ALL HIGH SCHOOL MATH SUBJECTS Full PreTests with Keys - RESEARCH BASED

87 qualified high school math teachers have been surveyed POST-COVID across the 6 subjects (algebra 1, algebra 2, geometry, precalculus, calculus, and statistics & probability). They are all a compilation of their answers to the question: what do you WISH students knew BEFORE taking the course? Each pre-assessment / pre-test is 9 to 11 packed pages in length! The pretests align with Common Core State Standards, is scaffolded and comes with step-by-step keys.

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Algebra 2 Pre-test

✫ See inside bundle for link to download!

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STATISTICS & PROBABILITY List of Topics (step-by-step key provided):

✫ Basic Algebra

• Order of operations
• Converting between fractions, decimals and percents (to in the future calculate and interpret probabilities, calculate margin of error and confidence intervals, interpret confidence levels and Type 1 and Type 2 error probabilities)
• Rounding to the nearest whole, tenth, hundredth, thousandth (to in the future calculate numerical summary statistics, test statistics, and confidence intervals)
• Operations of fractions
• Given a real-world linear equation, students identify the slope and y-intercept, and then explain what they mean in the context of the problem
• Plotting points and intervals on a number line (to in the future make and interpret dotplots)
• Find the distance between to points on a number line (to in the future calculate deviations from the mean)
• Evaluating an algebraic expression (to in the future calculate numerical summary statistics, test statistics, confidence intervals, z-scores and regression coefficients)
• Solving a linear equation (to in the future find percentiles for a normal distribution)
• Solving a rational equation (to in the future find z-scores)

✫ Probability Foundation:

• Define a factorial
• Simplify factorials
• Fundamental Counting Principle
• Permutation & Combination
• Basic probability problems (pulling out a blue marble from a bag, etc.)
• Complement of a set (to in the future define events and calculate their probabilities)
• How many total cards in a deck? How many suits? How many red? Black? etc.
• How many traditional sides does a die have? How many digits or letters in the alphabet are there? How many vowels? etc.
• Given a tree diagram, students use it to write out a sample space in set notation
• Find the intersection and union of a set (to in the future define events and calculate their probabilities)
• Venn diagram problem (to in the future understand probability rules and calculations)
• Matching real events with probabilities of them occurring from a 2023 study (chances of winning the lottery, getting struck by lightening, dating a supermodel, winning the Oscars, etc)

✫ Statistics Foundation:

• Find the sum of numbers
• Find the mean, median, mode, range of a set
• Interpreting and analyzing a pie chart & histogram (to in the future interpret graphical displays of data)
• Students complete a series of steps in a scaffolded way by also filling out the blanks in a chart. Ultimately, students are guided to find the standard deviation of a small data set with 5 elements
• Fill out a frequency table
• Students answer simple questions about finding the area under a curve (to in the future approximate probabilities for the bell curve using z-scores, P-values and understand graphical displays of data)

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ALGEBRA 1 List of Topics (step-by-step key provided):

✫ Algebra Basic Skills:

• Multiplication chart - no calculator
• Perform operations of integers and decimals - no calculator
• Order of operations (PEMDAS) - no calculator
• Convert a percent into a decimal & fraction in simplest form
• Review of inequality symbols
• Foundation. For example x^4 equals x times itself 4 times, versus 4x equals x added together 4 times.
• Properties of exponents
• Translate a sentence into a mathematical expression
• Simplifying radicals
• Properties of exponents
• Operations involving fractions
• Evaluating expressions

✫ Solving Inequalities & Equations:

• Solving & graphing an inequality
• Solving one-step and multi-step linear equations
• Solving using the "butterfly" or cross-multiplication method
• Solve a system of linear equations using all 3 methods (substitution, elimination & graphing methods)

✫ Linear Graphs & Forms of Linear Equation:

• Given a graph of a line, use rise over run to identify the slope
• Plot points in the coordinate grid
• Graph a line from slope-intercept form
• Find slope between two given points using the slope formula
• Given a graph, write the equation of the line in slope-intercept form.
• Given a standard form equation, convert to slope-intercept form
• Given an equation in slope-intercept form, convert to point-slope form
• Given an equation in slope-intercept form, identify the slope and y-intercept.
• Given a graph, identify the x and y intercepts

✫ Word Problems:

• Writing an exponential model y=a(1+r)^x and using it to answer a question.
• Given a word problem, students are asked to define their variables and then write an equation using function notation. Then they will answer questions based off of their equation.

