California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra (with Geometr) Diagnostic Test (EGAD) Stud topics Sample Test Answers to Sample Test Intermediate Algebra Diagnostic Test (IAD) Stud topics 8 Sample Test Answers to Sample Test 6 Calculus Readiness Diagnostic Test (CR) Stud topics 8 Sample Test Answers to Sample Test 7
Introduction Some classes at CSUS require that ou pass a mathematics diagnostic test in order to remain enrolled in the class. The diagnostic test determines if ou have the basic math skills necessar to be successful in that class. This stud guide has been developed to help ou review for the particular test ou need to take. There are diagnostic test stud guides in this booklet. The Intermediate Algebra Test (IAD) assumes ou can easil do the math in the Elementar Algebra (with Geometr) Diagnostic Test (EGAD), and the Calculus Readiness Diagnostic Test (CR) assumes ou can easil do the math in both the EGAD and IAD Tests. So, ou should review the diagnostic test (s) below the one ou need to pass for our class. To sta in this Math Class: Math 9, Math 7 Math Math 6A Math 9 Math 7A Statistics Math Take this Diagnostic Test: EGAD or IAD IAD CR
Elementar Algebra (with Geometr) Diagnostic Test (EGAD) The Elementar Algebra (with Geometr) Diagnostic Test (EGAD) is given b the Learning Skills Department at the end of LS 7B and LS. There are multiple choice questions and the test is 6 minutes long. The following is a list of Elementar Algebra topics covered on the EGAD. After that is an EGAD Sample Test with Answers. If ou find a section of the sample test questions difficult, use the topics list to help ou find a similar section in an Elementar Algebra tetbook. Then read and stud the tetbook until ou understand how to do those problems. This is also a good Sample Test to take when preparing for the IAD! Stud Guide: Elementar Algebra Diagnostic Test Topic I Arithmetic Operations Arithmetic operations with fractions and decimals Integral eponents and square roots of perfect squares Conversion between fractions and decimals Ordering of rational numbers Percentages Estimation and approimation Topic II Polnomials Simplification and evaluation of polnomials Basic operations with polnomials Special products Factoring monomial factors, trinomials, and special products Topic III Linear Equations and Inequalities Solving linear equations with numerical and literal coefficients Solving equations reducible to linear equations Solving linear inequalities Solving two linear equations b elimination and substitution Topic IV Quadratic Equations Solution of quadratic equations b factoring
Topic V Graphing Graphing points on the number line and in the coordinate plane Graphs of linear inequalities Inequalities in one unknown Graphs of simple linear equations Slope of a line Topic VI Rational Epressions Simplification of rational epressions Addition and Subtraction of rational epressions Multiplication and Division of rational epressions Comple rational epressions Topic VII Eponents and Square Roots Eponentiation with integral eponents Simplification, addition, subtraction, multiplication, and division of square roots Scientific notation Topic VIII Geometric Measurement Measurement formulas for perimeter, circumference, area, and volume of triangles, squares, rectangles, parallelograms, circles, cubes, rectangular solids, clinders, and spheres Sum of the interior angles of a triangle Properties of isosceles triangles Properties of similar triangles Pthagorean Theorem Topic IX Word Problems Problems involving arithmetic, percent, average, algebraic substitution, evaluation, ratio, and proportion Problems leading to one and two linear equations Problems from geometr
Elementar Algebra (with Geometr) Diagnostic Sample Test Questions Topic I Arithmetic Operations. Epress 7. Simplif: as a decimal eactl and rounded to the thousandths place. + 8. (.7 +.) =. Write ( ) as a power of. Topic II Polnomials. Multipl: ab ( a b a + ) 6. Factor completel: 9a b 7. Solve for : ( + 6)( ) = 8. If = and =, then + = 9. Multipl and simplif: ( ). Factor completel: a 7 a 6. Simplif: ( m m+ ) ( m m ). Multipl and simplif: ( w + )( v ) w( v + ). Factor completel: abz 9abz + abz Topic III Linear Equations and Inequalities. Solve for : + 7 7 = +. Solve for : a = c 6. Solve for : 8 =
