Praxis 11 Multiple subjects test Math

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Praxis 11 Multiple subjects test Math
2013-09-23 15:37:47
Math teaching

This is the study set for the Praxis II Multiple subjects Math
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  1. What are some concepts to help Kindergartners learn math?
    • position – top, middle, bottom, above, below, before, after, between, under, inside, outside, left, and right
    • visual attributes – same and different colors, shapes, and sizes; identifying items that are out-of-place or don't belong
    • sorting – by size, color, type, or shape; identifying an equal number, more, or fewer of a given item

    graphing – the use of picture graphs and using data from graphs

    patterns – identifying, copying, extending, and making patterns; finding patterns that are different or alike, making predictions from patterns

    measurements – longer and shorter; how much they weigh, heavier and lighter; how much an item can hold
  2. What is the Communicative Property?
    The product is the same regardless of the order of the factors.

    • For example:
    • 2 * 5 = 5 * 2.
  3. What is the Associative property?
    The product is the same regardless of grouping.

    • For example:
    • (2 * 5) * 3 = 2 * (5 * 3).
  4. What is the Distributive property?
    Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

    • For example:
    •  2 * (3 + 4) = (2 * 3) + (2 * 4) = 14
  5. What is the Zero Property?
    The sum of a number and 0 is that number. In multiplication, the product of a number and 0 is 0.

    • For example:
    • 3 + 0 = 3 and 3 * 0 = 0
  6. What is a Integer?
    The set of positive and negative numbers, including zero. Integers do not include fractions (1/3), decimals (0.56), or mixed numbers (7¾).
  7. What is a prime number?
    A whole number greater than 1 that has only two factors, itself and 1; that is, a number that can be divided evenly only by 1 and itself.
  8. What is a Composite number?
    A whole number greater than 1 that has more than two different factors. In other words, any number that is not a prime number. For example: The composite number 8 has the factors of 1, 2, 4, and 8.
  9. What is an even number?
    • Any integer that can be divided by 2 without leaving a remainder.
    • For example:
    • 2, 4, 6, 8, and so on.
  10. What is an Odd number?
    Any integer that cannot be divided evenly by 2.

    • For example:
    • 3, 5, 7, 9, and so on.
  11. What is a rational number?
    Rational numbers are the set of whole numbers, integers, decimals, and fractions
  12. What is a rational number?
    Rational numbers are the set of whole numbers, integers, decimals, and fractions. Rational numbers can be expressed as either a negative or positive value. Any terminating decimal that can be expressed as a fraction is a rational number. For example, 45.6 can be written as 456/10.
  13. What is a irrational number?
    Irrational numbers are numbers that are not rational. That is, like the square root of 2, they cannot be written as fractions or decimals because the number of decimal places is infinite and a recurring pattern does not exist within the number. For example, Pi () begins with 3.141592653 and continues without end, so Pi is an irrational number.
  14. What is a real number?
    Real numbers are the set of all rational and irrational numbers and are used in all applications of measuring, comparing, counting, or determining quantities.
  15. What is a factor?
    Factors are numbers that are multiplied together to obtain a product.

    • Example:
    • The Factors of 6 are 1,6,2,3
  16. What is a fraction and what are their parts?
    A fraction is a way to compare equal parts with a whole.

    • Example:
    • 5/8 is five parts out of 8 pieces

    Numerator (top) / Denominator (bottom)
  17. Describe place value for decimals.
    • .tenths, hundredths, thousands
    • .   1          3                  5       = .135
  18. Define Addition.
    increasing one number by adding one or more other numbers to attain a sum.

    • Example:
    • 2 + 4 = 6
    • 8 + 9 + 10 = 27
  19. What is Subtraction?
    finding the difference between two numbers or reducing one number by another.

    • For example:
    • 6 – 4 =2.
  20. Define Multiplication.
    a form of repeated addition in which two numbers are combined to give a product.

    • Example:
    • 3*2=6 is really 2+2+2=6
  21. Define Division.
    a form of repeated subtraction achieved by dividing one number by another number.

