Mathematics Review: Arithmetic, Algebra, and Geometry, Exams of Mathematics

Download Mathematics Review: Arithmetic, Algebra, and Geometry and more Exams Mathematics in PDF only on Docsity! Praxis 5003 Mathematics Study Guide place value system - ✔o️ne in which the position of a digit in a number determines its value base ten - ✔s️tandard system. Each place represents ten times the value of the place to its right. Place value chart - ✔a️ way to make sure digits are in the right place powers of 10 - ✔e️ach digit to the left of the decimal point increases progressively in powers of ten. Each digit to the right decreases progressively in powers of ten. rounding - ✔i️t's important to look at the number in the next smaller place. If this number is 5 or more, the number in the place we're rounding is increased by 1 and all other numbers are changed to 0. If it's less than 5 the number we're looking at stays the same and everything to the right is changed to 0. rational numbers - ✔i️ntegers, fractions, mixed numbers,and both terminating and repeating decimals. find the sum of 152.3 and 36.342 - ✔1️88.642 find the difference of 152.3 and 36.342 - ✔1️15.958 find the product of 3.52 and 4.1 - ✔1️4.432 find the quotient of 5.3 divided by 1.45 - ✔3️.7 addition - ✔i️ndicated by the expressions: sum, greater than, and, more than, increased by, added to, entire, total subtraction - ✔c️an be expressed by: difference, fewer than, minus, less than, decreased by multiplication - ✔i️s shown by: product, times, multiplied by, twice *may include each or per hour division - ✔i️s used for: quotient, divided by, ratio *may include each or per hour At his job, John gets paid $20 for every hour he works. If John made $940 in a week, how many hours did he work? - ✔9️40/20=47 remainder - ✔I️f a divisor does not divide evenly into a dividend we express the leftover amount as this. Usually indicated a fractional answer. algorithms - ✔m️ethods or strategies for solving problems partial sums method - ✔F️irst we sum the columns from left to right, then we add the column values. column addition method - ✔F️irst we add the digits in each column, then we perform the place caries from right to left. right to left addition - ✔t️raditional method. We sum the columns from right to left, performing carries mentally or writing them down. commutative property - ✔T️he property that says that two or more numbers can be added or multiplied in any order without changing the result. associative property - ✔C️hanging the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication left to right subtraction - ✔w️e decompose the second number into smaller values and perform the individual subtractions. (ex. to solve 335-78 we break 78 down into 70+8) partial differences method - ✔f️irst we operate on each column individually, being careful to record a sign of each result. Then we sum the results to yield the final answer same change rule - ✔t️akes advantage of the fact that subtraction is easier if the smaller number ends in zero. Thus, we change each number by the same amount to produce a smaller number ending in zero. (ex 335-78 becomes 337-80) partial products method - ✔w️e decompose each term into base-ten form, and multiply each pair of terms. ✔3️(4x) + 3(2)= 12x + 6 variables - ✔i️n algebraic expression these stand for unknown numbers evaluate x + 5 for x=3 - ✔x️ + 5 = 3 + 5 = 8 constant - ✔f️ixed numbers (ex. in 7x + 20y + 3, 3 is a constant as are 20 and 7.) terms - ✔p️arts of the expression separated by + or - factors - ✔p️arts that are multiplied together (ex 7x has the factors of 7 and x) coeficients - ✔c️onstant factors that multiply a variable (ex. in 7X + 20y + 3, 20 is the coefficient of y and 7 is the coefficient of x) graphing a linear inequality - ✔t️he dot will be hollow if the inequality sign is < or >. If the inequality sign is ≥ or ≤ the dot on the graph will be solid. The arrow goes the direction the inequality sign points. linear relationship - ✔a️ relationship in which a fixed change in one quantity results in a fixed change in another quantity. recurrence relation - ✔e️quation that defines a sequence recursively. Each term of the sequence is defined as a function of the preceding terms. point - ✔i️ndicates place or position. Has no length, width or thickness. An infinite number of lines can be drawn through one point. line - ✔c️onsidered a set of points. May be straight or curved, but commonly this term refers to