Rockhurst High School Algebra 1 Topics

Transcription

1 Rockhurst High School Algebra 1 Topics Chapter 1- Pre-Algebra Skills Simplify a numerical expression using PEMDAS. Substitute whole numbers into an algebraic expression and evaluate that expression. Substitute integers into an algebraic expression and evaluate the expression. Substitute fractions and decimals into an algebraic expression and evaluate the expression. Evaluate a numerical or algebraic expression using the TI-84. Know and understand the relationship between the set of Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, and Real Numbers. Estimate irrational numbers using the TI-84. Simplify an algebraic expression by combining like terms. Use the distributive property to simplify an algebraic expression. Translate a verbal expression into an algebraic expression. Know the algebraic meaning of the words like sum, difference, quotient, and product. Translate an English sentence into an equation. Know and use the properties of addition and multiplication of real numbers, including associative, commutative, identity, inverse, distributive, and closure.

2 Know the properties of equality, including symmetric, reflexive, transitive, addition, multiplication, subtraction, and division. Solve a linear equation with one transformation. Chapter 3 Solving Linear Equations with One Variable Solve a linear equation with two or more transformations. Solve a linear equation with variables on both sides. Solve a linear equation with fractions. Use the LCM to clear the fractions after using the distributive property. Solve a linear equation with decimals. Use your calculator to help with the operations. Identify a linear equation with no solution (contradiction) and a linear equation that is true for all real numbers (identity). Given a formula, substitute in the known values and solve the equation for the unknown variable. Solve an absolute value equation geometrically. exactly b units from a on a number line. x a b means find the values of x that are Solve a proportion by using cross products.

3 new original percent of change Find the percent of change. original 100 Read a word problem, set a proportion that describes the situation, and solve it. Chapter 4 Relations Know the definition of a relation and be able to identify a relation as a set of ordered pairs, a graph, using a table, and using a mapping diagram. Plot a set of points using the TI-84. State the inverse of a relation. Identify the domain and range of a relation. Use function notation to find f(a). Identify points and quadrants in the coordinate plane Chapter 5 Linear Equations with Two Variables Graph horizontal and vertical lines given their equations. x=a is a vertical line that intercepts the x-axis at a. y=b is a horizontal line that intercepts the y-axis at b. Identify an ordered pair as a solution to a linear equation in two variable. Create a table of values for a linear equation with two variables.

4 Graph a line by finding its x and y-intercepts. (the cover up method) Graph a line by finding its y-intercept and slope. (y=mx+b) Determine if two lines are parallel by using their slopes. Determine if two lines are perpendicular by using their slopes. Given a point and the slope of line find its equation by using the point slope formula. y y m( x ) 1 1 x Express the equation of a line in standard form. Ax+By=C where A,B, and C are integers and A>0 rise Given two points on a line find the slope by graphing and using m=. run y Given two points on a line find the slope using the slope formula: m= x y1 x 1. State the equation of a line given two points on the line. Find the average rate of change of a data set in the real world by using the slope formula. Given a scatter plot, find the equation of the line by using two points that you think best fits the data. Line of best fit

5 Enter a linear equation into the TI-84, graph it in an appropriate viewing window, and create a table of values. Use the TI-84 to find a line that best fits a set of points using LINREG. Create the scatter plot and the regression equation in an appropriate window. Use the regression equation and the table feature to predict what will happen in the future (extrapolation). Know the meaning of r, the correlation coefficient. Chapter 6 Linear Inequalities with One and Two Variables Solve a linear inequality in one variable, show its solution on a number line, and show its solution using interval notation. Know the logical definition of a compound statement connected by the words (and or) Solve a compound inequality using the word or (disjunction) as the union of the two sets of numbers. Show its solution on a number line and as an interval. Solve a compound inequality equation using the word and (conjunction) as the intersection of the two sets of numbers. Show its solution on a number line and as an interval. Solve an absolute value inequality(>) using the geometric definition. values of x that are more than b units from a. x a b means find the Solve an absolute value inequality(<) using the geometric definition. values of x that are less than b units from a. x a b means find the Read a word problem and identify an absolute value inequality as its solution.

