Praxis Core Math (5733)
Exam assessing fundamental math skills for educators.
Getting Started: Understanding the Praxis Core Math Exam
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Praxis Core Academic Skills for Educators: Mathematics (5733) — key terms, tricks & tips
Everything from the course in one searchable place: 242 entries. Use it to review before a practice test or look up a word you forgot.
242 results
Content Categories
Major sections of math topics covered on the exam.
Getting Started: Understanding the Praxis Core Math Exam
Number and Quantity
Category covering operations, ratios, percentages.
Getting Started: Understanding the Praxis Core Math Exam
Algebra and Functions
Category covering expressions, equations, graphs.
Getting Started: Understanding the Praxis Core Math Exam
Geometry, Probability, Statistics
Category covering shapes, data, likelihood.
Getting Started: Understanding the Praxis Core Math Exam
Multiple-choice
Question type where you select one best answer.
Getting Started: Understanding the Praxis Core Math Exam
Numeric Entry
Question type where you type in a numerical answer.
Getting Started: Understanding the Praxis Core Math Exam
Scaled Score
Converted raw score, typically 100-200.
Getting Started: Understanding the Praxis Core Math Exam
On-screen Calculator
The four-function calculator provided during the test.
Getting Started: Understanding the Praxis Core Math Exam
Praxis Core Math (5733) Overview & Structure
To remember the three content categories: 'NAGS' - Number, Algebra, Geometry/Stats.
Getting Started: Understanding the Praxis Core Math Exam
Praxis Core Math (5733) Overview & Structure
For California, the passing score for Praxis Core Math (5733) is 150. Remember to confirm your specific program's requirements, as some institutions may have higher standards.
Getting Started: Understanding the Praxis Core Math Exam
Praxis Core Math (5733) Overview & Structure
Not checking your state's specific passing score, which can vary.
Getting Started: Understanding the Praxis Core Math Exam
Praxis Core Math (5733) Overview & Structure
Spending too much time on one difficult question and running out of time for easier ones.
Getting Started: Understanding the Praxis Core Math Exam
Praxis Core Math (5733) Overview & Structure
Not practicing with the on-screen calculator, leading to slow calculations on test day.
Getting Started: Understanding the Praxis Core Math Exam
Diagnostic Test
An initial assessment to identify strengths and weaknesses.
Getting Started: Understanding the Praxis Core Math Exam
Study Plan
A structured schedule outlining study topics and time allocation.
Getting Started: Understanding the Praxis Core Math Exam
Active Learning
Engaging with material through practice, explanation, or creation.
Getting Started: Understanding the Praxis Core Math Exam
Official Resources
Study materials provided by the exam creator (ETS).
Getting Started: Understanding the Praxis Core Math Exam
Practice Test
A full-length simulation of the actual exam under timed conditions.
Getting Started: Understanding the Praxis Core Math Exam
Time Management
Strategically allocating time during both study and the exam.
Getting Started: Understanding the Praxis Core Math Exam
Effective Study Strategies for Praxis Core Math
To 'ACE' your Praxis Core Math: **A**ssess your knowledge, **C**reate a plan, **E**ngage actively!
Getting Started: Understanding the Praxis Core Math Exam
Effective Study Strategies for Praxis Core Math
The California Commission on Teacher Credentialing (CTC) emphasizes that candidates must demonstrate foundational math skills. Focus on understanding the underlying mathematical concepts, not just memorizing formulas, as questions often require applying principles to novel situations.
Getting Started: Understanding the Praxis Core Math Exam
Effective Study Strategies for Praxis Core Math
Only reviewing concepts you already know well, neglecting weak areas.
Getting Started: Understanding the Praxis Core Math Exam
Effective Study Strategies for Praxis Core Math
Passive studying, such as just rereading notes without practicing problems.
Getting Started: Understanding the Praxis Core Math Exam
Effective Study Strategies for Praxis Core Math
Not taking full-length practice tests under timed conditions before exam day.
Getting Started: Understanding the Praxis Core Math Exam
Integer
Whole numbers and their opposites, including zero.
Mastering Number Sense and Operations
Fraction
Represents a part of a whole; numerator over denominator.
