Review 3



Math 3 Honors: Unit 6 Name: _____________________________

Unit 6 Test Review Guide: Systems, Sequences, and Series

Section 1: Solve by GRAPHING and classify as inconsistent or consistent independent/dependent.

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Section 2: Solve by SUBSTITUTION and classify as inconsistent or consistent independent/dependent.

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Section 3: Solve by ELIMINATION and classify as inconsistent or consistent independent/dependent.

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Section 4: Graph the solution following systems of inequality.

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Section 5: System Word Problems

• Identify two variables, write two equations for your system, and solve that system using any method to answer the question.

13. A plane can travel 1680 miles in 3.5 hours with a tailwind (wind blows with direction of plane) and the same plane will travel the same distance in 4 hours with a headwind (wind blows against direction of plane travel). What is the speed of the plane in miles per hour and what is the speed of the wind assuming it is constant in miles per hour?

14. Jordan bought 3 boxes of pencils and 5 boxes of highlighters for $49.85. At the same store, Charles bought 5 boxes of pencils and 2 boxes of highlighters for $35.90. If Mr. Smith wanted to buy 2 boxes of pencils and 3 boxes of highlighters, then how much would he pay at the same store?

15. The difference of two numbers is 515. The larger number is 79 less than triple the smaller number. What is the smaller of the two numbers?

Section 6: Linear Programming

16. Graph the system of inequalities, name the coordinates of the vertices, and find the maximum and minimum values for quantity function f(x, y) based on the given constraints.

17. Graph the system of inequalities, name the coordinates of the vertices, and find the maximum and minimum values for quantity function g(x, y) based on the given constraints.

For #18 and #19: Write a system of inequalities (CONSTRAINTS) and Graph It. Write a quantity function and use the vertices of the system to answer the question.

18. There are a total of 85 workers’ hours available per day for production at a calculator manufacturer. There are 40 workers’ hours available for encasement and quality control each day. A graphing calculator requires 1.5 hours for production and 2 hours for encasement and quality control. A CAS calculator requires 0.5 hours for encasement and quality control and 1 hour for production time. If the profit of a graphing calculator is $50 and the profit of a CAS calculator is $65, then what is the maximum profit?

19. A club is making canvas tote bags and leather tote bags to raise money for fundraiser. For the canvas tote bags, they will use 4 yards of canvas and 1 yard of leather. For the leather tote bags, they need 3 yards of leather and 2 yards of canvas. They purchased 56 yards of leather and 104 yards of canvas to use. What is the maximum amount the fundraiser can earn for the club if each canvas tote bag earns them $20 and each leather tote bag earns them $35?

Section 7: System of Quadratics (Use substitution or elimination strategies)

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ARITHMETIC: an = a1 + d(n – 1) [pic]

GEOMETRIC: an = a1 (r)n – 1 [pic] [pic]

Section 8: Sequences

i. Find the NEXT THREE TERMS of the sequence

ii. Identify the sequence as ARITHMETIC, GEOMETRIC, or NEITHER

23. 8, 28, 98, 343, …

Next Three Terms:

Identify: ____________________

24. 4, 11, 15, 22, 26, …

Next Three Terms:

Identify: ____________________

25. 19.73, 17.39, 12.71, 10.37…

Next Three Terms:

Identify: ____________________

26. Find four arithmetic means of 8 and 53

27. Find three arithmetic means of 143 and 75

28. Find three geometric means of 24 and 1944

29. Find two geometric means of -16 and -54

Section 9: SERIES/ SUMMATIONS

Find the sum of the series, IF POSSIBLE:

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Given a10 = 128/651

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Given a8 = 57344

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