    • Example:
    • 20 ÷ 4 = 5 is twenty items divided into four piles which gives you five items in each pile
  22. What does PEDMAS mean?
    The way in which equations are solved.

    Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

    • Example:
    •       5 + 20 / 4 * (2+3)2 - 6 =
    • P    5 + 20 / 4 * 5- 6 =
    • E    5 + 20 / 4 * 25 - 6 =
    • D    5 + 5 * 25 - 6 =
    • M    5 + 125 - 6 =
    • A    130 - 6 =
    • S    124
  23. What is a cardinal Number?
    Cardinal numbers are the numbers we use for counting. They are, therefore, also called counting numbers or natural numbers
  24. What is a ordinal number?
    One that shows position?

    • Example:
    • 1st, 2nd, 3rd
  25. What is the least common denominator?
    The lowest multiple of one or more denominators of a fraction.

    • Example:
    • the lowest common denominator for 2/3 and 4/9 is 9, so the fractions can be expressed as 6/9 and 4/9 for easier computation or comparison
  26. What is the Greatest Common Factor?
    The largest number that is a factor of two or more numbers

    • Example:
    • The factors of 15 are 1, 3, 5, and 15; the factors of 35 are 1, 5, 7, and 35. Therefore, the greatest common factor of 15 and 35 is 5.
  27. What is the least common multiple?
    Least or lowest common multiple (LCM) – the smallest number that is a multiple of two or more numbers.

    • Example:
    • The multiples of 3 include 3, 6, 9, 12, 15, etc.; the multiples of 5 include 5, 10, 15, 20, etc. Therefore, the least common multiple of 3 and 5 is 15.
  28. What are equivalent fractions?
    Fractions that look different, but are actually the same.

    • Example:
    • 1/5 = 20/100 = 2/10 = 4/20
  29. What is a common simple fraction?
    A fraction that is commonly seen such as 3/4, 5/8, 1/2.
  30. What is a bar graph used for?
    Compare data.
  31. What is a line graph used for?
    Connects points to show a increase or decrease over time
  32. What is a pictograph?
    Uses pictures of symbols to show data.
  33. What are some problem solving strategies?
    • i) Use manipulatives or act out the problem
    • ii) draw a picture
    • iii) look for a pattern
    • iv) guess and check
    • v) use logical reasoning
    • vi) make an organized list
    • vii) make a table
    • viii) solve a simpler problem
    • ix) work backward.
  34. Ways to solve a word problem are?
    • Achieve an understanding of the problem by reading it carefully, finding and separating the information needed to solve the problem, and discerning the ultimate question in the problem.
    • Make a plan as to what needs to be done to solve the problem.
    • Solve the problem using the plan from step 2
    • Review the word problem to make sure that the answer is the correct solution to the problem and makes sense
  35. How do you find the percentage of a number?
    To find a percent of a number, the percent must first be changed to a decimal number. So 30% becomes 0.3. Then, 0.3 is multiplied by the number in question.

    Example: To find 30% of 33, multiply 0.3 * 33; the product is 9.9; that is, 9.9 is 30% of 33.
  36. How do you find the percentage of something?
    To find the percentage, you need to know the number of the part and the number of the whole. If you know only the separate numbers, you will have to add them to get the whole.

    Example: In the school cafeteria, 7 students from your class chose pizza, 9 chose hamburgers, and 4 chose tacos. To find any percentage, you first add 7 + 9 + 4 = 20. The percentages can be found by dividing 7, 9, and 4 each by the whole (20). Four out of 20 students chose tacos, and 4/20 = 1/5. Changing 1/5 to a percentage tells us that 20% of the students chose tacos.
  37. What is the Average?
    Average is the overall term for the central tendencies of numbers that are found by determining the mean, median, and mode. An average is a single value used to represent a collection of data.

    Found adding the data points up and dividing by the answer by the number of points added.

