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Praxis 5003 Mathematics Study Guide
place value system - ✔️one in which the position of a digit in a number determines its value base ten - ✔️standard system. Each place represents ten times the value of the place to its right. Place value chart - ✔️a way to make sure digits are in the right place powers of 10 - ✔️each 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 - ✔️it'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 - ✔️integers, fractions, mixed numbers,and both terminating and repeating decimals. find the sum of 152.3 and 36.342 - ✔️188. find the difference of 152.3 and 36.342 - ✔️115. find the product of 3.52 and 4.1 - ✔️14. find the quotient of 5.3 divided by 1.45 - ✔️3. addition - ✔️indicated by the expressions: sum, greater than, and, more than, increased by, added to, entire, total subtraction - ✔️can be expressed by: difference, fewer than, minus, less than, decreased by multiplication - ✔️is shown by: product, times, multiplied by, twice *may include each or per hour
division - ✔️is 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? - ✔️940/20= remainder - ✔️If a divisor does not divide evenly into a dividend we express the leftover amount as this. Usually indicated a fractional answer. algorithms - ✔️methods or strategies for solving problems partial sums method - ✔️First we sum the columns from left to right, then we add the column values. column addition method - ✔️First we add the digits in each column, then we perform the place caries from right to left. right to left addition - ✔️traditional method. We sum the columns from right to left, performing carries mentally or writing them down. commutative property - ✔️The property that says that two or more numbers can be added or multiplied in any order without changing the result. associative property - ✔️Changing the grouping of numbers will NOT change the value. For example: (7 +
- 8 = 7 + (4 + 8) also works with multiplication left to right subtraction - ✔️we 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 - ✔️first 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 - ✔️takes 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 - ✔️we decompose each term into base-ten form, and multiply each pair of terms.
the ski club has 85 members; 80% o the members are able to attend the meeting. How many members attend the meeting - ✔️What is 80% of 85? n=0.8 x 85 n= steps to solving a word problem - ✔️1. restate the problem
- write an equation
- solve prime numbers - ✔️numbers whose only factors are 1 and the number itself composite numbers - ✔️whole numbers that have more than 2 different factors factor 30 into prime factors - ✔️30= 5 x 6= 5 x 3 x 2 or 30= 3 x 10= 3 x 2 x 5 Greatest Common Factor (GCF) - ✔️the largest number that is a factor of all the numbers given in a problem. Least Common Multiple (LCM) - ✔️the smallest number that all of the given numbers will divide into. estimation - ✔️A way of making sure your answer is reasonable, rounding is a commonly used strategy (aka approximation) equation - ✔️expresses a complete idea and is equivalent to an English sentence. (ex. 7 added to a number is 28 less than the number or n+7=n-28) expression - ✔️encompasses only part of an idea similar to a phrase in the English language. (ex. 7 added to a number or n+7) linear algebraic expressions - ✔️1. remove parentheses and identify terms
- group like terms together
- add the like terms (2x + 3) + (3x -2) - ✔️=2x + 3 + 3x - 2 =2x + 3x + 3 - 2 =5x + 1 3(4x + 2) -
✔️3(4x) + 3(2)= 12x + 6 variables - ✔️in algebraic expression these stand for unknown numbers evaluate x + 5 for x=3 - ✔️x + 5 = 3 + 5 = 8 constant - ✔️fixed numbers (ex. in 7x + 20y + 3, 3 is a constant as are 20 and 7.) terms - ✔️parts of the expression separated by + or - factors - ✔️parts that are multiplied together (ex 7x has the factors of 7 and x) coeficients - ✔️constant 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 - ✔️the 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 - ✔️a relationship in which a fixed change in one quantity results in a fixed change in another quantity. recurrence relation - ✔️equation that defines a sequence recursively. Each term of the sequence is defined as a function of the preceding terms. point - ✔️indicates place or position. Has no length, width or thickness. An infinite number of lines can be drawn through one point. line - ✔️considered a set of points. May be straight or curved, but commonly this term refers to straight lines. Extends indefinitely in both directions plane - ✔️set of points composing a flat surface. No boundaries. line segment - ✔️line that has two end points ray - ✔️has exactly one end point. Extends indefinitely in one direction
rhombus - ✔️parallelogram with all sides of equal length square - ✔️rectangle with all sides of equal length T/F all squares are rhombuses. - ✔️true T/F all parallelograms are rectangles. - ✔️false. Some parallelograms are rectangles. T/F some rectangles are trapezoids. - ✔️False. Trapezoids only have one pair of parallel sides. T/F all rectangles are parallelograms - ✔️true triangle - ✔️polygon with 3 sides acute triangle - ✔️triangle that has exactly 3 acute angles right triangle - ✔️triangle with one right angle obtuse triangle - ✔️triangle with one obtuse angle equilateral triangle - ✔️triangle with all 3 sides measuring the same length isosceles triangle - ✔️triangle with 2 sides measuring the same length scalene triangle - ✔️triangle with no sides measuring the same length cylinder - ✔️two congruent circular bases that are parallel sphere - ✔️a space figure having all it's points the same distance from the center cone - ✔️a space figure having a circular base and a single vertex. pyramid - ✔️a space figure with a square base and 4 triangle shaped sides
tetrahedron - ✔️a 4 sided space triangle. Each face is a triangle. prism - ✔️space figure with two congruent, parallel bases that are polygons. net - ✔️a two-dimensional figure that can be cut out and folded up to make a three dimensional solid. perimeter - ✔️the sum of the lengths of the sides of any polygon area - ✔️the number of square units covered by a polygon rectangle area formula - ✔️LW rectangle perimeter formula - ✔️2(L+W) triangle area formula - ✔️1/2(BH) triangle perimeter formula - ✔️a+b+c parallelogram area formula - ✔️bh parallelogram perimeter formula - ✔️sum of lengths of sides trapezoid area formula - ✔️1/2 H(b1+b2) trapezoid perimeter formula - ✔️sum of lengths of sides coordinate plane - ✔️a plane with a point selected as an origin, some length selected as a unit of distance, and two perpendicular lines that intersect at the origin, with positive and negative direction selected on each line. unit conversion - ✔️new units/old units or what you want/what you have
1 cup ≈ 0.24 liters 1 pint ≈ 0.47 liters 1 quart ≈ 0.95 liters 1 gallon ≈ 3.8 liters mean - ✔️the average value of a data set median - ✔️the middle of a data set mode - ✔️the value that appears most often in a data set range - ✔️the difference between the highest and the lowest values in a data set variance - ✔️the average squared distance from each value of a data set to the mean. standard deviation - ✔️square root of the variance measure of central tendency - ✔️A measure of location of the middle (center) of a distribution of a set of data (i.e., how data clusters) inference - ✔️statement derived from reasoning. Helps us to interpret the data that is being presented. trend line - ✔️shows 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 - ✔️organizes data in numerical order along a number line. line graph - ✔️compares two variables, and each variable is plotted along an axis. bar graph - ✔️similar to histograms. However bar graphs are often used to convey information about categorical data. pie chart - ✔️aka circle graph. Represent relative amounts of a whole. scatter plots -
✔️compare 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 - ✔️A measure of the relationship between two variables stem and leaf plots - ✔️visually 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 - ✔️displays 5 statistics: minimum, maximum, and 3 quartiles. histogram - ✔️used to summarize information from large sets of data that can be naturally grouped into intervals. frequency - ✔️the number of times any particular data value occurs pictograph - ✔️uses small figures or icons to represent data sample space - ✔️in the study of probability this is a list of all possible outcomes of an experiment probability - ✔️measures the chance of an event