Mastering Number Sense and Operations
Decimal
A number using base-ten place value to represent parts of a whole.
Mastering Number Sense and Operations
Percent
A ratio meaning 'out of one hundred', denoted by %.
Mastering Number Sense and Operations
Numerator
The top number in a fraction, indicating parts taken.
Mastering Number Sense and Operations
Denominator
The bottom number in a fraction, indicating total equal parts.
Mastering Number Sense and Operations
Mixed Number
A number combining a whole number and a proper fraction.
Mastering Number Sense and Operations
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator.
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
FDP: 'Fractions, Decimals, Percents' are just 'Different Ways to Say Parts' of a whole. Remember FDP to convert and compare!
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
The Praxis Core exam frequently tests your ability to convert between fractions, decimals, and percents. Look for keywords like 'what percentage,' 'fraction of,' or 'decimal equivalent.' Be prepared to order sets of numbers presented in different forms.
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
Confusing negative integer operations (e.g., -5 - (-3) is -5 + 3 = -2).
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
Forgetting to find a common denominator when adding or subtracting fractions.
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
Incorrectly moving the decimal point when converting between decimals and percents (e.g., 0.5% is 0.005, not 0.05).
Mastering Number Sense and Operations
Numbers: Integers, Fractions, Decimals, & Percents
Not simplifying fractions to their lowest terms when required.
Mastering Number Sense and Operations
Ratio
A comparison of two quantities by division.
Mastering Number Sense and Operations
Proportion
An equation stating that two ratios are equal.
Mastering Number Sense and Operations
Exponent
Indicates how many times a base number is multiplied by itself.
Mastering Number Sense and Operations
Base (exponent)
The number being multiplied by itself in an exponent.
Mastering Number Sense and Operations
Square Root
A value that, when multiplied by itself, gives the original number.
Mastering Number Sense and Operations
Cube Root
A value that, when multiplied by itself three times, gives the original number.
Mastering Number Sense and Operations
Cross-Multiplication
Method to solve proportions: ad = bc for a/b = c/d.
Mastering Number Sense and Operations
Reciprocal
One divided by a number; used with negative exponents.
Mastering Number Sense and Operations
Ratios, Proportions, Exponents, & Roots
Ratios and Proportions: 'Ratio' is a 'Ratio' of two numbers. 'Proportion' means 'Pro' for equal, 'portion' for parts. Exponents: 'Ex' means 'out' or 'many times' (like 'exit'). Roots: 'Root' is the 'base' from which a number 'grows'.
Mastering Number Sense and Operations
Ratios, Proportions, Exponents, & Roots
The exam often tests the ability to solve real-world problems using ratios, proportions, and percentages. Look for keywords like 'for every,' 'per,' 'rate,' 'scale,' and 'similar' to identify ratio and proportion questions. Be prepared to simplify expressions involving integer exponents and to calculate square and cube roots of perfect squares and cubes.
Mastering Number Sense and Operations
Ratios, Proportions, Exponents, & Roots
Confusing the order of quantities in a ratio (e.g., 2:3 vs. 3:2).
Mastering Number Sense and Operations
Ratios, Proportions, Exponents, & Roots
Incorrectly applying exponent rules (e.g., adding exponents when dividing, or multiplying bases).
Mastering Number Sense and Operations
Ratios, Proportions, Exponents, & Roots
Forgetting that a negative exponent means taking the reciprocal, not a negative number.
Mastering Number Sense and Operations
Order of Operations
The sequence for performing arithmetic operations.
Mastering Number Sense and Operations
PEMDAS
Acronym for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Mastering Number Sense and Operations
BODMAS
Acronym for Brackets, Orders, Division, Multiplication, Addition, Subtraction.
Mastering Number Sense and Operations
Estimation
Finding an approximate value or answer.
Mastering Number Sense and Operations
Rounding
Simplifying a number to a nearby value for estimation.
Mastering Number Sense and Operations
Number Line
A visual representation of numbers in order.
Mastering Number Sense and Operations
Interval
The space or distance between two points on a number line.