✫ Polynomials:

• Factoring polynomials (AC method, GCF, Difference of Perfect Squares, & by Grouping)
• Given a polynomial expression: combine like-terms, identify the constant, and identify the coefficient of the leading term.
• Given two functions f and g, evaluate f(2), g(1), and f(-1) + g(-3)

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ALGEBRA 2 List of Topics (step-by-step key provided):

✫ Algebra Basic Skills:

• Multiplication chart - no calculator
• Perform operations of integers and decimals - no calculator
• Order of operations (PEMDAS) - no calculator
• Operations of rational expressions
• Rationalize the denominator and keep in simplest radical form
• Foundational concepts. For example x^4 equals x times itself 4 times, versus 4x equals x added together 4 times.
• Properties of exponents
• Simplifying radical expressions, also with imaginary solutions

✫ Solving Inequalities & Equations:

• Solve a quadratic equation by factoring
• Solve a quadratic equation using the quadratic formula
• Solve a quadratic equation using the Complete the Square method
• Solving & graphing an inequality
• Solving one-step and multi-step linear equations
• Solving using the "butterfly" or cross-multiplication method
• Solve a logarithmic and exponential equation
• Solve a system of linear equations using all 3 methods (substitution, elimination & graphing methods)

✫ Graphs & Functions:

• Identify whether the relation & its inverse is a function.
• Identify whether the function is one-to-one
• Identify the domain and range
• Given a graph, identify the x and y intercepts.
• Given two functions f and g, making evaluations, find the composition of functions, and find the inverse function of f.
• Sketch the graph of parent functions
• Sketch the graphs of transformations of parent functions

✫ Word Problems:

• Write an exponential model y=a(1+r)^x to describe the word problem, and then predict an answer using the model.
• Given a word problem using function notation, students answer questions based on the model
• Given a word problem, students identify the slope & y-intercept of the model, and then use critical thinking skills to identify what those values mean in the context of the real world problem

✫ Polynomials:

• Factoring polynomials (AC method, GCF, Difference of Perfect Squares, Sum of Cubes, & by Grouping)
• Given a polynomial expression: identify the degree, leading coefficient, constant, number of terms, and classification (monomial, binomial, etc)
• Square a binomial and simplify
• Operations of polynomials, including long or synthetic division

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CALCULUS List of Topics (step-by-step key provided):

✫ Trigonometric Functions:

• Fill out the radian and coordinate pairs in the unit circle, either from memory or by using reference & coterminal angles
• Evaluate trig functions with coterminal angles
• Solve trigonometric equations (also knowing trig identities & factoring)
• Given a trig function, identify the amplitude, period, phase shift and vertical shift
• Sketch sine, cosine, and tangent parent function
• Verify trig identities

✫ Solving Equations:

• Find the zeros of a quadratic equation using the factoring method
• Solve a quadratic equation using the quadratic formula
• Solve a quadratic equation using the Complete the Square method
• Solve logarithmic and exponential equations
• Solve trigonometric equations (also knowing trig identities & factoring)
• Solve a system of linear equations

✫ Polynomials & Functions:

• Factoring polynomials (AC method, GCF, Difference of Perfect Squares, & by Grouping)
• Given a polynomial expression, identify the degree, leading coefficient, constant, number of terms, and determining the maximum number of distinct roots
• Find the difference quotient (in preparation for evaluating a limit)
• Determine whether a function is continuous or not
• Find the End Behavior of a graph (in preparation for limits)
• Find the domain and range of a function
• Matching section: Match the type of function to its corresponding equation (periodic, linear, quadratic, cubic, rational, logarithmic, piecewise, even, odd, & exponential).
• Evaluating different types of functions (piecewise, polynomial, trigonometric, logarithmic)

✫ Rational Functions & Expressions:

