What to Expect on the Placement Exam

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Kelley Ferguson
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1 What to Epect on the Placement Eam Placement into: MTH o MTH The ACCUPLACER placement eam is an adaptive test ceated by the College Boad Educational Testing Sevice. This document was ceated to give pospective CLC student and othe inteested paties an oveview of how the placement eam woks and the types of questions one might epect to see on it. Geneal Infomation: The eam is computeized and is not timed. Questions ae pesented in a multiple-choice fomat. No patial cedit is awaded. Scatch pape is povided. Handheld calculatos ae not allowed. The testing softwae povides a pop-up calculato fo use on some questions. Thee is a limit to the numbe of times a student may take the placement eam. CLC Mathematics depatment wants each student to do as well as possible on the placement eam and makes the following ecommendations: Pepae fo the eam. Don t take it cold. Studying fo the eam may decease the numbe of math classes you ae equied to take. Fee pactice questions/answes ae available online at the Accuplace website, located at Othe eview mateials ae available at the Math Cente. (847) Take the eam when you ae ested and efeshed. Allow plenty of time fo testing so that you can ela and fully concentate on what you ae doing. Tiple-check answes befoe moving on to the net question. The compute only knows if you answe is ight o wong. It cannot tell the diffeence between a caeless mistake, a mino eo, o a majo eo. Stay calm if you don t know the answe to a question. Remembe that the placement test is adaptive and is used to test many levels of mathematics. It inceases o deceases the level of the questions based on you pevious answes. A student desiing to place into College Algeba (MTH ) o Pecalculus (MTH 45) must fist pass the twelve question Basic Algeba potion of the eam. The student will then be given the oppotunity to answe questions fom the College Mathematics potion of the eam. Any student intending to place into College Algeba o Pecalculus via the Math Placement Eam must be poficient with the types of algeba eecises illustated as eamples fo enty into Intemediate Algeba (MTH 08). In addition, the student must be poficient with the types of eecises illustated in this document. NOTE: The eamples povided below ae not intended to be a complete list of poblem types. The eamples ae simply illustations of poblem types. MTH o MTH 44 Placement Eam As of June, 07

2 . The student must be completely poficient with all aspects of linea equations in two vaiables, lines, and linea functions. The student must be able to go fom the gaph to the equation and vice vesa. Eamples: 9 Gaph the following: y 7; y 8; y ; y What value must a take on fo the line defined by y a 7 to be paallel to the line defined by y 8? What value must a take on fo the line defined y a 7 to be pependicula to the line defined by y 8? d) Wite the equations of the following lines.. The student must be poficient with all popeties of eal valued eponents and be able to simplify epessions involving them. Eamples: Simplify the following: 4.5 y z y z q a b b a q q b q qz z. The student must be able to ecognize the equation of and the gaph of simple quadatic functions along with hoizontal and vetical tanslations of them. Eamples: Gaph the following: y 5 y y ( ) 5 y ( ) Which equation below could coespond to the following gaph? i) y 5 ii) y iii) y ( ) 5 iv) y ( ) MTH o MTH 44 Placement Eam As of June, 07

3 4. The student must be able to solve simple linea and non-linea systems of equations. Eamples: Solve the following systems of equations. y 8 y 7 6 y y 7 0 y z z y 4 5. The student must be able to solve simple linea and non-linea equations, which involve factions. Eamples: Solve the following equations. 5 ( ) a c d) b 6 b a 6. The student must be able to pefom composition of functions. Eample: Given: f ( ) and g( ) What is f(g())? What is g (f ())? What is f(-)? d) What is g(g())? 7. The student needs to be able to solve quadatic equations using factoing, the zeo facto technique, and the quadatic fomula. Eamples: Solve the following The student must be able to add and subtact modeately difficult algebaic factions using least common denominatos. Eamples: z z z 5 4 4z 8 z MTH o MTH 44 Placement Eam As of June, 07

4 9. The student must be able to multiply and epand polynomials. Eamples: Pefom the following multiplications ( 7y)( y)(6 8) ( y 5z 4w) ( y 5z ) 0. The student must be able to facto common factos fom a vaiety of algebaic epessions. Eamples: Recognize the Geatest Common Facto (GCF) and facto the epession. a baz ca yzp zyq y ( )(p 7) (4 q)(p 7) (p 7). The student must be poficient with factoing algebaic epessions. Eamples: Completely facto the following. 7 5z 64q 5 8 d) ( )( 7) ( )( 7). The student must be poficient with simplifying all types of ational algebaic epessions including comple algebaic factions. Eamples: Simplify the following algebaic epessions ( 5 ) 4 d) a b e) a b f) a ab b a b. The student must be poficient with simple absolute value epessions, equations and inequalities. Eamples: Solve fo : + 6 Solve fo : 7? if < 0 d)? if >0 a ab ab b MTH o MTH 44 Placement Eam As of June, 07

5 4. The student must be poficient with the basics of eponential and logaithmic functions. Eamples: If log5, then i) 5 ii) 5 iii) 5 iv) 5 The gaph shown could be the gaph of i) y log ii) log 5 iii) y iv) y The invese function coesponding to the function y log b is given by i) y b ii) b y iii) b log y iv) y log b MTH o MTH 44 Placement Eam As of June, 07