7. Solve for and : = = 8. Solve for and : + = and = 9 9. Solve for : 7 < 8. Solve for : 7 = Topic IV Quadratic Equations. Solve for : ( ) + =. Solve for : + 7 =. Solve for : ( 7) = 6. Solve for :. Solve for : + = + 6 = 6. OMIT Solve for : = 7. Solve for : 6 = Topic V Graphing 8. Graph the point (, ) 9. Epress the graph shown in interval notation. 6. Graph and on the same set of aes. 6
. Find the midpoint of this line segment. (, ) (, ). What if anthing can be said about the following lines: I. = 7 II. + = 6 III. = A. (I) is parallel to (II) B. (II) is parallel to (III) C. (I) is perpendicular to (III) D. (I) is perpendicular to (II) E. Both A and B are true F. Both B and D are true G. None of the above are true.. If (a, b) denotes the coordinates of the point P in the graph below, then where is the point with coordinates (a, b)? - P - 7
. What is the equation of this line? - -. Graph > 6. Graph + 7. Where does graph on this number line? 8. Graph the solution set for this inequalit: < 9. Find the slope of the line passing through the points (, ) and (, ).. Which line is the graph of =? L L L L 8
Topic VI Rational Epressions. If = and =, then =. Simplif:. Simplif:. Simplif: ( + )( ) 6 + + 6 ab+ ab + ab ab. Find the quotient of the following: + 6. Add and simplif: + + 7. Subtract and simplif: 8. Divide and simplif: + + Topic VII Eponents and Square Roots 9. Evaluate:. Evaluate: 6 6 ( )( )( a ) ( a )( )( ). Simplif: 8. Evaluate:. Epand: ( ) 9
. Multipl: ( ab )( ba ). Epand and simplif: ( ) 6. If >, then 7. Simplif: 7 = 6a + 6b 8. Simplif: 8 + 9. Simplif and epress with positive eponents: 6. Simplif: ( 7ab )( ab ) ab 6. Simplif and epress with positive eponents: z z 7 6. Simplif and epress with positive eponents: ( )( ) 6. Epress the following in scientific notation: a),6, b).6 6. Epress the following in standard notation: a). b) 6.6 Topic VIII Geometric Measurement 6. In the rectangle ABCD shown, find the length of AC. B C A D
66. Find the measure of Θ in the triangle ABC. Θ C 9 9 66º A B 67. Find the surface area of the rectangular prism pictured here. Find the volume also. 8 68. The area of a circle is π. Find the radius of the circle. 69. Lines L and L are parallel and AB = EF. What is true about the areas of ABDC and EFHG? A B F E L C D G H L 7. Find the measure of angle X. Lines m and m are parallel. m º X 77º m
7. Find the area of the shaded region. 6 9 7. Find the measure of angle A. 8 A 7. Find the measure of X in this figure. X 96º 7º X 7. Find the measure of in this right triangle. 6º 7. Find the length of in this right triangle. º 6
76. The radius of the circle is. What is the perimeter of the square? What is the area of the square? 77. Find the length of in the figure shown here. 7 78. These triangles are similar. Find. 6 79. Find the measure of BEC if CED is a right angle. C B A º E D 8. Triangle ABC is similar to triangle DEF.. Find the length of DF. E B 7 9 A C D F
Topic IX Word Problems 8. The length of a rectangle is times its width plus inches. If the perimeter is inches, how wide is the rectangle? 8. An item is sold for $8. If this price is % more than the cost, what is the cost of the item? 8. A number is divided b and then multiplied b 7. The result is. Find the number. 8. Two integers have a sum of and a product of. What are the numbers? 86. Ruth has $. in change consisting of onl nickels and dimes. If she has coins altogether, how man nickels and how man dimes does she have? 87. A triangle has an area of 6. If its base is half of its height, what is the base of the triangle? 88. $9 is invested in two accounts. Account A pas % annual interest and account B pas 6% annual interest. In one ear a total of $8 is earned in interest. How much was invested in each account? 89. The sum of three consecutive integers is. Find the numbers.