Mastering Number Sense and Operations
Order of Operations, Estimation, & Number Line
Please Excuse My Dear Aunt Sally! This classic helps you remember Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Mastering Number Sense and Operations
Order of Operations, Estimation, & Number Line
The Praxis Core Mathematics (5733) exam frequently tests the order of operations in multi-step problems, often embedding them within word problems or algebraic expressions. Look for keywords like 'evaluate,' 'simplify,' or 'calculate the value of' when multiple operations are present.
Mastering Number Sense and Operations
Order of Operations, Estimation, & Number Line
Performing addition/subtraction before multiplication/division.
Mastering Number Sense and Operations
Order of Operations, Estimation, & Number Line
Not working multiplication/division or addition/subtraction from left to right.
Mastering Number Sense and Operations
Order of Operations, Estimation, & Number Line
Incorrectly interpreting the scale or intervals on a number line.
Mastering Number Sense and Operations
Real Numbers
All numbers that can be represented on a number line.
Mastering Number Sense and Operations
Rational Numbers
Numbers expressible as a fraction p/q (q≠0).
Mastering Number Sense and Operations
Irrational Numbers
Numbers that cannot be expressed as a simple fraction.
Mastering Number Sense and Operations
Absolute Value
A number's distance from zero on the number line; always non-negative.
Mastering Number Sense and Operations
Scientific Notation
A number written as a × 10^n, where 1 ≤ |a| < 10.
Mastering Number Sense and Operations
Coefficient
The 'a' in a × 10^n, where 1 ≤ |a| < 10.
Mastering Number Sense and Operations
Real Numbers, Absolute Value, & Scientific Notation
R.I.N.W.N. (Real, Irrational/Rational, Integers, Whole, Natural) helps remember the number system hierarchy.
Mastering Number Sense and Operations
Real Numbers, Absolute Value, & Scientific Notation
The Praxis Core exam often tests your ability to identify number types. Pay close attention to keywords like 'integer,' 'rational,' and 'irrational.' For scientific notation, be ready to convert both ways and perform basic operations, especially multiplication and division.
Mastering Number Sense and Operations
Real Numbers, Absolute Value, & Scientific Notation
Confusing negative signs inside and outside absolute value bars (e.g., -|5| = -5, but |-5| = 5).
Mastering Number Sense and Operations
Real Numbers, Absolute Value, & Scientific Notation
Incorrectly moving the decimal point when converting to/from scientific notation, leading to the wrong exponent sign or value.
Mastering Number Sense and Operations
Real Numbers, Absolute Value, & Scientific Notation
Forgetting to adjust exponents when adding or subtracting numbers in scientific notation.
Mastering Number Sense and Operations
Unit of Measurement
A standard quantity used to express a physical quantity.
Mastering Number Sense and Operations
Customary System
Measurement system used in the US (e.g., inches, pounds).
Mastering Number Sense and Operations
Metric System
Decimal-based measurement system (e.g., meters, grams).
Mastering Number Sense and Operations
Conversion Factor
A ratio equal to one, used to change units without changing value.
Mastering Number Sense and Operations
Dimensional Analysis
Method using conversion factors to convert between units.
Mastering Number Sense and Operations
Prefixes (Metric)
Indicators like kilo-, centi-, milli- showing powers of ten.
Mastering Number Sense and Operations
Volume
Amount of space an object or substance occupies.
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
King Henry Died By Drinking Chocolate Milk: Kilo, Hecto, Deka, Base, Deci, Centi, Milli. This helps remember metric prefixes in order!
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
The Praxis Core exam expects you to be proficient in converting between common units within the same system (e.g., feet to inches) and sometimes between systems (e.g., miles to kilometers). Look for keywords like 'convert,' 'how many,' or 'what is the equivalent' in problem statements. Remember that 1 inch = 2.54 centimeters is a common inter-system conversion you might need.
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
Forgetting to include units in your final answer, making it ambiguous.
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
Incorrectly setting up conversion factors (e.g., multiplying instead of dividing, or vice-versa).
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
Confusing metric prefixes (e.g., thinking a centimeter is larger than a meter).
Mastering Number Sense and Operations
Units, Conversions, & Number Problem Solving
Not performing all necessary conversions in multi-step problems.