    • Example:
    • my data is (2,3,4,5,6) 

    2+3+4+5+6 = 20

    there are 5 data points

    20/5 =4 so the average of this set is 4
  38. What is the Mean?
    The formula is: sum of values ÷ number of values
    Mean is a measure of the general size of the data

    • Example:
    • See average example
  39. What is the Median?
    • Median is the middle value of a distribution that is arranged in size order
    • The formula is: median = 1/2 (n + 1)
  40. What is the Mode?
    Mode is the value(s) that occur most often in a distribution.

    • Example:
    • in the list of 21, 23, 23, 25, 27, 27, 27, 28, 30, the value 27 occurs most often and is, therefore, the mode
  41. What is Absolute value?
    The Absolute Value of a number is its distance from zero. Therefore, -3 and +3 have the same absolute value of 3
  42. What are some strategies in helping students develop number sense?
    • Frequently asking students to make their calculations mentally and rely on their reasoning ability. Answers can be checked manually afterwards, if needed.
    • Having a class discussion about solutions the students found using their minds only and comparing the different approaches to solving the problem. Have the students explain their reasoning in their own words.
    • Modeling the different ideas by tracking them on the board as the discussion progresses.
    • Presenting problems to the students that can have more than one answer
  43. What are the measurements of motion?
    • Speed – the measure of distance moved over time.
    • Formula: rate = distance ÷ time.

    Velocity – the measure of distance moved in a particular direction over a period of time. Velocity is a vector quantity, meaning it has both magnitude (size) and direction. Often measured in mph or kph, velocity is expressed, for example, as 150 mph on a bearing of 45 degrees.

    Acceleration – the rate of change of velocity. Also a vector quantity, acceleration is most often measured in meters per second. The formula for calculating acceleration equals change of velocity divided by time taken. For example, a sports car is considered fast if it can accelerate from 0-100 kph in 4 seconds.
  44. What is Ratio?
    A ratio is a comparison of two quantities in a particular order.


    I there are 14 computers in a lab, but the class has 20 students, there is a ratio of 14 to 20

    20:14 or 20/14
  45. What is a proportion?
    A proportion is the relationship of change in two quantities. A direct proportion describes a quantity that increases with an increase in another quantity or decreases with a decrease in the other quantity.

    • Example:
    • if a sheet cake can be cut to serve 18 people and 2 sheet cakes can serve 36 people, the number served is directly proportional to the number of cakes.
  46. What is Inverse proportion?
    Inverse proportion describes a quantity that increases as the other quantity decreases.

    • Example:
    • The time of a car trip decreases as the speed increases, so the time is inversely proportional to the speed.
  47. How do you calculate Simple Interest?
    Formula: Simple interest = Principle * Rate of interest * Time ÷ 100

    • Example:
    • If a person invests $1,000 at an interest rate of 5% per annum, that would be 1,000 * 5 * 1 ÷ 100 or 5,000 ÷ 100 = $50
  48. How do you calculate Compound Interest?
    Formula: Compound interest = Principle * (1 + interest rate [i.e. the multiplier])Time – Principle

    • Example:
    • $1,000 invested for 3 years at 5% interest would be 1,000 * (1.05)3 - $1,000 = 1157.63 – 1,000 = $157.63
  49. Define Domain and Range.
    Domain: The set of values to which a function is applied.

    Range: The set of values to which the results belong.
  50. Define a Composite Function.
    A combination of two or more functions; the second and subsequent functions are represented by different letters.

    • Example:
    • f◦g(x) means “f of g of x;” g is calculated first and that answer is used in the function, f
  51. What is a1 =
    a1 = 1
  52. What does 1n=
  53. What is a square root?
    A number that is times by itself or raised by the power of two
  54. Solve:
    51/4 * 53/4
    51/4 * 53/4 = 5 1/4+3/4 = 51 =1
  55. Solve:
    (an)m = an*m
  56. Solve:
  57. What does am*an =
  58. Define a Inverse function.
    An operation or series of operations that reverses a function; usually written as f -1(x).
  59. What is a perfect square?
    A perfect square is a number that has an integer for a square root. In other words the square come out as a whole number.
  60. How many perfect squares are there fro 1 to 100?
    There are ten one for each number from one to 10
  61. True or False

    All perfect squares can have a positive and negative square.