Answers to the EGAD Sample Diagnostic Test..6 and.67. 8..67. 6. ab ab + ab 6. a+ b a b ( )( ) 7. = 6, = 8. 7 9. +. a+ a... ( )( ) m + m+ wv 7w + v ab z a z b + 8abz. = 7. a+ c = 6. = 8 7. =, = 8. =, = 9. > 7. =. =, =. =, =. =, =. = ±. =, = 6 6. OMIT =±, ± i 7. =, = ( ) 8. 9. [ 6, ).. (, ). F... (a, b) P = (a, b) = + or + = 6
6. 7. 7. 9 ( )( 8. 9.. a.. 8.. 6 9 6 a b + ). + 8. 9.. L. 7 9.. +.. 6. + b + ab a 6 + ( )( ) 6. 7 7. 9a + b 8. 9. 6. 6. 6a z 6. 6. a).6 6 b).6 6. a), b).66 6. 66. 8º 67. Surface area: square units Volume: cubic units 68. 69. The are equal. 7. 8º 7. square units 7. 6º 7. 6º 6
7. 7 7. 76. Perimeter: units Area: square units 77. 78. 79. º 8. 9 8. (7, 8) 8. 6 inches 8. $ 8. 8. 7 and 86. 7 nickels and 8 dimes 87. 88. $78 in account A $ in account B 89. 7, 8, 9 7
Intermediate Algebra Diagnostic Test (IAD) The Intermediate Algebra Diagnostic Test (IAD) is required in order to sta in these Math classes: Math 7,, 6A, 9, 7A, and Statistics. The IAD has multiple choice questions. The test time is 6 minutes. NO CALCULATORS are allowed. What score do ou need? For this Math course: If our score is Then Math 7 or 7A 8 or less 9 to to to 8 9 or more Math, 6A, 9 Stats 8 or less 9 to to 6 7 to or more Take LS 7AB or LS Take Math 9 Take Math 9 or Math Advisor qualification for course Qualifies for course Take LS 7AB or LS Take Math 9 Take Math Advisor qualification for course Qualifies for course The following is a list of topics covered on the IAD. That is followed b an IAD Sample Test with answers which has problems in the same order as the topics list. If ou find a section difficult, use the IAD Stud Topics list to help ou find a similar section in an Intermediate Algebra tetbook. Read and work problems in the tet until ou understand how to do these problems. You ma also find it helpful to do the Elementar Algebra Diagnostic (with Geometr) Test (EGAD) Sample Test as well. Stud Guide: Intermediate Algebra Diagnostic Test Topic I Elementar Operations Simplification of algebraic epressions Laws of Eponents with positive integral eponents Scientific notation Absolute Value Topic II Rational Epressions Simplification, addition, subtraction, multiplication, division or rational epressions Comple rational epressions 8
Topic III Eponents and Radicals Laws of eponents with rational and literal eponents Numerical and algebraic calculations with rational eponents and radicals Factorization and simplification of algebraic epressions with rational and literal eponents and radicals Rationalization techniques Topic IV Linear Equations and Inequalities Solution on one and two linear equations Solution of equations reducible to a linear equation Solution of linear equalities Topic V Quadratic Polnomials, Equations, and Inequalities Polnomial algebra Factorization Completing the square Solution of quadratic equations b factoring and the quadratic formula Solution of quadratic inequalities Comple numbers Topic VI Graphing and Geometr Points in the coordinate plane Distance in the coordinate plane Slope and intercepts and quadratic equations Graphs of linear and quadratic equations Topic VII Logarithms and Functions Numerical and literal function evaluation Definition and rules of logarithms Logarithmic and eponential equations Topic VIII Word Problems Problems involving percents, average, ratio, and proportions Problems leading to linear and quadratic equations Problems from geometr 9