Mastering Number Sense and Operations
Expression
Numbers, variables, operations; no equals sign.
Algebraic Reasoning and Functions
Equation
Two expressions set equal with an '=' sign.
Algebraic Reasoning and Functions
Inequality
Compares expressions using <, >, ≤, ≥, ≠.
Algebraic Reasoning and Functions
Variable
A symbol (usually a letter) representing an unknown value.
Algebraic Reasoning and Functions
Constant
A fixed numerical value without a variable.
Algebraic Reasoning and Functions
Algebraic Expressions, Equations, & Inequalities
EQuality has an 'EQ' like 'equals,' while INequality has 'IN' for 'not equal.'
Algebraic Reasoning and Functions
Algebraic Expressions, Equations, & Inequalities
The Praxis Core Mathematics exam often tests your ability to translate verbal descriptions into algebraic expressions or equations. Look for keywords like 'is,' 'equals,' 'total,' 'sum,' 'difference,' 'product,' 'quotient,' 'less than,' 'greater than,' 'at least,' or 'at most' to correctly set up your statements.
Algebraic Reasoning and Functions
Algebraic Expressions, Equations, & Inequalities
Forgetting the order of operations (PEMDAS) when simplifying expressions.
Algebraic Reasoning and Functions
Algebraic Expressions, Equations, & Inequalities
Not performing the same operation to both sides of an equation or inequality.
Algebraic Reasoning and Functions
Algebraic Expressions, Equations, & Inequalities
Failing to reverse the inequality sign when multiplying or dividing by a negative number.
Algebraic Reasoning and Functions
Linear Equation
An equation whose graph is a straight line.
Algebraic Reasoning and Functions
Slope-Intercept Form
y = mx + b, where m is slope, b is y-intercept.
Algebraic Reasoning and Functions
Slope (m)
The rate of change; rise over run.
Algebraic Reasoning and Functions
Y-intercept (b)
The point where the line crosses the y-axis (x=0).
Algebraic Reasoning and Functions
System of Equations
Two or more equations with the same variables.
Algebraic Reasoning and Functions
Substitution Method
Solving a system by replacing a variable with an expression.
Algebraic Reasoning and Functions
Elimination Method
Solving a system by adding/subtracting equations to cancel a variable.
Algebraic Reasoning and Functions
Solution to a System
The point (x, y) that satisfies all equations.
Algebraic Reasoning and Functions
Linear Equations & Systems of Equations
LINE: L-ook for the variable. I-solate it. N-ever forget to balance. E-xamine your answer.
Algebraic Reasoning and Functions
Linear Equations & Systems of Equations
The Praxis Core exam often presents linear equations and systems within realistic contexts. Look for keywords like 'per hour,' 'per item,' 'total cost,' or 'difference' to help formulate your equations. Be prepared to solve for variables or interpret the meaning of the solution in the context of the problem.
Algebraic Reasoning and Functions
Linear Equations & Systems of Equations
Forgetting to perform an operation on BOTH sides of the equation.
Algebraic Reasoning and Functions
Linear Equations & Systems of Equations
Incorrectly distributing negative signs when solving equations or substituting.
Algebraic Reasoning and Functions
Linear Equations & Systems of Equations
Solving for one variable in a system but forgetting to find the value of the other variable.
Algebraic Reasoning and Functions
Function
A relation where each input has exactly one output.
Algebraic Reasoning and Functions
Domain
The set of all possible input values (x-values) for a function.
Algebraic Reasoning and Functions
Range
The set of all possible output values (y-values) for a function.
Algebraic Reasoning and Functions
Vertical Line Test
A visual test to determine if a graph represents a function.
Algebraic Reasoning and Functions
Input
The independent variable, typically 'x', fed into a function.
Algebraic Reasoning and Functions
Output
The dependent variable, typically 'y' or 'f(x)', produced by a function.
Algebraic Reasoning and Functions
Relation
Any set of ordered pairs (x, y).
Algebraic Reasoning and Functions
Functions: Domain, Range, & Graphs
DR. XI ROY: Domain is X, Input. Range is Y, Output. Remember 'DR' for Doctor, and 'XI ROY' for the variables they represent!
