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Unit 1.1 Real NumbersStudents Learning Targets (SWBAT):Represent real numbersOrder and Interval NotationsUse basic properties of algebraUse properties of integer exponents to simplify expressionsWrite scientific notationNotes:Assignment 1.1:Find the decimal form for the rational number. State whether it repeats or terminates.-37/815/99-13/65/37Describe and graph the interval of real numbers.x≤2-2≤x<5(-∞,7)[-3,3]x is negative.Use an inequality to describe the interval of real numbers.[-1,1)5238755270500(-∞,4]3638550246380 x is between -1 and 2Use interval notation to describe the interval of real number.x>-3-7<x≤-2x is greater than-3 and less than or equal to 4.x is positive.Convert to inequality and interval notation. State whether the interval is bounded or unbounded.(-3,4]-3,-1(-∞,5)[-6,∞)Use both inequality and interval notation to describe the set of numbers. Bill is at least 29 years old.No item at Sarah’s Variety Store costs more than $2.00.Salary raises at the State University of California at Chico will average between 2% and 6.5%.Use the distributive property to write the factored form or the expanded form of the given expression.a(x2+b)y-z3cax2+dx2a3z+a3wIdentify which algebraic property or properties are illustrated by the equation.3xy=3(xy)a2b+-a2b=0a2b=ba2(x+3)2+0=(x+3)2ax+y=ax+ayx+21x+2=1a?x+y=x+y2x-y=2x-2ySimplify the expression. x4y3x2y5(3x2)2y43y2(4x2)2(2xy)-3(x-3y2)-4(y6x-4)-2(4a3ba2b3)(3b22a2b4)The following data gives the revenues in thousands of dollars for public elementary and secondary schools for the 2003-04 school year.SourceAmount (in $1000)Federal36,930,339State221,802,107Local and Intermediate193,175,805Total45,908,251Write the amount of revenue in dollars obtained from the source in scientific notation.FederalStateLocal and IntermediateTotalUnit 1.2 Linear Equations and InequalitiesStudents Learning Targets (SWBAT):Solve linear equations and linear inequalities.Solve for a variable in a linear equationNotes:Assignment 1.2Determine if it is a solution for the given value of x.2x2+5x=3;x=-31-x2+2=3;x=-2(x-2)1/3=2;x=10Solve the equation.3t-4=82x-3=4x-54-2x=3x-64-3y=2y+44(y-2)=5y12x+13=113x+14=123-4z-52z+3=z-17Solve the equation. Support your answer with a calculator.2x-34+5=3x2x-4=4x-53Solve the inequality.x-4<22x-1≤4x+33x-1≥6x+82≤x+6<9-1≤3x-2<725-3x+32x-1≤2x+15x+74≤-32y-32+3y-15<y-112x+3+2x-4<13(x-3)Explain how the second equation was obtained from the first.x-3=2x+3, x-12=x-2The formula for the perimeter P is a rectangle is P=2(L+W). Solve this equation for W.The formula for the are A of a trapezoid is A=12hb1+b2. Solve the equation for b1.The formula for Celsius temperature in terms of Fahrenheit temperature is C=59F-32. Solve the equation for F.Unit 1.3 Solving Equations Graphically, Numerically, and AlgebraicallyStudents Learning Targets (SWBAT):Solve equations graphicallysolve quadratic equationsapproximate solutions of equations graphicallysolve equations by finding intersectionsNotes:Assignment 1.3Solve the equation graphically by finding x-intercepts. Confirm by suing factoring to solve the equation.x2-x-20=0x2-8x=-15Solve the equation by extracting square roots.4x2=252(x-5)2=17(2x-3)2=169Solve the equation using the quadratic formula.x2+8x-2=02x2-3x+1=03x+4=x2x2-2x+6=2x2-6x-26Solve the equation graphically by finding x-intercepts.4x2+20x=-23x3+x2+2x-3=0x2+4=4xSolve the equation graphically by finding intersections.x-8=2x+1=2x-32x-3=x2x2-3x=12-3(x-2)x+2-2x+3=0x+7=-x2+5x2+4x-1=7Graph the inequality.2x+5y≤7x2+y2<9y<x2+1Solve the system of inequalities.y≥x2-2y≤2x+3y≥x2x2+y2≤4 x2+y2≤9y≥xThe equationx29+y24≤1 defines y as two implicit functions of x. Solve for y to find the two functions and draw the graph of the equations.Unit 1.4 Radicals and Rational ExpressionsStudents Learning Targets (SWBAT):Simplify radical expressionsRationalize the denominatorManipulate rational exponentsNotes:Assignment 1.4:Find the indicated real roots.Square roots of 81Fourth roots of 81Cube roots of 64Fifth roots of 243square roots of 16/9Cube roots of -27/8Evaluate the expression without using a calculator.144-163-21664253-6427Simplify by removing factors from the radicand.28835003-25041922x3y43-27x3y643x8y6596x10Rationalize the denominator.1543215x23x2yConvert to exponential form.3(a+2b)25x2y3Convert to radical form.a34b14x23y13x-53Simplify the exponential expression.a35a13a32x2y412-8x6y-323p2q41227q3p613Simplify the radical expression.9x-6y416y8z-234x2y2?32x2y59ab6?527a2b-12175-428x3-4xy218x2y+2y3Unit 1.5 Inverse FunctionsStudents Learning Targets (SWBAT):Find inverse functionsDetermine if a function has an inverse using it’s graphNotes:Assignment 1.5:Find the equation for the inverse relation.y=4x-1y=5x+13y=-23x+2y=-35x+75fx=x7fx=4x4, x≥0fx=-25x3fx=2x3-69Graph the function f. Then use the graph to determine whether the inverse of f is a function.fx=-x-5fx=14x2-fx=13x3fx=x+4fx=4x4-5x2-6The maximum hull speed v (in knots) of a boat with a displacement hull can be approximated by v=1.35l where l is the length (in feet) of the boat’s waterline. Find the inverse of the model. Then find the waterline length needed to achieve a maximum speed of 7.5 knots.The body surface area A (in square meters) of a person with a mass of 60 kilograms can be approximated by the model A=0.2195h0.3964 where h is the person’s height (in centimeters). Find the inverse of the model. Then estimate the height of a 60 kilogram person who has a body surface area of 1.6 square meters. ................
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