Intermediate Algebra Diagnostic Sample Test Questions Topic I Elementar Operations 6. Epress in scientific notation: (.7 )(. ). Epress in scientific notation:.8. 7. Simplif: 9. Add and simplif: ( ) ( ) ( ). If = ( ) and a =, then a = a 6. If a =, evaluate: a a+ + Topic II Rational Epressions 7. Add and simplif: 8. Add and simplif: + + + + + 9. Simplif: ( + ) ( ) +. Simplif: + + + +. Simplif: +
. Simplif: + + + Topic III Eponents and Radicals Assume all variables are positive real numbers. Evaluate: 8. Simplif:. Simplif: 6 + + 6z ( ab )( a b) 6. Simplif: ab 7. Simplif: ( ) ( 6 ) 8. Simplif: 9. Simplif:. Simplif:. Simplif: 8a + a a + 6a 6 a a + z z. Epress without radical signs:. Epress without radical signs: 7 z. Solve for :. Simplif: =
6. Rationalize the denominator: 7 Topic IV Linear Equations and Inequalities 7. Solve this sstem of equations: 8. Solve this sstem of equations: + = = = + = 9. Solve for : =. Solve for m: 7 9m > ( m+ ). Solve for : ( ) ( 7) = ( + 9) Topic V Quadratic Polnomials, Equations, and Inequalities. Multipl: ( )( + ). Factor:. Solve for :. Solve for : a 9a b + = + = 6. If ou solve this equation b completing the square, what do ou add to each side of the equation? + = 7. Solve for : + + = OMIT 8. Solve for t: t 6t + = OMIT 9. Solve for a: a a =. Simplif: i i
. Solve for z:. Solve for a: z z+ = = + a a ( )( ). For what values of m is m m >? Topic VI Graphing and Geometr. Find the equation of the line which passes through the points (, ) and (7, ).. Find the equation of the line with a slope of which passes through the point (, ) 6. Find the distance between points A and B in the graph shown below. - - - 7. What is the midpoint between the points (, ) and (7, ) 8. Find the quadratic function whose graph is shown in the figure below.
9. Find the slope of the line, L, shown in the figure below. - - - -. Graph the equation: =. Graph the equation: =. Graph the equation:. OMIT. Find the value of : = 7. OMIT 6. OMIT 7. OMIT 8. OMIT 9. OMIT 6. OMIT
Topic VII Logarithms and Functions ( ) = + ( ) 6. If f, then f u = = + +, find. h 6. If f ( h ) h f ( ) 6. Write log = in eponential form. b a 6. Solve for : = 6 6. Solve for : log = 66. Evaluate: log6 6 log + = 67. Solve for : ( ) log + log 7 = 68. Solve for : ( ) 69. Simplif: log log log77 = 6 Topic VIII Word Problems 7. You can echange $. for.7. How man pounds ( ) can ou get for $? 7. The side of a square is doubled. How much does the area change? 7. If 7% of a number is 6, what is the number? 7. is to 8 as is to what number? 7. The product of two numbers is 8. Their sum is. What are the numbers? 7. A rectangle has an area of and a perimeter of 6. What are the dimensions of the rectangle? 76. Five times a positive number is equal to the difference of the square of that number and 6. What is the number?
