Test 2 – Math 96

1. Test 2 – Math 96 Flash Cards

2. Test 2 Functions: Domain & Range Systems of Equations Word Problems – Mixture, investment & DRT Polynomials: add, subtract, multiply, & divide Factor

3. Does the graph represents a function. State the domain and the range.

4. Does the graph represents a function. State the domain and the range. • Vertical line test - if a vertical line will only touch the graph at most 1 time – then the graph represents a function. • Domain: how far left , how far right • Range: how low, how high • Included use [ ] • Not included use ( )

5. Does the graph represents a function. State the domain and the range. Domain: Range: Function?

6. Does the graph represents a function. State the domain and the range. Domain: (-4, 5] Range: (4, -3] Function? Yes 

7. Solve this system of equations by using the Substitution method.

8. Solve this system of equations by using the Substitution method. • Isolate 1 variable in 1 of the equations; • substitute that information into the other equation. • Solve for the value of the other variable. • Go back and evaluate with the isolated variable.

9. Solve this system of equations by using the Substitution method. Solve:

10. Solve this system of equations by using the Substitution method. Solve:

11. Solve this system of equations by using the Addition/Elimination method.

12. Solve this system of equations by using the Addition/Elimination method. • If necessary, multiply one of both equations by a number so that when the two equations are added together one of the variables is eliminated. • Solve for the remaining variable; go back to one of the original equations – substitute in the value and solve for the other variable.

13. Solve this system of equations by using the Addition/Elimination method. • Solve

14. Solve this system of equations by using the Addition/Elimination method.

15. Solve system of equations by either the Substitution or Addition method.

16. Solve system of equations by either the Substitution or Addition method. • To use the substitution method if a variable is isolated. • To use the addition method when both variables are on the same side of the equation.

17. Investment word problem, set up a system of equations & solve it.

18. Investment word problem, set up a system of equations & solve it. • 1st equation – amounts: what was invested. • 2nd equation – value: sum of percentages time amount equal the interest. • Solve by one of the above methods.

19. Investment word problem, set up a system of equations & solve it. • Bret has $50,000 to invest, some at 12% and the rest at 8%. If his annual interest earned is $4,740, how much did he invest at each rate?

20. Investment word problem, set up a system of equations & solve it. • Bret has $50,000 to invest, some at 12% and the rest at 8%. If his annual interest earned is $4,740, how much did he invest at each rate?

21. For the following mixture word problem, set up a system of equations and solve it.

22. For the following mixture word problem, set up a system of equations and solve it. • 1st equation – amounts: ounces, pounds, liter, etc. • 2nd equation – value: $ or % multiplied to the amount added together and equal to the $ or % multiplied to the total amount. • Solve by one of the above methods.

23. For the following mixture word problem, set up a system of equations and solve it. Victor mixes a 20% acid solution with a 45% acid solution to create 100 ml of a 40% acid solution. How many ml of each solution did he use?

24. For the following mixture word problem, set up a system of equations and solve it. Victor mixes a 20% acid solution with a 45% acid solution to create 100 ml of a 40% acid solution. How many ml of each solution did he use?

25. For the following D = RT word problem, set up a system of equations and solve it.

26. For the following D = RT word problem, set up a system of equations and solve it. • Label 2 equations: • Formula: (rate) (time) = distance mph hour miles • total time ( t ) and (total – t) • total distance ( d ) and (total – d)

27. For the following D = RT word problem, set up a system of equations and solve it. A sailboat leaves the island traveling at 35 mph. Five hours later a hydrofoil begins to pursue the sailboat at a speed of 60 mph. How far from the island will they meet?

28. For the following D = RT word problem, set up a system of equations and solve it. A sailboat leaves the island traveling at 35 mph. Five hours later a hydrofoil begins to pursue the sailboat at a speed of 60 mph. How far from the island will they meet?