Algebraic Reasoning and Functions
Functions: Domain, Range, & Graphs
The Praxis Core exam often presents graphs and asks you to identify the domain and range using interval notation or inequalities. Pay close attention to whether endpoints are included (closed circles, brackets) or excluded (open circles, parentheses) and if the graph extends infinitely (infinity symbol).
Algebraic Reasoning and Functions
Functions: Domain, Range, & Graphs
Confusing domain (x-values) with range (y-values). Always remember D comes before R, and X comes before Y.
Algebraic Reasoning and Functions
Functions: Domain, Range, & Graphs
Incorrectly applying the Vertical Line Test. If a vertical line touches the graph more than once, it's NOT a function.
Algebraic Reasoning and Functions
Functions: Domain, Range, & Graphs
Forgetting to consider restrictions on the domain, such as division by zero or taking the square root of a negative number.
Algebraic Reasoning and Functions
Quadratic Equation
A polynomial equation of degree two (ax^2 + bx + c = 0).
Algebraic Reasoning and Functions
Polynomial
Expression with variables, coefficients, and non-negative integer exponents.
Algebraic Reasoning and Functions
Degree of a Polynomial
The highest exponent of the variable in a polynomial.
Algebraic Reasoning and Functions
Arithmetic Sequence
A sequence with a constant difference between consecutive terms.
Algebraic Reasoning and Functions
Common Difference
The constant difference between terms in an arithmetic sequence.
Algebraic Reasoning and Functions
Geometric Sequence
A sequence with a constant ratio between consecutive terms.
Algebraic Reasoning and Functions
Common Ratio
The constant ratio between terms in a geometric sequence.
Algebraic Reasoning and Functions
Factoring
Breaking down an expression into a product of simpler expressions.
Algebraic Reasoning and Functions
Quadratic Equations, Polynomials, & Sequences
QUAD-FORM: 'Q'uick 'U'se 'A'lways 'D'elivers 'F'ast 'O'utcomes 'R'eally 'M'uch!
Algebraic Reasoning and Functions
Quadratic Equations, Polynomials, & Sequences
The Praxis Core Mathematics (5733) expects you to solve quadratic equations by factoring, using the quadratic formula, and by taking square roots. Be ready to identify arithmetic and geometric sequences and apply their nth-term formulas.
Algebraic Reasoning and Functions
Quadratic Equations, Polynomials, & Sequences
Forgetting the ± when taking the square root to solve quadratic equations.
Algebraic Reasoning and Functions
Quadratic Equations, Polynomials, & Sequences
Incorrectly identifying whether a sequence is arithmetic or geometric, leading to using the wrong formula.
Algebraic Reasoning and Functions
Quadratic Equations, Polynomials, & Sequences
Making calculation errors when substituting values into the quadratic formula, especially with negative numbers.
Algebraic Reasoning and Functions
Rate
A ratio comparing two different quantities with different units.
Algebraic Reasoning and Functions
Percentage
A rate, number, or amount in each hundred.
Algebraic Reasoning and Functions
Keywords
Words in a problem that indicate specific mathematical operations.
Algebraic Reasoning and Functions
Problem Solving with Algebra
To solve word problems, remember 'UTSC': Understand, Translate, Solve, Check. It's like a four-step dance to your answer!
Algebraic Reasoning and Functions
Problem Solving with Algebra
On the Praxis Core, pay close attention to the specific question asked in word problems. Sometimes you'll calculate an intermediate value, but the question might ask for something else, like the remaining amount or the total. Double-check what the question is truly asking for before selecting your answer.
