Algebra II Unit 1: Foundations of Functions Linear Equations Day 1. HW: Linear Equations WS 1. 3 Quiz 2.1, 2.2, and 2.

Transcription

1 Algebra II Unit 1: Foundations of Functions Aug 25 School Starts Class rules, etc Relations and Functions HW: Relations and functions WS Linear Equations Day 1 HW: Linear Equations WS Linear Equations Day 2 HW: Linear Equations WS 2 29 Review Packet Quiz 2.7A Linear Inequalities HW: Review packet HW: Linear Inequalities WS Sept 1 Holiday 2 Practice HW: Practice WS 3 Quiz 2.1, 2.2, and Direct Variation Linear Applications HW: Linear Applications WS Linear Applications HW: Linear Applications WS 2 HW: Direct Variation WS 8 Review 9 Foundations of Functions Test over Chapter 2 10 Order of Operations Algebraic Expressions & Function Operations Solving Equations HW: Order of Operations WS pages 1-2 HW: Algebraic Expressions & Function Operations WS pages 3-4 HW: Solving Equations WS pages Literal Equations HW: Literal Equations WS pages Solving Equations Practice CW/HW: Mixed Practice WS pages Solving Equations Quiz HW: Factoring WS 1 pages Solving Inequalities HW: Solving Inequalities WS pages Solving Inequalities (compound) HW: Solving Compound Inequalities WS pages Review 23 Foundations of Functions Test over Chapter 1 24 Transformations 25 Transformations 26 Transformations CW/HW: Review Sheet pages HW: Factoring WS 2 Page Transformations 30 Transformations Oct 1 Cumulative Test 2 Transformations 3 Half Day Transformations ***All assignments subject to change!!

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3 Name. Date Period Perform the indicated operations. Order of Operations WS 1. (17-9) ii. (4 + 9) ( ) (5--9)2+ 2 (7-8) (3-7) (3 + 4) (2-2)

4 6. a2+[3+(6+3)] i t (3 + 3)+ 4(-5 '9) , _3 8. 5(9-8). 6-I (0-7) (6.6) [-144-(-102)] [-7ÿ- (-53)]+2

5 Name. Date Period Evaluate for the given values of the variables. Algebraic Expressions & Function Operations WS 1. -k2- (3k-5n)+ 4n; k= -1 andn= (2c+d)- d; c = 5 and d = (2X+l)-2(X-3) ; X "ÿ -3 x+6 4.ÿ(ÿ ÿ ÿ( +'ÿ-'-x--'--'x--" ;x= -2 3x a al;a = 4 6. y2+ 3; y= 7.ÿ(ÿ ÿ ÿ( ÿÿ'-x--ÿ--'x--" ;x= -2 4x x2- (4x-Sy)+ 4y; x= -3 andy= -2 4(2X-5)-2(x-2) 9. x+9 ; x = y2-13; y = ÿfÿ

6 Simplify by combining like terms (Zx + y) - 2(2x + y) 1(x2+ y2)_ S(x2 + y2) (x2+x+1)- 4(-x2-x+1) 14. 2X2 + X + 3(3X2 -- X) y2 y2 15. _+Y+ Z b - (4a - 2b) Let f(x) = 2x + 5 and g(x) = x2-3x + 2. Perform each funcfion operation. 17. f(x)+ 9(x) 18. 3f(x) g(x) - f (x) f(x) 20. g(x) g(x) + f(x) 22. 9(x) f(x) - g(x) 24. f(x) f(x) - 2g(x) + 5

7 Name Date Period ' Solving Equations WS x = x (x + 4) = (1-2x) = -S(2x - 1) 4. 9(3-2x) = -6(3,1 - S) 5. 7(x+l)-3x--S+4(2x-1) 6. 3(x-2)-s=8-a(x-4) 7. 2x+4(x+l)=6 ( x+ 32_) 8. --=24 4ÿ [- ÿ-]- ÿ ÿ 3ÿ-= x-15= -5x Ex=S 12. 5(x-4)-1= -7x The length of a rectangle is 3 cm greater than its width. The perimeter is 24 cm. Find the dimensions of the rectangle.

8 14. One side of a triangle is 1 inch longer than the shortest side and is 1 inch shorter than the longest side. The perimeter is 17 inches. Find the dimensions of the triangle The sides of a rectangle are in the ratio 3:2. What is the length of each side if the perimeter of the rectangle is 55cm? 16. The sides of a triangle are in the ratio 3:4:5. What is the length of each side if the perimeter of the triangle is 30cm? 17. The sum of 4 consecutive odd integers is List the integers in order from least to greatest. 18. Find 3 consecutive even integers such that the sum of the first and third is 54 more than the second. List the integers in order from least to greatest. 19. The perimeter of a rectangular park is 624 yards. If the length of the park is 8 yards more than 3 times the width, find the dimensions of the park. 20. The length of a rectangular garden is 5 feet less than 4 times the width. If the perimeter of the garden is 200 feet, find the dimensions of the garden.