6 What to Epect on the Placement Eam Placement into: MTH o MTH 44 Solutions. The student must be completely poficient with all aspects of linea equations in two vaiables, lines, and linea functions. The student must be able to go fom the gaph to the equation and vice vesa. Eamples: Gaph the following: y 7; y 8; 9 y ; y What value must a take on fo the line defined by y a 7 to be paallel to the line defined by y 8? Answe: y 8, so y 4. a / What value must a take on fo the line defined y a 7 to be pependicula to the line defined by y 8? Answe: y 8, so y 4. a -/ MTH o MTH 44 Placement Eam As of June, 07

7 d) Wite the equation of the following lines. Slope 4/ Slope 4.5/.5 y-intecept 4 y-intecept 0 4 y 4 y. The student must be poficient with all popeties of eal valued eponents and be able to simplify epessions involving them. Eamples: 4.5 y z y z q q a b b a q q qz z b y q. z a b a b q 6 6 ( q z ) q z 6 q z. The student must be able to ecognize the equation of and the gaph of simple quadatic functions along with hoizontal and vetical tanslations of them. Eamples: Gaph the following: y 5 y y ( ) 5 y ( ) MTH o MTH 44 Placement Eam As of June, 07

8 Which equation below could coespond to the following gaph? Answe: i) y 5 ii) y iii) y ( ) 5 iv) y ( ) 4. The student must be able to solve simple linea and non-linea systems of equations. Eamples: Solve the following systems of equations. y 8 y solutions fo (, y) 0 0 ( 9 ) 4()( ) (),, 6 y y ( 6 4 7) Solution: (, 5) y z z y 4 4 z z z z 6 z Solution: 9,4, 5, 5 MTH o MTH 44 Placement Eam As of June, 07

9 5. The student must be able to solve simple linea and non-linea equations, which involve factions. Eamples: 5 ( ) 0 ( ) ( ) ( ) ( )( ) 0 ( because it would cause division by 0 in the oiginal poblem a c d) b b a bc a a b bc a a b bc a ( a b ) 6. The student must be able to pefom composition of functions. Given: f ( ) and g( ) Eamples: What is f(g())? f(g()) ( ) What is g (f ())? g (f ()) What is f(-)? f(-) ( ) d) What is g(g())? g(g()) -(-) The student needs to be able to solve quadatic equations via factoing and the zeo facto technique and also via the quadatic fomula. Eamples: Solve the following. 0 ( 4)( ) 0, so 4 o ( 5)( ) 0, so o ()(7) 6 8 () MTH o MTH 44 Placement Eam As of June, 07

10 8. The student must be poficient with and be able to add and subtact modeately difficult algebaic factions using least common denominatos. Eamples: ( - 4)( + ) z z z 5 4 4z 8 z z z 0z 48 4z( z )( z ) ( )( )( ) 9. The student must be able to multiply and epand polynomials. Eamples: ( 7y)( y)(6 8) 6 0 y 48 6y 40y 68y ( z y 5 ) ( w y 5z 4 ) y 0 yz 5z 6w 4w 6wy 40wz 9 y 0z 4y 0yz 5z 0. The student must be able to facto common factos fom a vaiety of algebaic epessions. Eamples: a baz ca a ( bz c ) yzp zyq y y( zp zq ) ( )(p 7) (4 q)(p 7) (p 7) (p 7)( 4 q ) (p 7)(4 q ) ( p 7)(4 q ). The student must be poficient with factoing algebaic epessions. Eamples: 7 ( )( 4) 5 q z 64 ( 5z 8q)(5z 8q) 5 8 ( )(7 ) d) ( )( 7) ( )( 7) ( )(5) 0( ) MTH o MTH 44 Placement Eam As of June, 07

11 . The student must be poficient with simplifying all types of ational algebaic epessions including comple algebaic factions. Eamples: ( ) ( 7)( ) ( )( )( 4) ( )( 4) ( ) (5 )( 4) 4 ( 5 ) 4 ( 4) (5 ) 4 d) ( ) ( ) ( ) ( )( ) a b a b a ab b a b e) a b a b ( a ( a ( a ( a a b a b a b a b f) a ab ab b b a ab ab ab b a ab b(a a b ab a( ab ). The student must be poficient with simple absolute value epessions, equations and inequalities. Eamples: Solve fo : o + -6, so 5 o -7 Solve fo : 7 7 7, so 4 0 and - 5? if < 0 if < 0,, so - + d)? if >0 if > 0,, so + MTH o MTH 44 Placement Eam As of June, 07

12 4. The student must be poficient with the basics of eponential and logaithmic functions. Eamples: If log5, then i) 5 ii) 5 iii) 5 iv) 5 The gaph shown could be the gaph of i) y log ii) log 5 iii) y iv) y The invese function coesponding to the function y log b is given by i) y b ii) b y iii) b log y iv) y log b MTH o MTH 44 Placement Eam As of June, 07

Practice Integration Math 120 Calculus I Fall 2015

Practice Integration Math 120 Calculus I Fall 2015 Pactice Integation Math 0 Calculus I Fall 05 Hee s a list of pactice eecises. Thee s a hint fo each one as well as an answe with intemediate steps... ( + d. Hint. Answe. ( 8 t + t + This fist set of indefinite