Rational Numbers. Integers. Irrational Numbers
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1 EOC Review: Pre-Algebra Unit Rational Numbers Integers Irrational Numbers Ex: Matrices: Ex 1: Ex 2: Ex 3: Unit 1 Equations Equations To solve an equation, use your calculator. STEPS: 1. Menu 2. Algebra (#3) 3. Numerical Solve (#1) 4. Type in equation 5. Put a comma (,) at the end, and then the variable afterwards Ex 1: 2x + 5 = 6x 3 Ex 2: 6(x + 1) = 2/3(9x + 12) Ex 4: Ex 3: 4x + 10 = 2(2x + 5)
2 Solve: cd = f + gh for h Dimensional Analysis Must Know Conversions!!!! Ex 1: The sea horse swims at a rate of feet per hour. Use dimensional analysis to convert this speed to inches per minute. Ex 2: A car is traveling at 50 miles per hour. How many feet per second is the car traveling? Unit 2 Inequalities Inequalities: o Solve the same as equations o If there is a negative with the variable, flip the sign o Variable must always be on the left, the answer must be on the right o > and < are open circles on the number line o and are closed circles on the number line o > and are to the right on the number line o < and are to the left on the number line
3 Ex 1: y 4y + 18 Ex 2: 4m 3 < 2m + 6 Ex 3: 2(k 3) > 6 + 3k 3 Ex 4: What is the solution to this inequality? Ex 5: Which graph represents the solutions of this inequality? -2(x + 5) > 3x Ex 6: Which inequality in one variable represents the set of numbers that satisfies this statement? Five less than eight times a number is greater than 11. Unit 3 Relations and Functions Relation: 4 Main types of Relations: Function: Inverse:_ Ex 1: Express the relation {(3,2), (-1,4), (0,-3), (-3,4), and (-2,-2)} as a table, graph, and a mapping. Tell the domain and range.
4 A. What is the domain of the relation? B. What is the range of the relation? D. What is the inverse of the relation as ordered pairs? E. Is the inverse of the relation a function? Explain your answer. C. Is the relation a function? Explain your answer.
5 Unit 4 Linear Functions VERY IMPORTANT FOR EOC!!! Linear Function: X and y intercepts: What is an x intercept? What is the y coordinate for ALL x intercepts? What is a y intercept? What is the x coordinate for ALL y intercepts? How do you always write intercepts? Try These: Find the x and y intercepts of the following equations. ex1. 9x - 6y = 18 ex2. 5x + 4y = 15 ex3. 21x + 42y = 63 Slope: What are the 4 definitions of slope?
6 The ramp from a dock to a boat rises 4 feet for every 14 feet of run. What is the slope of the ramp? Slope-Intercept Form: What is the equation for slope-intercept form? What does the m represent? What does the b represent? What two things do you need to write an equation in slope-intercept form? a. b. Ex 1: What is the equation 4x + 6y = -12 in slope intercept from?
7 Ex 2: What is the equation of the line that passes through the point with coordinates (-5, 3) and has a slope of Ex 3: What is the equation of this line? Ex 4: Use function notation to represent the function shown in this graph: Ex 5: Which equation has this graph? Ex 6: Which is the graph of
8 Ex 7: Which is the graph of the line that passes thorugh the point with the coordinates of (1, 3) and has a slope of ½? Point-Slope Form: 1. What is the equation for point- slope form? 2. What two things do you need to write an equation in point-slope form? 3. Where do you plug in the slope?- 4. Where do you plug in the point? Parallel and Perpendicular Lines: Parallel Equations: Perpendicular Equations: Example 1: Write an equation of a line in slope-intercept form that is parallel to y = -3x - 2 and goes through (-1, -2)
9 Example 2: Write the equation of a line in slope-intercept form that is perpendicular to x + 4y = 12 and passes through (0, -3) Example 3: Which of the lines whose equations are given below is perpendicular to y = 4x + 3? Scatter Plots: Steps: 1. Enter your data into the lists and spreadsheets on the home screen of the calculator (looks like excel sheet) 2. Go back to the home screen and open data and statistics (looks like a bar graph) 3. Add your x and y variables 4. Press menu; pick analyze (#4) recession (#6) and y = mx + b (#1) Ex 1: Translations: What affect does slope have on a graph? m > 1 0<m<1_ m < 0
10 Systems of Equations: Find the solution in the calculator: 1. Menu 2. Algebra (#3) 3. Solve Systems of Linear Equations (#2) 4. Type in two equations
11 Monomials: Steps:
12 Polynomials, Scientific Notation and Radicals: Quadratics and Factoring:
13
14 Direct and Inverse:
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College Algebra (MATH 1203, 1204, 1204R) Departmental Review Problems For all questions that ask for an approximate answer, round to two decimal places (unless otherwise specified). The most closely related