straight lines. Extends indefinitely in both directions plane - ✔s️et of points composing a flat surface. No boundaries. line segment - ✔l️ine that has two end points ray - ✔h️as exactly one end point. Extends indefinitely in one direction perpendicular - ✔i️f two lines intersect at exactly one point and create right angles parallel - ✔t️wo lines in the same plane that do not intersect. angle - ✔i️ntersection of two rays. right angle - ✔m️easures 90 degrees acute angle - ✔m️easures more than 0 degrees but less than 90 degrees obtuse angle - ✔m️easures more than 90 degrees but less than 180 degrees. straight angle - ✔m️easures 180 degrees reflexive angle - ✔m️easures more than 180 degrees and less than 360 degrees polygon - ✔s️imple, closed, two-dimensional figures composed of line segments and are named according to the number of sides they have quadrilateral - ✔p️olygon with 4 sides trapezoid - ✔q️uadrilateral with exactly one pair of parallel sides isosceles trapezoid - ✔t️he non parallel sides of this trapezoid are congruent congruent - ✔H️aving the same size and shape parallelogram - ✔q️uadrilateral with two pairs of parallel sides supplementary angles - ✔T️wo angles whose sum is 180 degrees rectangle - ✔p️arallelogram that contains a right angle rhombus - ✔p️arallelogram with all sides of equal length square - ✔r️ectangle with all sides of equal length T/F all squares are rhombuses. - ✔t️rue T/F all parallelograms are rectangles. - ✔f️alse. Some parallelograms are rectangles. T/F some rectangles are trapezoids. - ✔F️alse. Trapezoids only have one pair of parallel sides. T/F all rectangles are parallelograms - ✔t️rue triangle - ✔p️olygon with 3 sides acute triangle - ✔t️riangle that has exactly 3 acute angles right triangle - ✔t️riangle with one right angle obtuse triangle - ✔t️riangle with one obtuse angle equilateral triangle - ✔t️riangle with all 3 sides measuring the same length isosceles triangle - ✔t️riangle with 2 sides measuring the same length scalene triangle - ✔t️riangle with no sides measuring the same length cylinder - ✔t️wo congruent circular bases that are parallel sphere - ✔a️ space figure having all it's points the same distance from the center cone - ✔a️ space figure having a circular base and a single vertex. pyramid - ✔a️ space figure with a square base and 4 triangle shaped sides 1 cup ≈ 0.24 liters 1 pint ≈ 0.47 liters 1 quart ≈ 0.95 liters 1 gallon ≈ 3.8 liters mean - ✔t️he average value of a data set median - ✔t️he middle of a data set mode - ✔t️he value that appears most often in a data set range - ✔t️he difference between the highest and the lowest values in a data set variance - ✔t️he average squared distance from each value of a data set to the mean. standard deviation - ✔s️quare root of the variance measure of central tendency - ✔A️ measure of location of the middle (center) of a distribution of a set of data (i.e., how data clusters) inference - ✔s️tatement derived from reasoning. Helps us to interpret the data that is being presented. trend line - ✔s️hows the correlation between two sets of data. Can be positive (both sets of data increase), negative (one set of data increases and one decreases), or no correlation. line plot - ✔o️rganizes data in numerical order along a number line. line graph - ✔c️ompares two variables, and each variable is plotted along an axis. bar graph - ✔s️imilar to histograms. However bar graphs are often used to convey information about categorical data. pie chart - ✔a️ka circle graph. Represent relative amounts of a whole. scatter plots - ✔c️ompare two characteristics of the same group of things or people and usually consist of a large body of data. Shows how much one variable is affected by another. correlation - ✔A️ measure of the relationship between two variables stem and leaf plots - ✔v️isually similar to line plots. Best suited for small sets of data. Stem: the digits in the greatest place value of the data values Leaves: the digits in the next greatest place values box-and-whisker plot - ✔d️isplays 5 statistics: minimum, maximum, and 3 quartiles. histogram - ✔u️sed to summarize information from large sets of data that can be naturally grouped into intervals. frequency - ✔t️he number of times any particular data value occurs pictograph - ✔u️ses small figures or icons to represent data sample space - ✔i️n the study of probability this is a list of all possible outcomes of an experiment probability - ✔m️easures the chance of an event