mac 1105

Mrs. MizellFall 2014

MAC 1105Test 1

Review and

Practice Solutions

MAC 1105 Test 1 Review 1.4 – 1.8• You will need to have your own graphing calculator for the test. • You may not share calculators or use any type of communication device in place of a calculator. • Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. • If you miss one test, your final exam score will be substituted. A second missed test is a zero.

• There are twenty objectives on the exam. • Keep in mind that test questions will be in a random order and not in the order that appears below.

Objective Section Suggested Text Problems1) Solve a quadratic equation that is in factored form. 1.4 p. 148: 1(b) (middle of the page)2) Solve a quadratic equation by factoring. 1.4 p. 191: 41, 453) Complete the square. 1.4 p. 191: 474) Solve a quadratic equation using the quadratic formula. 1.4 p. 191: 435) Use the discriminant to determine the number and type of solutions of a quadratic equation. 1.4 p. 191: 53, 556) Work applications of quadratic equations (geometry) 1.5 p. 191: 597) Work applications of quadratic equations (projectile motion) 1.5 p. 191: 658) Solve an equation graphically. 1.6 See notes.9) Solve a rational equation. 1.6 p. 192: 82 (Answer {2, 3})10) Solve radical equations involving one radical. 1.6 p. 192: 7311) Solve equations using substitution. 1.6 p. 192: 7912) Given interval notation, write inequality notation. 1.7(R.1) p. 14: 67, 69, 7113) Given inequality notation, write interval notation. 1.7(R.1) p. 14: 61, 63, 6514) Solve a linear inequality. 1.7 p. 192: 87, 8915) Solve a compound inequality (and). 1.7 p. 192: 93(b)16) Solve a compound inequality (or). 1.7 p. 192: 93(a)17) Solve an absolute value equation (absolute value on one side). 1.8 p. 193: 10518) Solve an absolute value equation (absolute value on both sides) 1.8 p. 193: 10719) Solve an absolute value inequality (less than). 1.8 p. 192: 103(c)20) Solve an absolute value inequality (greater than). 1.8 P. 192: 103 (d)

Objective Guidelines1) Solve a quadratic equation that is in factored form. Set each factor equal to zero and solve.2) Solve a quadratic equation by factoring. Make sure all terms are on the right and a zero is on the left. Factor and set each factor equal to zero. Solve.3) Complete the square. Take ½ of the middle (second) term and square it.4) Solve a quadratic equation using the quadratic formula.5) Use the discriminant to determine the number and type of solutions of a quadratic equation. D = 0 → one real rootD > 0 → two real rootsD < 0 → two imaginary roots6) Work applications of quadratic equations (geometry) Set up a quadratic equation and solve.7) Work applications of quadratic equations (projectile motion) Set up a quadratic equation and solve.8) Solve an equation graphically. Y1 – left side of the equationY2 – right side of the equationZoom 6Adjust the window to see the intersection2nd calc 5The answer is the x – coordinate of the intersection.9) Solve radical equations. Factor the denominators.Find the LCDDetermine which values to exclude.Multiply by the LCD.Solve.Remember to exclude values that cause a denominator to be zero.10) Solve radical equations involving one radical. Isolate the radical, square both sides, solve.

11) Solve equations using substitution. Let = middle term (without the coefficient). Solve for Solve back for 12) Given interval notation, write inequality notation. See notes. [ ] → ( ) → <, >13) Given inequality notation, write interval notation. See notes and above.14) Solve a linear inequality. Solve just like a linear equation. If you multiply or divide both sides by a negative, reverse the direction of the inequality.15) Solve a compound inequality (and). The solution is the intersection of both solutions (both).16) Solve a compound inequality (or). The solution is the union of both solutions (either).17) Solve an absolute value equation (absolute value on one side).18) Solve an absolute value equation (absolute value on both sides)19) Solve an absolute value inequality (less than). |u| < a |u| a 20) Solve an absolute value inequality (greater than). |u| > a u> a or u < −a|u| ≥ a u≥ a or u ≤ −a

To study for the test:• Complete the first ALEKS objective (HW 1: 1.4 – 1.8). In order to receive the bonus, your HW 1 percentage must be greater than or equal to 80% (without rounding).• Complete the practice test and check your solutions.• Set up a study system (note cards for example) for each of the 20 objectives in the chart above.• Review your notes and worksheets for each of the 20 objectives in the chart above.• Work the suggested text problems for each of the 20 objectives in the chart above.• It is always possible that some questions may not be exactly like those on the practice test (objectives will remain unchanged). Some of these questions may ask you to analyze or synthesize what we’ve learned but if you prepare by studying your notes and your worksheets (as well as this review), you will be ready to complete those questions as well.

Practice Test Solutions

1) Identify the type of equation and solve the equation by choosing an appropriate method.

3) Indicate the constant that is needed to complete the square.a)

5) Use the discriminant of the quadratic equation to determine the number and type of solutions of the equation.

6) A rectangular garden has a length 6 more than three times the width. If the area of the garden is 144 square feet, find the length and width.

7) The height of a ball after t seconds when thrown straight up is given by the function When will the height of the ball be 40 feet?

• You can solve this on the graphing calculator or by using the quadratic formula. On the graphing calculator:1. Place the function in Y12. Place 40 in Y23. Graph the function using a window that is large enough to see the curve and the two intersections. [0,10] for x and [0, 200] for y works well.4. Use 2nd calc 5 twice to find both points of intersection. The x coordinates are the two times.

7) (Quadratic Formula)

8) Identify the type of equation and solve the equation by choosing an appropriate method. Please round your answer to the nearest thousandth. Sketch the graph (from your calculator).

You could also solve by substitution.

12) Write the inequality notation for each interval. You do not have to graph the inequality.a) b) c) d)

13) Write the interval notation for each inequality. You do not have to graph the interval.

a) b)c) d)

14) Solve the following inequality. Write your answer in interval notation.

3 (𝑥−2 )+2≤𝑥−8𝑜𝑟 4 (𝑥+1 )+2>−2𝑥+4

19) Solve the following inequality. Graph the solution on the number line and write your answer in interval notation.

Additional Practice

3) Indicate the constant that is needed to complete the square.a) b)

3) Indicate the constant that is needed to complete the square.a)

5) Use the discriminant of the quadratic equation to determine the number and type of solutions.

6) A rectangular table is twice as long as it is wide. The area is 800 What are the dimensions of the table ?

7) The height of a ball after t seconds when thrown straight up is given by the function

When will the ball reach a height of 70 feet?

7) On the graphing calculator

7) Quadratic Formula

𝑥4−11𝑥2+28=0

11¿ 𝑥4−11𝑥2+28=0

a)b)c)d)

a)b) c) d)

3 (5−2𝑥 )≥ 4 (𝑥+5 )

3 𝑦−6≤−12𝑎𝑛𝑑−2 𝑦 <10

𝑚+1≤6𝑜𝑟13𝑚<−2

mac 1105

type of equation

test questions

rational equation

practice test objectives

missed test

practice test solutionsmrs

compound inequality

given inequality notation

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