29. Solve this system of equations with 3 unknowns.

30. Solve this system of equations with 3 unknowns. • Use the elimination method and 2 of the original equations to make equation 4. • Use the other original equation and an already used original equation to eliminate the same variable and make equation 5. • Use equations 4 and 5 to eliminate another variable; put value back into 4 or 5, put both values back into and original equation.

31. Solve this system of equations with 3 unknowns. • 1) x + y + z = 8 • 2) x + 2y – z = 3 • 3) 2x – y + z = 3

32. Solve this system of equations with 3 unknowns. • 1) x + y + z = 8 • 2) x + 2y – z = 3 • 3) 2x – y + z = 3 • 1) x + y + z = 8 • 2) x + 2y – z = 3 • 4) 2x + 3y = 11 • 2) x + 2y – z = 3 • 3) 2x – y + z = 3 • 5) 3x + y = 6 • 4) 2x + 3y = 11 • -9x – 3y = -18 • -7x = -7 • -7 -7 • x = 1 • 2x + 3y = 11 • 2(1) + 3y = 11 • -2-2 • 3y = 9 • 3 3 • y = 3 • Solve for z • x + y + z = 8 • (1) + (3) + z = 8 • 4 + z = 8 • -4 -4 • z = 4

33. Add or Subtract the polynomials as indicated. Simplify your answer.

34. Add or Subtract the polynomials as indicated. Simplify your answer. • Combine like terms − • Beware of subtraction outside of the parentheses, change all the signs inside the parentheses.

35. Add or Subtract the polynomials as indicated. Simplify your answer.

36. Add or Subtract the polynomials as indicated. Simplify your answer.

37. Multiply the following polynomials as indicated. Simplify your answer.

38. Multiply the following polynomials as indicated. Simplify your answer. • If there is an “outside” exponent, write the base as many time as indicated by the exponent. • Use the distributive property. • Simplify your answer by combining like terms.

39. Multiply the following polynomials as indicated. Simplify your answer.

40. Multiply the following polynomials as indicated. Simplify your answer.

41. Use long division, where R is less than the degree of D.

42. Use long division, where R is less than the degree of D. • Divide the leading term of the denominator into the leading term of the numerator. • Multiply back to all terms that were in the denominator. • Subtract, better yet, add the opposite. • Repeat above steps till degree “inside” is less than the degree “outside”.

43. Use long division, where R is less than the degree of D.

44. Use long division, where R is less than the degree of D.

45. Factor completely – 2 Terms

46. Factor completely – 2 Terms • Always look for a common factor • immediately take it out to the front of the expression all common factors, show what’s left inside ONE set of parenthesis • Identify the number of terms. If there was a common factor, then look at the number of terms left inside the parenthesis. • If there are only two terms, see if it is the sum or difference of perfect cubes or squares • a2 – b2 = (a + b)(a – b) • a3 – b3 = (a – b)(a2 + ab + b2) OR • a3 + b3 = (a + b)(a2 – ab + b2) • To factor the sum and difference of cubes, write what you see without exponent 3, “square” “smile” “square”, the second sign is different, the last sign is always plus.

47. Factor completely: 40 – 5y3

48. Factor completely: 40 – 5y3 • Common: 5(8 – y3) • See exponent 3: 5(23 – y3) • 5(2 – y)(4 + 2y + y2)

49. Factor completely – 3 Terms

50. Factor completely – 3 Terms • Always look for a common factor • immediately take it out to the front of the expression all common factors • show what’s left inside ONE set of parenthesis • Identify the number of terms. • If there are three terms, and the leading coefficient is positive: • find all the factors of the first term, find all the factors of the last term • Within 2 sets of parentheses, • place the factors from the first term in the front of the parentheses • place the factors from the last term in the back of the parentheses • NEVER put common factors together in one parenthesis. • check the last sign, • if the sign is plus: use the SAME signs, the sign of the 2nd term • if the sign is minus: use different signs, one plus and one minus • “smile” to make sure you get the middle term • multiply the inner most terms together then multiply the outer most terms together, and add the two products together.