    • For example:
    • The square root of 9 is +3 and -3 because 3 * 3 = 9 and -3 * -3 = 9.
  62. What is a Algorithm?
    Algorithms are systematic, problem-solving procedures used to find the solution to a mathematical computation in a finite number of steps. Algorithms look for the right answer.


    • We are 50 miles from home and traveling at 60 miles an hour.
    • Since there are 60 minutes in a hour we are traveling at a mile a minute. Therefore we should be home in precisely 50 minutes
  63. What is an estimate?
    Estimates look for a answer that is close to the right answer.


    We are 50 miles from home and traveling at 60 miles an hour we should be home in a little under an hour.
  64. What is scientific notation?
    A way of writing very large numbers.

    234,000,000 = 2.34 * 108

    Count the numbers to the right of the decimal to get the power

    0.0000234 = 2.34*10-5
  65. 18 / 6
    which one is the dividend?
  66. When dividing what is the remainder?
    The left over pieces
  67. 18/6

    Which number is the quotient?
  68. What is the Vertical axis?
    Vertical Axis is the up-and-down number line on a graph.
  69. What is the Horizontal Axis?
    Horizontal Axis is the left-to-right number line on a graph.
  70. On a graph what is the Scale?
    Scale is the marked intervals on the vertical or horizontal axis of a graph that represent the units being measured.

    • Example:
    • A common scale is from 1 to 10, with intervals of 1 (1, 2, 3, 4, 5, 6, 7, 8, 9, and 10).
  71. On a Graph what is an Interval?
    Interval is the fixed distance between the numbers on the scale of a graph.

    • Example:
    • If the axis reads 2001, 2002, 2003, 2004, then the graph represents one year intervals of data.
  72. On a graph what is a Coordinate?
    Coordinates are the points on the graph that indicate the intersection of two data numbers.

    • Example:
    • A graph that shows 60% of a goal was reached in November would have a point placed where 60 and November meet on the graph.
  73. What does the Roman numeral "I" Stand for?
    I = 1
  74. What does the Roman numeral "V" Stand for?
  75. What does the Roman numeral "X" Stand for?
  76. What does the Roman numeral "L" Stand for?
  77. What does the Roman numeral "C" Stand for?
    C =100
  78. What does the Roman numeral "D" Stand for?
  79. What does the Roman numeral "M" Stand for?
  80. What is the quadratic formula?
  81. In a graph what is a Point?
    A location found by its coordinates; usually represented on diagrams by a small dot or two crossed lines
  82. In a graph what is a Line Segment
    the part of a straight line between two points, thus having a fixed length
  83. In a graph what is a Transversal line?
    A line that crosses two or more other lines
  84. In a graph what is a Horizontal line?
    a line or plane that follows the horizon, at a right angle to the vertical
  85. In a graph what is a Vertical line?
    A line or plane that is at a right angle to the horizon
  86. In a graph what is a Perpendicular Line?
    A line or plane that is at a right angle to another line or plane
  87. In a graph what is a Parallel Line?
    A set of lines or curves that never cross and are the same distance apart at every point along the lines
  88. In a graph what is a Collinear Line?
    Points that lie in a straight line or share a common straight line
  89. What is a Plane?
    Dimensional object, with length and width
  90. What is a Coplanar?
    Points that lie on the same plane, or share a common plane.
  91. What is a Solid?
    A three-dimensional object, with a length, width, and thickness
  92. What is a quadrant?
    One of the four regions that is formed on a plane by the x and y axis
  93. What is a null or zero angle?
    A angle with zero degrees rotation.
  94. What is a whole turn angle?
    An angle that has turned 360 degrees
  95. What is a Right Angle?
    A 90 degree angle.
  96. What is a straight angle?
    180 degrees
  97. What is an Acute angle?
    One that is less then 90 degrees
  98. What is an Obtuse angle?
    One that is larger then 90 degrees but smaller then 180 degrees.
  99. What is a Reflex angle?
    An angle that is greater then 180 degrees.
  100. What is a Positive angle?
    An angle that is measured counter clockwise.
  101. What is a negative angle?
    An angle that is measured clockwise.
  102. What is a polygon?
    A shape that forms three or more vertices.
  103. What formula can be used to calculate the sum of the interior angles of a polygon?
    • 180(n-2)
    • where n = the number of sides of the polygon


