2021 Year End Algebra Review Answers 1-100-1

86. Box and whisker plot

Lower extreme: lowest number Lower quartile: median of lower ½ #s Median: middle number Upper quartile: median of upper ½ #s Upper extreme: highest number 25% of data is between LE and LQ, 25% is between LQ and Median, 25% is between Median and UQ, and 25% is between UQ and UE... 100% total Interquartile range (IQR) = UQ - LQ... 50% of data Finding an outlier- # way out there compared to other #s 1. IQR * 1.5 2. Take answer and subtract from LQ 3. Take #1's answer and add to UQ 4. Any # lower than your #2 answer or greater than your #3 answer is an outlier. Outliers influence mean and range a lot

70. What is the formula for finding the nth term of an arithmetic sequence?

(chapter 4) 𝑎𝑛 = 𝑎1 + 𝑑(𝑛 − 1)

73. What is the midpoint formula?

(𝑥1+𝑥2/2,𝑦1+𝑦2/2)

88. Stem and Leaf Plot

- Key 2|4 = 24 The grey is the stem (tens place in this case) and the leaves are on the outside (ones place) Numbers should be in order from least to greatest with the smaller numbers being closest to the stem Numbers on left: 22,22,22,27,35,47,49 Numbers on right: 21,24, 25,25,26,31,32,32,37,45

85. Triangle Inequality Theorem

- The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In the figure, the following inequalities hold a+b>c

84. Scale Factor

- Used with maps, blue prints, etc. Shrinks or enlarges objects. PROPORTIONAL to original Ex. ½ inch = 3 ft where room's measurements on blueprint are 3 ½ inches by 4 inches... use a proportion to solve S.F. Room inches .5 = 3.5_ feet 3 x S.F Room inches .5 = 3_ feet 3 x ** Room is 21 feet by 18 feet

89. Finding probability of larger sample size

- Using the probability of favorable outcomes, set up a proportion to find the probability of the larger sample size. Example: The probability of tossing an even number on a six sided dice is ½. Therefore, the probability of tossing an even number on 600 die is 300 because: 1/2 = 𝑥/300

87. Compound Probability

- multiply the probability of the first favorable outcome by the probability of the second favorable outcome.

47. Any (nonzero) number to the zero power is equal to what?

1

81. How do you clear the memory on the graphing calculator?

2nd, +, 7, 1, 2

21. What are the 3 rules for standard form?

A is non-negative; A, B, & C are integers; A, B, C have a GCF of 1

95. Explain how to find relative frequency (including joint, marginal, and conditional relative frequency).

A ratio that contains a subtotal value over a total value. Joint Relative Frequency=joint frequency/table total. Marginal Relative Frequency=marginal frequency/table total. Conditional Relative Frequency=joint frequency/marginal frequency.

7. Definition of a function.

A relation where each x is paired with exactly one y

98. What is an outlier?

A value in a data set that is much less or much greater than the rest of the data. An outlier is 1.5 times the interquartile range less than the lower quartile or greater than the upper quartile.

38. What should the answer to a system look like?

An ordered pair (intersection point)

6. Definition of a relation.

Any set of ordered pairs

69. What is the difference between an arithmetic and geometric sequence?

Arithmetic sequences add the same number each time, and geometric multiplies by the same number each time

9. How do you use the vertical line test to tell if a graph is a function?

As the vertical line passes over the graph, the vertical line can only intersect the graph one time

34. What must you do if you multiply or divide both sides of an inequality by a negative number?

Change the inequality sign

33. What is the difference between correlation and causation?

Correlation is the relationship between two variables. Causation is when one variable directly causes the other variable.

82. Show a picture of parallel lines cut by a transversal and label all of the angle relationships.

Corresponding Angles Ex. 𝑚∠4 ≅ 𝑚∠8 Alternate Interior Angles Ex. 𝑚∠4 ≅ 𝑚∠6 Alternate Exterior Angles Ex. 𝑚∠1 ≅ 𝑚∠7 Consecutive Interior Angles Ex. 𝑚∠4 + 𝑚∠5 = 180°

15. What is the rate of change formula?

Difference in the dependent variable/ Difference in the independent variable Rate of change is the same as slope in the context of a word problem.

94. What is a two-way table?

Displays categorical data for two variables.

76. Explain how to find the distance between two points on a coordinate plane using the Pythagorean Theorem.

Draw the vertical and horizontal distance between the two points to form a right triangle and then use the Pythagorean Theorem.