9 Name Date Literal Equations WS Period Solve each formula for the indicated variable. State the restrictions. 1, R(rÿ + r2) = rÿr2 for R 2, R(r2 + r2) = rÿr2 for r2 3. s = 2rcr2 + 2 rcrh for h 4. h = vt - St2forv 5. s= ½gt2forg 6. V= rcr2hforh Solve each equation for x. State the restrictions. 7. ÿ(x+l)=g 8. ax+bx=c 9, bx-cx=c cx+clx=e li. rx+8=y 12, y=-rx 3 13, The measure of the supplement of an angle is 20 more than 3 times the measure of the original angle. Find the measures of the angles. 14. The measure of an angle and its complement differ by 22. Find the measure of the angles.

10 15. Find 4 consecutive odd integers whose sum is 184. List the integers in order from least to greatest. 16. Find 4 consecutive even integers such that the sum of the second and fourth is 76. List the integers in order from least to greatest. 17. Two buses leave the depot at the same time traveling in opposite directions on a straight road. The first bus averages 5 mph more than the second bus. If they are miles apart after 1.5 hours, how fast is each bus going? 18. Enrique cycled to his grandmother's house at 15 km/hr and returned home over the same route at 18 km/hr. If the whole trip took 7 hours and 20 minutes, how far does he live from his grandmother's house? (Hint: First find the time for each part of the trip.) 19. A truck and a car travel the same route, the truck at 72 km/hr, and the car at 80 kin/hr. If the car leaves 1 hour after the truck, how long does it take the car to overtake the truck? 20. At 6:00 AM, a freight train leaves the station at 40 mph. At 7:30 AM, a passenger train leaves the same station at 64 mph, going in the same direction. At what time will the passenger train overtake the freight train?

11 ALG II Name Mixed Practice WS Date Period Solve the following equations x (3x- 5) = -4x x-1= -3(1-2x) x+5=3(2x+7) 3x (3x-4)+ 12=3x-10 Solve for the indicated variable. State any restrictions on the variable. 7. A = p + prt for t 8. 3x+4y= -12 fory 3 9. m = 4Psr for p 10. 4m- 2n = 9 for n Solve the following word problems. 11. The lengths of the sides of a triangle are consecutive odd integers. The perimeter of the triangle is 117 meters. Find the lengths of the sides of the triangle. List the sides in order from shortest to longest. 12. The length of a rectangle is 4 more than 3 times its width, Find the dimensions of the rectangle if its perimeter is 216 cm.

12 13. The measure of an angle is 43 more than its complement. Find the measure of both angles. 14. Two cyclists start from the same place at the same time. They travel in opposite directions. One averages 10 mph and the other 12 mph. After how long will they be 66 miles apart? 15. Mark drove to visit his grandparents at an average speed of 75 kin/hr. He returned home in heavy traffic along the same route at an average speed of 50 kin/hr. It took 45 minutes longer to return home than it did to get to his grandparent's house. How long did it take him to get home? 16. Starting one hour later, Jonathan sets out walking at 8 km/hr to overtake his younger sister who averages 5 kin/hr. How long will it take him to overtake his sister? 17. Each of the equal sides of an isosceles triangle is 5 feet less than 3 times the third side. The perimeter is 74 feet. Find the lengths of each side of the triangle. 18. Find three consecutive even integers whose sum is -72. List the integers in order from least to greatest. 19. Twice the cost of a television increased by $60 is $536. Find the cost of the television. 20. The measure of an angle is 30 more than twice its supplement. Find the measures of both angles.

13 Name. 1. x2 + 7x + i0 Date Factoring WS 2. x2+6x+8 Period 3. x2-9x x2 + Sxy + 6y2 5. x2+x-56 6, x2-x-6 7. x2+12x X x X X , 3x xy + 4Sy x2-2x x2-3x x2-13x x2-22x-75 1ÿ. 3X x , 5x2-15x x2 + 2xy - 3Sy x2 + 9x x2 + 14x x2-21x x2 - lox + 8

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15 Name Date Period t Solving Inequalities WS Solve each inequality. Express the answer in inequality notation. Graph the solution x _> x-15> y _> (x-2)-6> x-13<6(x-2) x- (3x- 1)] > 4(3x- 7) 7. -7(3x - 7) + 21x _> x >7(8-2x) x < 5(7-3x) ÿ(x-12)_x+a 3 11, ÿ(x-12)> x x- (2x- 7)] < 2(3x- 5) 13. The length of a picture frame is 3 inches greater than the width. The perimeter is less than 52 inches. Describe the dimensions of the frame. 14. The lengths of the sides of a triangle are in the ratio 5:6:7. Describe the length of the longest side if the perimeter is not more than [54 cm.

