouping symbols or 2. Exponents 3. Multiplication/ Division (left to right) 4. Addition /Subtraction (left to right) Topic 2: Fractions vs Decimals. To convert a fraction into decimal, we divide the numerator by the denominator. Example I: write this fraction to the form of decimal. When converting a decimal into a fraction we: Find the lowest place value of the number Write the decimal as a whole number over this number Simplify the result Example II: Write this decimal to the form of fraction Topic 3: Exponent Exponent: the exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the vase number. Example: Base: The number that is going to be raised to a power. Example: is the base and 3 is exponent or power. 2

3 Topic 4: Ratio & Proportion Alex counted 24 marshmallows in 3 servings. At this rate, how many marshmallows are in 12 servings? Strategy: 1. Set up a proportion: write ratios for the number of marshmallows to the number of servings number of marshmallows in 3 servings 3 servings number of murshmellows in 12 serings 12 servings 2. Find the value in the proportion: (lets x represent the number of marshmallows) x x x Topic 5: Algebra Solving Equations By Using The Addition, Subtraction Or Multiplication Property Of Equality. Check the solution: Example I: Solve for x. 5x (subtract 3 from both sides) 5x 15 5x x 3 (divide both sides of equation by 5) Note: do not forget to check you work always 5(3)+318 Example II: evaluate the equation x 2 + 5x 12 for x2. Just plug x2 in the equation and simplify it (5)(2) Example III: Simplify the equation 5x 2 + 6xy 11xy 2x 2 + y 3 5x 2 2x 2 + 6xy 11xy + y 3 3x 2 5xy + y 3 (for simplification first we combine the like terms) 3

4 Important algebra properties that you should remember: 1. Commutative property change order Associative property Associate with Different Group move parentheses (6+3)+26+(3+2) 3. Identity property for addition or multiplication Zero for addition & One for multiplication to keep the number s identity 0+33 & Inverse property for addition or multiplication Add a number to its opposite, the answer is 0. Example: 2+ (-2) 0 or multiply a number by its reciprocal, the answer is 1. Example: Distributive property Give out, distribute number to each part 2 (3+4) Zero product property Zero times any number is zero Topic 6: Inequalities. Note: you solve inequalities the same way you solve equality except.. If you multiply or divide each side of an inequality by a negative values, you need to switch the direction of the inequality to keep the statement true. 4

5 Topic 6: Angle relationships Notes: m < means the measure of angle and means congruent or equal in measure Vertical angles Complementary angles Supplementary angles Angles that are opposite each other across two intersecting lines. m < 1 m < 3 m < 2 m < 4 Two angles whose sum is 90. m < 1 + m < 2 90 Two angles whose sum is 180. m < 1 + m < Topic 7: Geometry You should know the following formulas and be able to use them to find the area or perimeter of a geometric figure. Perimeter of a polygon the sum of all the sides. Figure Perimeter P Area A 1. Square 2. Rectangle 3. Parallelogram 4. Triangle 5. Trapezoid 6. circle 4s 2l + 2w s1 + s2 + s3 + s4 S1 + s2 + s3 S1 + s2 + s3 + s4 Circumference 2πr s 2 Lw Bh 1 2 bh 1 (b1 + b2)h 2 πr 2 ( r is radius of the circle) 5

6 Find each answer. (Use number line or chip board to find your answers) Answers: ( 4) ( 18) ( 12) ( 23) ( 14) ( 9) ( 8) 9. Considering the order of operation solve the following problems ( 2) ( 2) + 12 ( 3) 4 ( 2) ( 2) ( 8) 6 + 6( 3) ( 9) 4. 7 ( 6) 11 ( ( 10) 5 2) (5 (6 7) 3) (18 (12 10)) (8 36 ( 2) 16) 12 2(8 (5 9) 10) Warm- up: 1. 5/8 + 1/