• Given a rational function: identify the domain, infinite discontinuity (vertical asymptote), point discontinuity (hole), equation of the horizontal asymptote, and then sketch the function
• Operations of rational expressions which involves factoring, including long/synthetic division

✫ Miscellaneous:

• Sketch the graph of multiple types of parent functions & transformations of those parent functions (shifts, shrinks, stretches, and reflections)
• Algebra basic foundation: For example x^4 equals x times itself 4 times, versus 4x equals x added together 4 times. Also, review of properties of exponents

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PRECALCULUS List of Topics (step-by-step key provided):

✫ Algebra Basic Skills:

• Multiplication chart - no calculator
• Perform operations of integers in terms of pi (no calculator). This gets students used to the idea when adding/subtracting radian measurements, which is in terms of pi.
• Foundation. For example x^4 equals x times itself 4 times, versus 4x equals x added together 4 times.
• Properties of exponents
• Operations of radical expressions
• Operations involving fractions
• Evaluating expressions

✫ Complex Numbers:

• Simplifying a radical expression with an imaginary solution
• Operations of complex numbers

✫ Solving Equations:

• Solve one-step and multi-step linear equations
• Find the zeros of a quadratic equation using the factoring method
• Solve an equation involving rational functions (combining like-terms and solving using the "butterfly" or cross-multiplication method)
• Solve a quadratic equation using the quadratic formula
• Solve a quadratic equation using the Complete the Square method
• Solve the system of linear equations
• Solve logarithmic and exponential functions

✫ Polynomials:

• Factoring polynomials (AC method, GCF, Difference of Perfect Squares, Sum of Cubes, & by Grouping)
• Given a polynomial expression, identify the degree, leading coefficient, constant, number of terms, and classifying it (monomial, binomial, etc)
• Operations of polynomials, including squaring a binomial & long division
• Given a polynomial graph, identify whether the relation & inverse is a function, and whether it is a one-to-one function. Also to identify the domain and range as well as the zero(s).

✫ Miscellaneous:

• Find the domain of a rational function
• Sketch the graph of multiple types of parent functions & transformations of those parent functions (shifts, shrinks, stretches, and reflections)
• Solving a right triangle
• Solving a non-right triangle using the Law of Sines

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GEOMETRY List of Topics (step-by-step key provided):

✫ Geometry Foundation:

• Find the distance between two points using the formula
• Find the midpoint of two points using the formula
• Plotting a square and rectangle on a coordinate grid, then finding the area and perimeter of each
• Given a circle with a diameter, find the area and circumference.
• Pythagorean Theorem
• SohCahToa
• Solve for missing angle (using inverse) or side (pythag. theorem) in a right triangle
• Triangle sum theorem to find the missing angle
• Use triangle sum theorem to set up an equation and solve for x
• Write a proportion for similar triangles (scaffolded and guided to do so), and then cross-multiplying to solve for x
• Matching/vocab section: identify the point, line, ray, line segment, angle, and plane

✫ Algebra Basic Skills:

• Multiplication chart - no calculator
• Perform operations of integers - no calculator
• Order of operations (PEMDAS) - no calculator
• Review of inequality symbols
• Foundation. For example x^4 equals x times itself 4 times, versus 4x equals x added together 4 times
• Properties of exponents
• Simplifying radicals
• Operations involving fractions
• Evaluating expressions

✫ Solving Equations:

• Solving one-step and multi-step linear equations
• Solving using the "butterfly" or cross-multiplication method
• Solve a quadratic equation using the quadratic formula
• Solve the system of linear equations

✫ Graphs & Linear Equation Forms:

• Given a graph of a line, use rise over run to identify the slope
• Graph a line from slope-intercept form
• Plot points in the coordinate grid
• Find slope between two given points using the slope formula
• Given a graph, write the equation of the line in slope-intercept form.
• Given a standard form equation, convert to slope-intercept form
• Given an equation in slope-intercept form, convert to point-slope form
• Given an equation in slope-intercept form, identify the slope and y-intercept.
• Given a graph, identify the x and y intercepts
• Identify whether the lines are parallel, perpendicular, or neither

✫ Polynomials:

• Factoring polynomials (AC method, GCF, Difference of Perfect Squares, & by Grouping)