Algebraic Reasoning and Functions
Problem Solving with Algebra
Misinterpreting keywords (e.g., 'less than' vs. 'minus')
Algebraic Reasoning and Functions
Problem Solving with Algebra
Not defining variables clearly or consistently
Algebraic Reasoning and Functions
Problem Solving with Algebra
Forgetting to check the answer in the context of the original problem
Algebraic Reasoning and Functions
Problem Solving with Algebra
Making calculation errors after correctly setting up the equation
Algebraic Reasoning and Functions
Polygon
Closed 2D shape with straight sides
Exploring Geometric Concepts
Vertex
A corner where two sides meet
Exploring Geometric Concepts
Equilateral
Triangle with 3 equal sides/angles
Exploring Geometric Concepts
Isosceles
Triangle with at least 2 equal sides/angles
Exploring Geometric Concepts
Scalene
Triangle with no equal sides/angles
Exploring Geometric Concepts
Quadrilateral
Polygon with four sides
Exploring Geometric Concepts
Parallelogram
Quadrilateral with two pairs of parallel sides
Exploring Geometric Concepts
Trapezoid
Quadrilateral with at least one pair of parallel sides
Exploring Geometric Concepts
Basic Geometric Shapes & Properties
To remember the order of polygons by sides: Tri (3), Quad (4), Pent (5), Hex (6), Oct (8). Think of a 'tricycle' (3 wheels), 'quad bike' (4 wheels), 'pentagon' building (5 sides), 'hexagon' nut (6 sides), and 'octopus' (8 arms).
Exploring Geometric Concepts
Basic Geometric Shapes & Properties
The Praxis Core exam often tests your ability to identify and differentiate between various quadrilaterals. Be sure to know the exact definitions for trapezoid, parallelogram, rectangle, rhombus, and square, including which properties are shared and which are unique to each shape.
Exploring Geometric Concepts
Basic Geometric Shapes & Properties
Confusing a rhombus with a square: A rhombus has four equal sides, but its angles don't have to be 90 degrees. A square is a rhombus with 90-degree angles.
Exploring Geometric Concepts
Basic Geometric Shapes & Properties
Misidentifying a trapezoid: A trapezoid only needs *one* pair of parallel sides. Some definitions say *exactly* one pair, but the ETS exam typically uses 'at least one pair'.
Exploring Geometric Concepts
Basic Geometric Shapes & Properties
Assuming a shape is regular: Unless stated, do not assume a polygon has equal sides and angles. Always rely on given information or explicit markings.
Exploring Geometric Concepts
Perimeter
The total distance around a 2D shape.
Exploring Geometric Concepts
Area
The amount of surface a 2D shape covers.
Exploring Geometric Concepts
Surface Area
The total area of all surfaces of a 3D object.
Exploring Geometric Concepts
Units
Standard measures (e.g., feet, m², cm³).
Exploring Geometric Concepts
2D Shape
Has length and width, but no depth.
Exploring Geometric Concepts
3D Object
Has length, width, and depth.
Exploring Geometric Concepts
Perimeter, Area, Volume, & Surface Area
PAVS: 'P'erimeter is 'A'round, 'A'rea is 'V'acant space (2D), 'V'olume is 'S'pace inside (3D), 'S'urface area is 'A'll the faces.
Exploring Geometric Concepts
Perimeter, Area, Volume, & Surface Area
On the Praxis Core, pay close attention to the units requested in the answer choices. A common trick is to provide options with incorrect units (e.g., square units for perimeter). Always ensure your final answer's units match the quantity being measured.
Exploring Geometric Concepts
Perimeter, Area, Volume, & Surface Area
Confusing units (e.g., using square units for perimeter or linear units for area).
Exploring Geometric Concepts
Perimeter, Area, Volume, & Surface Area
Mixing up formulas for area and volume, especially for similar shapes (e.g., cylinder area vs. volume).
Exploring Geometric Concepts
Perimeter, Area, Volume, & Surface Area
Forgetting to include all faces when calculating surface area of a 3D object.
Exploring Geometric Concepts
Pythagorean Theorem
a² + b² = c² for right triangles.
Exploring Geometric Concepts
Right Triangle
A triangle with one 90-degree angle.
Exploring Geometric Concepts
Legs
The two shorter sides of a right triangle.
Exploring Geometric Concepts
Hypotenuse
The longest side, opposite the right angle.
Exploring Geometric Concepts
Coordinate Plane
A 2D plane with x and y axes.
Exploring Geometric Concepts
Distance Formula
Calculates length between two points.
Exploring Geometric Concepts
Midpoint Formula
Finds the center of a line segment.
Exploring Geometric Concepts
Coordinates
Ordered pair (x, y) locating a point.