30. How do you find the line of best fit on a graph and from a table?

Graph-draw a line that goes through as much data as possible and splits any remaining data evenly. Table (using a graphing calculator)-STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter

37. What are some ways to solve a system?

Graphing, Substitution, and Elimination

58. What are four methods for solving a quadratic equation?

Graphing, square roots, factoring, and the quadratic formula

62. What is the discriminant formula?

How many solutions if you get a negative, zero, or positive number? 𝑏^2 − 4𝑎𝑐 If the discriminant is negative, the answer is no solution. If the discriminant is zero, there is one real root. If the answer is positive, there are two real roots.

53. What does "a" tell you?

If the parabola opens up or down (if the vertex is a minimum or maximum) and the width of the parabola

78. How do you know your final answer of a radical expression is in simplest form?

If there are no perfect square factors under the radical, no fractions under the radical, and no radicals in the denominator

8. What's the short cut for recognizing a function in ordered pair form?

If you notice that there is an x value repeated with a different answer for the y value

66. How will you know if the exponential equation is growth or decay?

In equation form: If b is greater than one, it is growth. If b is less than one and greater than zero, it is decay.

67. How will you know if the exponential graph is showing growth or decay?

In graph form: The graph of growth will increase from left to right (a plane taking off). For decay, the graph decreases from left to right (a plane landing).

43. What is the rule of multiplying two powers with the same base?

Keep the base, add the exponents

45. What is the rule for taking a power to a power?

Keep the base, multiply the exponents

44. What is the rule of dividing two powers with the same base?

Keep the base, subtract the exponents

36. For linear inequalities, if it is greater than, where do you shade?

Less than? Greater than=shade above, Less than=shade below

60. What should be the first step when you factor?

Look for a GCF

4. Describe how to write an algebraic proof when solving an equation. Name the properties of equality.

Make a two column chart with statements and reasons. The first statement is the original problem and the reason is given. Each step of the work should be shown and a property (numeric or equality) listed as the reason for the work. Properties of equality: Addition, Subtraction, Multiplication or Division

46. What is the rule for changing a negative exponent into a positive?

Move it to the opposite location (numerator/denominator) of the fraction bar and make the exponent positive

35. If an absolute value equation is equal to a negative, what is the answer?

No solution

91. Define rational numbers.

Numbers that can be written as the ratio of two integers (in decimal form, they repeat or terminate)

92. Define irrational numbers.

Numbers that cannot be written as the ratio of two integers

39. When will a system have no solution?

Parallel lines

27. What is true about the slopes of parallel lines? Their y-intercepts?

Parallel lines have the same slopes, but different y-intercepts

28. What is true about the slopes of perpendicular lines? Their y-intercepts?

Perpendicular lines have slopes that are both opposite and reciprocal and can have the same or different y-intercepts

90. List the volume formulas for prisms, cylinders, pyramids, cones, and spheres.

Prisms/Cylinders: 𝑉 = 𝐵ℎ Pyramids/Cones: 𝑉 = (1/3)𝐵ℎ Spheres:𝑉 = (4/3)𝜋𝑟^3

1. What word indicates to use parenthesis when translating a verbal sentence into an algebraic one?

Quantity

23. If given two points, how do you use your calculator to get the equation?

STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter

40. When will a system have infinitely many solutions?

Same line (coinciding lines)

31. What is a residual?

Show an example. The difference between the observed value and predicted value.

26. How do you find the x and y-intercepts of an equation?

Substitute 0 for y and solve for x. Substitute 0 for x and solve for y

22. If you are given a point and a slope, explain how to find the equation.

Substitute the x, y, and m and solve for b. Write the equation using m and b

99. What is mean absolute deviation?

The average distance each data value is from the mean.

32. What is a correlation coefficient and what does it tell you about the scatter plot/ line of best fit?

The correlation coefficient is "r," and it tells you how closely your data fits the line of best fit. The r values range between -1 through +1.

10. How can you tell if a graph, table, or equation is showing a linear model?

The graph shows a line, the table shows consistent numbering for the x values and repeated addition (or subtraction) of the same number for the y values, the equation can be written as slope-intercept form 𝑦 = 𝑚𝑥 + 𝑏 (the exponent of x must be one) or be a special linear equation 𝑥 = 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑟 𝑦 = 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟

83. What is the Exterior Angle Theorem for triangles?

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

54. If the abs value of "a" was really small, what would be true of the graph?

The parabola would be wide.

63. How many solutions should x²=16 have?

Two

13. What is the slope of a vertical line?

Undefined

57. How do you find the vertex? When is the vertex a minimum value? A maximum value?

Use the formula 𝑥 = −𝑏/2𝑎 to find the x-value, substitute the x-value into the original equation, and solve for y. The vertex is an ordered pair The vertex is a maximum if the parabola opens down and a minimum if it opens up

77. Explain how to find the length of the diagonal of a rectangular prism.

Use the Pythagorean Theorem to find the floor (2-D) diagonal and then use the Pythagorean Theorem to find the space (3-D) diagonal.