16 15. Find the lesser of 2 consecutive integers with a sum greater than The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip? 17. Less than 40 feet of fencing were used to enclose a rectangular lot that has a length 12 feet less than 3 times its width. Describe the width of the lot. 18. A rectangular tablecloth is to be 18 inches longer than it is wide. If Erika has at most 244 inches of lace trimming to sew around the cloth, what is the greatest possible width of the tablecloth. 19. A pentagon has two equal sides and three sides measuring 12 cm, 9 cm, and 13 cm. Find the length of the two equal sides if the perimeter is 56 cm. 20. The length of a rectangular sign is 10 feet less than twice its width. Find the dimensions of the sign if the perimeter is 118 feet.

17 Name Date Period I Solving Compound Inequalities WS Solve each compound inequality. 1. 3x _ -12 and 8x <_ 16 Express the answer in inequality notation. Graph the solution. 2. 7x > -35 and 5x < x > 3 or 9x < x _< -27 or 4x _> < 2x - 4 < < 3x + 2 < >4x-3> _1-5x> x-4>16or3x+2< x+3<lSor4x-2> x _<18 or - Sx <_ x < -64 and 5x > x _<12 or- 7x <_ x>30and18x< <4-2x_<5

18 16. A baker needs between 40 Ibs and 50 Ibs of a flour-sugar mixture that contains ten times as much flour as sugar. What are the possible weights of flour the baker can use? 17. Between 15,000 cubic yards and 16,000 cubic yards of earth must be trucked away from a construction site. The trucks can remove 1,000 cubic yards per day and 10,500 cubic yards have already been removed. How many days are needed? 18. By how much should a machinist decrease the length of a rod that is 4.78 cm long if the length must be within 0.02 cm of 4.5 cm? 19. A contractor estimated that her expenses for a construction project would be between $700,000 and $750,000. She has already spent $496,000. How much more can she spend and remain within her estimate? 20. The sum of three consecutive integers is equal to 9 less than 4 times the smallest integer. Find the 3 integers. List in order from least to greatest.

19 Algebra II Foundations of Functions Test I Review I Solve each equation (2x + 1) = 7x - 3(7 + x) Date 3x Period 3. 8x 2(2x 7)= 3x Let f(x)= 5x+2 and g(x)= x2-5x+4. Perform the following function operations. a. f(x)+g(x) b. 2g(x) - 3f(x) + 4 c. f(x)-g(x) Solve each inequality. Graph the solution set on a number line. Put the answer in inequality notation. 6. 2(x - 3) + 7 < x < 3(x - 5) 8. 3x-2 <4or2x-6 >x <2x+6 <18

20 10. 5x-4 >16 or 3x + 2 < <2x-6 <22 l Solve the following literal equations & state any restrictions. 12. V =ÿr2h for h 13. G = 2abc 3 for c Solve *he following word problems. 14. A car leaves a city *raveling a* a ra*e of 52mph. One hour later, a second car leaves from the same place, along the same road traveling at 65mph. How long will it take the second car 1o overtake the first? 15. Find 3 consecutive even integers whose sum is -66. List the integers in order from least to greatest. 16. The measure of an angle is 50 less than *he measure of i,s complemen,. Find *he measures of bo*h angles.

21 17. Two hikers walking in opposite directions start from camp at the same time. The average rate of the westbound hiker is 4mph more than the rate of the eastbound hiker. If they are 20 miles apart after 2.5 hours, what is the rate of each hiker? 18. The length of a rectangle is 6 feet more than twice its width. If the perimeter of the rectangle is 288 feet, what are the dimensions of the rectangle? 19. The perimeter of an isosceles triangle is 250 inches. Find the lengths of the sides if the lengths of the 2 equal sides are twice the length of the base. 20. The measure of an angle is 86 more than the measure of its supplement. Find the measures of both angles. 21. Find four consecutive odd integers whose sum is 336. List the integers in order from least to greatest. 22. The length of a rectangle is loft less than twice its width. The perimeter is 442ft. Find the dimensions of the rectangle.

22 23. At the same time, two buses leave a depot and travel in opposite directions on a straight road. The first bus averages 5 mph more than the second bus. If they are 142 ½ miles apart after '1 ½ hours, how fast is each bus going? Solve the following problem by writing an inequality. 24. The length of a rectangular yard is 50 ft and its perimeter is less than 170 ft. Describe the width of the yard. Solve the following problem by writing a compound inequality. 25. By how much should a machinist decrease the length of a rod that is 47.8 cm long if the length must be within.3 cm of 45cm.

23 Name Date Factoring WS 2 Period 1, 2x2 -- lox , x2-xy-72y2 3. 2X2 + 14X X x X x x2-4x x2-12x x2 +9x x2 + xy - 6y x2-1Sx x2-20xy + 32y2 12. x2-8x x2-10x x2-20xy - 48y x2 + 2xy - 40y2 16. x2-3xy + 2y2 17. x2-5x X2 -- 6X x2 + 6xy y2 20. X2 + 7X , 5X X + 75