6 Graph an absolute value function by finding creating a table of values. Graph an absolute value function on the TI-84. the graph. y a x h k Describe how h, k, and affect Identify points that satisfy a linear inequality in two variables. Graph a linear inequality in two variables in the x-y coordinate system. Identify a linear inequality in two variables that can be used to solve a word problem. Graph the linear inequality and identify points that will satisfy it graphically and algebraically. Chapter 7 Linear Systems Know the three things that can happen when two lines are graphed in the x-y plane. Solve a system by substitution. Solve a system by elimination. Solve a system by graphing. Solve a system using the TI-84, graphing the two lines in an appropriate window, and using the Intersect command. Solve a system using the POLYSMLT application on the TI-84. Solve a word problem by setting up a system of equations (mixture and round trip problems) Solve a system of 3 equation and 3 unknowns algebraically and using POLYSMLT** Chapter 8 Laws of Exponents Know and use the eight laws of exponents. Write a decimal number in scientific notation. Write a number in scientific notation in decimal notation.

7 Multiply and divide numbers written in scientific notation. Raise a number written in scientific notation to a power. Create a table and graph an exponential equation. Understand the meaning of the word asymptote. Know and use the law of exponential growth. A A0 r (1 )t Know and use the law of exponential decay. A A0 r (1 )t r Know and use the law of compounded growth. A A0 n (1 )nt Model an exponential growth (decay) problem using the table and graph feature of your TI-84. Chapter 9 Polynomials and Factoring Identify a polynomial by degree and number of terms. (monomial, binomial, trinomial, constant, linear, quadratic, cubic) Add and subtract polynomials by combining like terms. Multiply polynomials monomial x polynomial binomial x binomial in your head binomial x trinomial trinomial x trinomial Raise a polynomial to a power. Divide polynomials polynomial /monomial term by term polynomial /binomial long division Find the GFC of two monomials Factor a polynomial use the (-1) technique factor out the GCF factor a trinomial into two binomials

8 factor the difference of two perfect squares factor by grouping * Solve a polynomial equation by factoring. Read a word problem and set up a polynomial equation to solve it. Understand the concept of multiple roots and the first fundamental theorem of algebra. Chapter 10 The Quadratic Formula Simplify a radical. Solve a quadratic equation using the quadratic formula. Give the answer in simplest radical form and estimate the solution using the TI-84. Recognize how the discriminant identifies the nature of the solutions to a quadratic equation. b 4ac 0= two real roots b 4ac 0= one real root b 4ac 0=two unreal roots Solve word problems that lead to a quadratic equation especially those concerning projectiles. b Graph a parabola by finding its vertex x= and plotting points to left and points a to the right of the vertex. Understand that the roots (zeroes) of a quadratic equation really represent the x- intercepts of its graph. Understand the symmetry of the graph of a parabola. Graph a parabola on the TI-84 using the zero command to find its x-intercept. Use the POLYSMLT application to find the zeroes of a polynomial equation.

9 Chapter 11 Irrational Numbers Add and subtract irrational numbers. Multiply irrational numbers. Divide irrational numbers (rationalize the denominator by using conjugates). Use the Pythagorean Theorem to find the missing side of a right triangle. Know and use the distance formula. Know and use the midpoint formula. Know the definition of sina, cosa, and tana. Use the definitions of your trigonometric functions to find a missing side or missing angle in a triangle. Solve a radical equation understanding the concept of extraneous solutions. Chapter 1 Rational Expression Identify excluded values of a rational expression. Graph a rational expression. Identify the excluded value as an asymptote or removed point. * Simplify rational expression. Multiply rational expressions. Divide rational expressions. Simplify a complex rational expression.* Solve a rational equation. Understand extraneous solutions. Solve word problems that have rational equations as solutions (work problems, the lens law, resistors in parallel).