56. How do you find the axis of symmetry?

Use the formula 𝑥 = −𝑏/2𝑎

80. What is an extraneous solution?

Values (solutions) that do not make the original equation true

100. What is standard deviation?

Variation from the mean.

75. What is the Pythagorean Theorem formula?

What kind of triangle do you use it on? 𝑎^2 + 𝑏^2 =𝑐^2 , 𝑟𝑖𝑔ℎ𝑡

16. What is the direct variation formula?

What letter represents the constant of variation? 𝑦 = 𝑘𝑥; k is the constant of variation (𝑘 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 𝑖𝑛 𝑎 𝑑𝑖𝑟𝑒𝑐𝑡 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛)

41. When is it best to use your graphing calculator to solve a system?

When both equations are in slope intercept form

59. When should you use square roots to solve the quadratic equation?

When the equation is in 𝑦 = 𝑎𝑥^2 − 𝑐 form (NO bx term)

79. When would a radical equation produce no solution?

When the radical is equal to a negative

51. What would you do to simplify (𝑥 + 𝑦) ² ?

Write out the binomial factors and FOIL

93. Explain how to change 0. 5̅ into a fraction.

Write two equations that can be subtracted to convert the repeating decimal into a fraction. Let 𝑥 = 0. 5̅ (The first equation needs to have the decimal in front of the repeating number(s).) Let 10𝑥 = 5. 5̅ (The second equation needs to have the decimal after the repeating number(s).) When you subtract the second and first equations, the result is 9𝑥 = 5. Solve for x, 𝑥 = 5/9.

2. What letter is the domain? Range? Output? Input? Independent variable? Dependent variable?

X=Domain, Input, and Independent Variable Y=Range, Output, and Dependent Variable

42. What keys do you press on your graphing calculator to solve a system?

Y=, enter equations, 2 nd TRACE (Calc), 5 (intersection), ENTER, ENTER, ENTER. If graph does not show intersection point, adjust the window

14. What is the slope of a horizontal line?

Zero

65. What does 'a' and 'b' stand for?

a is the initial amount, and b the growth or decay factor

50. List the steps to divide two numbers in scientific notation.

a) Divide the numbers. b) Divide the powers of 10. c) Make adjustments to put in scientific notation.

49. List the steps to multiply two numbers in scientific notation.

a) Multiply the numbers. b) Multiply the powers of 10. c) Make adjustments to put in scientific notation.

96. How do you know if the data distribution in a histogram is normal or skewed? Draw an example of each.

can't find an image

19. What does m and b stand for?

m=slope, b=y-intercept

48. When dividing two numbers in scientific notation using a calculator, you need to use

parentheses.

11. Slope is the ratio of

the rise to run.

17. How do you find "k"?

y divided by x

55. What does the "c" stand for?

y-intercept

74. What is the distance formula?

√(𝑥2 − 𝑥1)^2 + (𝑦2 − 𝑦1)^2

72. What is the recursive formula for arithmetic and geometric sequences?

𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐: 𝑎𝑛 = 𝑎𝑛−1 + 𝑑 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐: 𝑎𝑛 = 𝑎𝑛−1 ∗ 𝑟 State the first term and 𝑛 ≥ 2.

20. What is the standard form of a line?

𝐴𝑥 + 𝐵𝑦 = 𝐶

71. What is the formula for finding the nth term of a geometric sequence?

𝑎𝑛 = 𝑎1 ∗ 𝑟^(𝑛−1)

3. What is the PERCENT of change formula?

𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒/𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 = %/100

61. What is the quadratic formula?

𝑥 = (−𝑏±√𝑏^2−4𝑎𝑐)/2𝑎

24. What is the special equation of an undefined line?

𝑥 = 𝑎𝑛𝑦 𝑛𝑢𝑚𝑏𝑒𝑟

68. What is the compound interest formula?

𝑦 = 𝐶(1 +𝑟/𝑛)^𝑛𝑡

64. What is the standard form of an exponential equation?

𝑦 = 𝑎 ∗ 𝑏^𝑥

25. What is the special equation of a zero sloped line?

𝑦 = 𝑎𝑛𝑦 𝑛𝑢𝑚𝑏𝑒𝑟

52. What is the standard form of a quadratic equation?

𝑦 = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐

18. What is the slope-intercept form of a line?

𝑦 = 𝑚𝑥 + 𝑏

12. What is the slope formula?

𝑦2−𝑦1/ 𝑥2−𝑥1