    • A triangle has three sides n=3.
    • 180 (3-2)=180(1)=180
  104. How many sides does a Triangle have?
  105. How many sides does a Quadrilateral have?
  106. How many sides does a Pentagon have?
  107. How many sides does a Hexagon have?
  108. How many sides does a Heptagon or septagon have?
  109. How many sides does a Octagon have?
  110. How many sides does a Nonagon have?
  111. How many sides does a Decagon have?
  112. How many sides does a Hendecagon have?
  113. How many sides does a Dodecagon have?
  114. How many sides does a Quindecagon have?
  115. How many sides does a Icosagon have?
  116. What is a equiangular polygon?
    One in which all of the angles are equal.
  117. What is a equilateral polygon?
    One in which all of the sides are equal.
  118. What is a convex polygon?
    One in which one or more interior angles are greater than 180°.
  119. What is a regular polygon?
    One in which all the sides and interior angles are equal.

    Examples of regular polygons are squares, equilateral triangles, regular pentagons, and regular hexagons.
  120. What is a tessellation?
    Tessellation is the combination of one or more shapes such that, when repeated, the pattern covers a surface plane without leaving any gaps or overlaps.
  121. What is a regular tessellation?
    One in which all of the shapes are the same size and angle.

    Only three regular polygons tessellate in the Euclidean plane: triangles (in a pyramid shape), squares (in a block), and hexagons.
  122. What is a semi-regular tessellation?
    A semi-regular tessellation is a tessellation made up of more that one type of regular polygon.
  123. What is a Scalene triangle?
    The sides are all different lengths, so all three angles are different as well.
  124. What is a Isosceles triangle?
    Has two equal sides; the angles opposite these sides are also equal. An isosceles triangle has one line of symmetry that divides the triangle into two identical right-angled triangles
  125. What is a equilateral triangle?
    Has three equal sides; each angle measures 60°. An equilateral triangle has three lines of symmetry, each of which divides the triangle into two identical right-angled triangles.
  126. What is an acute angled triangle?
    All three interior angles are less than 90°
  127. What is an Obtuse angled triangle?
    One interior angle is greater than 90°
  128. What is a right angled triangle?
    One interior angle is equal to 90°; the other two angles are complementary, meaning they sum to 90°.
  129. What are side-side-side (SSS) triangles?
    Two triangles in which all three sides of one are equal to all three sides of another, but positioned differently.
  130. What are side-angle-side (SAS) triangles?
    Are two triangles in which two sides and the included angle of one triangle are the same as the other, but positioned differently.
  131. What are Angle-angle-side (AAS) triangles?
    Two triangles in which two angles and any side on one triangle are the same as that of the other, but positioned differently.
  132. What are Right-angle-hypotenuse-side (RHS) triangles?
    Two triangles in which the hypotenuse and one side of a right-angled triangle are the same as the other, but positioned differently.
  133. What are similar triangles?
    Same shape but not the same size.
  134. What is the Pythagorean theorem?
  135. What is a polyhedron?
    A polyhedron is a solid that has a surface area made of a series of polygons. The polygons are called "faces," and the lines where they meet are called "edges." The corners where three or more faces meet are called "vertices."
  136. Euler's therm is what
    (V)ertices - (E)dges +(F)aces =2

    • Example:
    • A cube has 8 vertices, 12 edges, and 6 faces, so 8 – 12 + 6 = 2.