Exploring Geometric Concepts
Pythagorean Theorem & Coordinate Geometry
For the distance formula, think 'Subtract, Square, Add, Square Root!' (Subtract x's, Square it. Subtract y's, Square it. Add results. Take Square Root.)
Exploring Geometric Concepts
Pythagorean Theorem & Coordinate Geometry
The California Educator Credentialing Examinations (CTEL) often require applying these formulas in real-world contexts, such as finding the shortest path or verifying geometric properties of shapes on a grid. Look for keywords like 'distance between,' 'midpoint of,' or 'right angle' to signal these concepts.
Exploring Geometric Concepts
Pythagorean Theorem & Coordinate Geometry
Applying the Pythagorean Theorem to non-right triangles.
Exploring Geometric Concepts
Pythagorean Theorem & Coordinate Geometry
Confusing the x and y coordinates when using the distance or midpoint formulas.
Exploring Geometric Concepts
Pythagorean Theorem & Coordinate Geometry
Forgetting to take the square root at the end of the distance formula or Pythagorean Theorem.
Exploring Geometric Concepts
Translation
Sliding a figure without changing orientation.
Exploring Geometric Concepts
Reflection
Flipping a figure over a line.
Exploring Geometric Concepts
Rotation
Turning a figure around a fixed point.
Exploring Geometric Concepts
Dilation
Resizing a figure by a scale factor.
Exploring Geometric Concepts
Complementary Angles
Two angles whose measures sum to 90°.
Exploring Geometric Concepts
Supplementary Angles
Two angles whose measures sum to 180°.
Exploring Geometric Concepts
Transversal
A line intersecting two or more other lines.
Exploring Geometric Concepts
Vertical Angles
Opposite angles formed by intersecting lines, always equal.
Exploring Geometric Concepts
Transformations, Angles, & Lines
For transformations, remember 'TRRD': Translation (Slide), Reflection (Flip), Rotation (Turn), Dilation (Resize-Stretch/Shrink).
Exploring Geometric Concepts
Transformations, Angles, & Lines
The Praxis Core often uses diagrams without explicit labels for parallel lines. Look for arrows on the lines to indicate they are parallel. Be prepared to identify angle relationships and solve for unknown values in complex figures.
Exploring Geometric Concepts
Transformations, Angles, & Lines
Confusing complementary (90°) and supplementary (180°) angles.
Exploring Geometric Concepts
Transformations, Angles, & Lines
Misidentifying angle relationships (e.g., calling alternate interior angles corresponding angles).
Exploring Geometric Concepts
Transformations, Angles, & Lines
Incorrectly applying transformation rules, especially reflections and rotations on a coordinate plane.
Exploring Geometric Concepts
Bar Graph
Compares quantities across different categories.
Data Analysis and Probability
Line Graph
Shows trends or changes in data over time.
Data Analysis and Probability
Pie Chart
Illustrates parts of a whole as proportions.
Data Analysis and Probability
Histogram
Displays the distribution of continuous data intervals.
Data Analysis and Probability
Scatter Plot
Shows the relationship between two variables.
Data Analysis and Probability
Axis Labels
Describe what is measured on the horizontal/vertical lines.
Data Analysis and Probability
Legend
Explains symbols, colors, or patterns in a graph.
Data Analysis and Probability
Scale
The range and intervals of values on an axis.
Data Analysis and Probability
Data Interpretation & Representation
To remember what to look for when interpreting data: 'TALK' to your graph! Title, Axes, Legend, Key features.
Data Analysis and Probability
Data Interpretation & Representation
The Praxis Core exam often presents real-world scenarios with data displays. Pay close attention to the title, axis labels, and legend. Questions might ask you to find specific values, calculate differences, or identify trends. Be aware of how scales can be manipulated to exaggerate or minimize data.
Data Analysis and Probability
Data Interpretation & Representation
Ignoring the title and axis labels, leading to misinterpreting what the graph is actually showing.
Data Analysis and Probability
Data Interpretation & Representation
Not checking the scale of the axes, especially the y-axis, which can be manipulated to exaggerate or minimize trends.
Data Analysis and Probability
Data Interpretation & Representation
Confusing histograms with bar graphs; histograms show continuous data in intervals with no gaps between bars.