7 / (3 3 6 )( ) 11. ( 4 5 )(8 19 ) 12. ( )( ) 13. (9 8 9 )(8 6 8 ) 14. (8 2 7 ) (4 7 ) 15. ( ) ( 3 5 ) 16. ( ) ( 6 5 ) 17. (1 2 3 ) ( 3 8 ) 7

8 Word Problem: 1. Ethan writes 1/6 of a page in 1/12 of a minute. How much time does it take him to write a full page? 2. Robinson s hotel room rent is $80. His food bill is $30 and the taxi costs him $20. His company deposits his salary of $100 into his bank account. What would be the balance remaining after paying his monthly expenses? 3. Aiden walked 1/8 of a mile in 1/16 of an hour. Compute the unit rate as the complex fraction. 4. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it take him to fill the bottle? 5. Michael plays 1/5 of a song in 1/15 of a minute. How much time will it take him to play an entire song? 6. Each day, Foster uses 4 bags of milk for tea for her family and tenant. In how much of a day will they use 1/2 of a bag of milk? 7. There were 22 oranges in the basket. Out of these, 19 were eaten by kids. Mom bought one and a half dozens of oranges and refilled the basket. How many oranges are there in the basket? 8

9 8. Which is bigger, one seventh of 14 or half of 36? 9. Bob can draw 14 shapes in 7 minutes. How long does it take Bob to draw 28 shapes at the same rate? 10. In the school election, James ran against Andrew for secretary. James received 75% of the votes. If 240 students votes, how many votes did James receive? 11. How many 1/3-cup servings are in 3/4 of a cup of tea? 12. The football team lost 5 yards on 3 plays in a row. Which of the following could represent the change in field position? 13. At a certain college, the ratio of men to women is 6 to 5. If there are 1500 men, how many women are there? 14. George is making 8 gallons of Tropical trip punch. He has already poured in 1 3/4 gal of pineapple juice and 2 ½ gal of orange juice. The only other ingredient is 7-up does George need? 9

10 15. George went to the general store to buy provisions. He bought food items worth $35. He had a $25 gift card for the store and he also paid $5 in cash. How much debt does George have with the store? 16. Ali drove 220 km in 5 hours. What was his average rate of speed? 17. Rose read 20 pages every day during summer. How many pages does she read in whole summer vacation? (Assume summer vacation is 90 days) 18. If Jenna scores 96 points in 6 games, how many points does he score, on average, per game? 19. Julian is moving from his home town of Sedona, Arizona. He knows he is going to face a big temperature change, and he is getting ready. The hottest it gets in Sedona is 112 degrees F. the hottest it gets in Juneau is 72 degrees F. approximately what temperature change will Julian experience? 20. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position? 10

11 Convert to fractions Convert into decimals Rewrite in exponent form: (-3) (-3) (-3) (-3) 4. (-8) (-8) (-8) (-8) (-8) (-8) Rewrite in expanded form: 2. ( 12) 4 3. (2) 9 4. ( 24)

12 6. ( 7) 2 7. ( 1 2 )3 8. ( 3 4 )2 9. (2 1 2 )5 10. (10) (100) 2 Simplify each expression (6m 3) + 6(1 + 4m) (9n 9) 3. 4x 10x 2x 4. v + 12v 5. 5( 2n + 4) + 2(n + 3) x + 4x + 9 7x 7. 4a 3b 2a 8b 8. 4 x 3 +3x 2 y + 2xy 2 6y 3 + 5x 3 25y 3 + 3xy x 2 +2xy + 4y 2 +6x 2 5xy + 3y 2 +9x 2 25y a + a 2 5(a 2) 11. n n Solve for x /2 x x x x 20 12

13 16. 1/3 x x 5 17 Solve and graph. 1. 2x x 5 > n < 7 13

14 4. r + 13 < 9 5. X x k 10 14

15 8. P X 12 < 11 Find the value of x and explain how you found it. 15

16 Find perimeter and are of each shape (Hypotenuse 10mm) (Hypotenuse 10m) 6. (Hypotenuse 20ft) 16