Data Analysis and Probability
Mean
The average of a data set; sum of values divided by count.
Data Analysis and Probability
Median
The middle value in an ordered data set.
Data Analysis and Probability
Mode
The most frequently occurring value in a data set.
Data Analysis and Probability
Outlier
A data point significantly different from others.
Data Analysis and Probability
Central Tendency
Measures describing the center of a data set.
Data Analysis and Probability
Spread (or Dispersion)
Measures describing the variability of data.
Data Analysis and Probability
Measures of Central Tendency & Spread
MMM-R: Mean, Median, Mode, Range. Remember them in this order to keep them straight!
Data Analysis and Probability
Measures of Central Tendency & Spread
For the Praxis Core, be prepared to not only calculate these measures but also to interpret what they mean in context. Pay attention to keywords like 'average,' 'middle value,' or 'most frequent.'
Data Analysis and Probability
Measures of Central Tendency & Spread
Forgetting to order the data before finding the median.
Data Analysis and Probability
Measures of Central Tendency & Spread
Confusing mean with median, especially when outliers are present.
Data Analysis and Probability
Measures of Central Tendency & Spread
Incorrectly calculating the range by not identifying the absolute highest and lowest values.
Data Analysis and Probability
Probability
A numerical measure of the likelihood an event will occur.
Data Analysis and Probability
Outcome
A possible result of an experiment or event.
Data Analysis and Probability
Favorable Outcome
An outcome that satisfies a specific condition.
Data Analysis and Probability
Theoretical Probability
The expected probability based on mathematical reasoning.
Data Analysis and Probability
Experimental Probability
The probability based on actual results from trials.
Data Analysis and Probability
Independent Events
Events where the outcome of one does not affect the other.
Data Analysis and Probability
Multiplication Rule
Used to find the probability of two or more independent events.
Data Analysis and Probability
Sample Space
The set of all possible outcomes of an experiment.
Data Analysis and Probability
Basic Probability & Independent Events
INDEPENDENT events? Just MULTIPLY! If one doesn't care what the other does, their chances combine by multiplying.
Data Analysis and Probability
Basic Probability & Independent Events
The Praxis Core exam often uses real-world contexts for probability questions, like classroom scenarios or survey results. Pay attention to keywords like 'randomly selected,' 'with replacement,' or 'without replacement' as they dictate the type of probability calculation needed.
Data Analysis and Probability
Basic Probability & Independent Events
Confusing 'and' (multiplication) with 'or' (addition, for mutually exclusive events).
Data Analysis and Probability
Basic Probability & Independent Events
Forgetting to simplify fractions when calculating probability.
Data Analysis and Probability
Basic Probability & Independent Events
Not checking if events are truly independent before multiplying probabilities.
Data Analysis and Probability
Permutation
Arrangement where order matters.
Data Analysis and Probability
Combination
Selection where order does not matter.
Data Analysis and Probability
Factorial
Product of an integer and all positive integers below it (n!).
Data Analysis and Probability
Dependent Events
Outcome of one event affects another.
Data Analysis and Probability
Without Replacement
Item removed is not put back, altering probabilities.
Data Analysis and Probability
Permutations, Combinations, & Dependent Events
Permutations: 'P' for 'Positions' (order matters). Combinations: 'C' for 'Committees' (order doesn't matter).
Data Analysis and Probability
Permutations, Combinations, & Dependent Events
The Praxis Core often uses keywords like 'arrangement,' 'order,' 'positions,' or 'sequence' for permutations, and 'selection,' 'group,' or 'committee' for combinations. For dependent events, look for 'without replacement' or scenarios where the pool of choices changes.
Data Analysis and Probability
Permutations, Combinations, & Dependent Events
Confusing permutations and combinations: Always ask if order matters.
Data Analysis and Probability
Permutations, Combinations, & Dependent Events
Forgetting to adjust probabilities for dependent events: If an item isn't replaced, the total count and specific counts change.
Data Analysis and Probability
Permutations, Combinations, & Dependent Events
Incorrectly calculating factorials or misapplying the formulas.
Data Analysis and Probability