Answers to the Intermediate Algebra Sample Test....6... 6. 7. + + 8. + + 9. ( )( ( ) ) + + ( ). +. +. ( + )( ) ( + )... + 6 + 9z 6. 6ab 7. 6 8. 6a a + a 9... a z. =. ( ).. z 7 7 6 = z 8 = = 6. 7 7. =, = 8. =, = 9. =. 7 m <. 7 =. + 7. a ( + b )( b ).. 6. Add 9 = or = ( )( )( ) + + = =± i, ± 7. ± = 8., 9. a = 7 (onl 7 checks). + i 9. ± i z =. ± a = 6
. m <, m >. = + or + 6 = 6 6. = 6. 6 7. 8. 9...., = + m = - - - -, and,. OMIT.. 6. OMITTED 6. 6. u 6u + 6. a = b 6. = 6. = 66. 67. = 6 68. = 8 ( cannot be ) 69. 7..7 7. times 7. 7. 98 7. and 6 7. 8 76. 9 7
Calculus Readiness DiagnosticTest (CR) The Calculus Readiness Diagnostic Test (CR) is required in order to remain enrolled in Math. There are 6 multiple choice questions on this eam and the test has a 9 minute time limit. No calculators are allowed. What score do ou need: If our score is Then 7 or less Take Math 9 8 to 6 Take Math 7 to Advisor qualification for Math 9 to Qualifies for Math 9 6 to Advisor qualification for Math or more Qualifies for Math The following Precalculus Stud Topics list covers the topics on the Calculus Readiness Test. This section is then followed b sample test questions arranged in the same topical order. If ou find a section difficult, use the Precalculus Stud Topics List to help ou find a similar section in a Precalculus tetbook. Then read and work problems in the tet until ou understand how to do these problems. You ma also find it helpful to work through the EGAD and IAD Sample Tests. Calculus Readiness Test Stud Topics Topic I Rational Epressions Addition, Subtraction, Multiplication, Division of rational epressions Comple rational epressions Topic II Eponents and Radicals Laws of Eponents Calculations with eponents and radicals Conversion between radicals and eponents Rationalization techniques Topic III Linear Equations, Inequalities, Absolute Value Solution of one and two linear equations Solution of equations reducible to linear equations Graphs of linear inequalities Solution of linear inequalities 8
Simplification of epressions involving absolute value Solution of equations and inequalities involving absolute value Topic IV Polnomials and Polnomial Equations Polnomial algebra Factorization Completing the square Solution of polnomial equations b factoring Solution of quadratic equations b quadratic formula Graphs of quadratic equations Solution of quadratic inequalities Topic V Functions Function concept and notation Function evaluation and composition Graphs of translations, reflections, and absolute value functions Topic VI Trigonometr Right angle trigonometr Trigonometric functions and circular functions Radian and degree measure Special angles Trigonometric identities Graphs of trigonometric functions Topic VII Logarithmic and Eponential Functions Definition and laws of logarithms Evaluation of logarithmic epressions Graphs of logarithmic and eponential functions Inverse relation between logarithm and eponential functions Logarithmic and eponential equations Topic VIII Word Problems Problems involving percent, average, ratio, and proportion Problems leading to linear and quadratic equations Problems from geometr 9
Calculus Readiness Sample Test Questions Topic I Rational Epressions Simplif the following:. 9 6 9 + + +. 9. u v 7v 6v uv + 9.. + + ( + b)( b) ( b )( + b) ( b)( b ) 6. a b b a 7. 8. + m m m m m m+ m Topic II Eponents and Radicals 9. Evaluate: 8 Simplif the following:. 6
. ( a + b )( a b ).... 6 + + 6z ( )( ) a b c a b c a a + b 6. ( m b+ ) 7. 6 8. ( ) 8 9. ( )( ) m 6 m m. + 7 8 Rationalize the following:... Solve for : = 7 + Topic III Linear Equations, Inequalities, and Absolute Value a b. Solve for : = ( )
. Solve for a: a + = 7 6. Solve for : + = + + 7. Solve this sstem of equations: 8. Solve this sstem of equations: + = = 8 = + = 7 9. If m =, evaluate. Find the equation of this line: - - - - -. Solve for :. Given the points (, ) and (, ), find the area of the right triangle formed b the line through those points, the -ais, and =. Topic IV Polnomials and Polnomial Equations. Solve for :. Solve for : 6 + = + + = =. Solve for : ( )( ) 6. If ou wanted to complete the square, what would ou add to both sides? = 7. Solve for : =
8. Simplif: + + 9. Find the values of a so that the following has distinct real roots: a 7. Solve for :. Graph: > = 6. Graph: + =. Graph: = +. Graph: =. If =, =, and z =, evaluate z z z 6. Find the vertical and horizontal asmptotes of f ( ) Topic V Functions 7. Find f() when f ( ) 8. If f ( ) 9. If f and. If f ( ) = a + + b =, find f +. = + ( )( + ) ( ) = g( ) = +, find: a) f ( g( )) and b) go f ( ) + =, for what does f() =?. Find f t if f () t = t ( ). Graph: f ( ) f = + =. Graph: ( )
g =. Find the domain and range of ( ). Epress the domain and range of g( ) ( ) eact answers, no decimals). 6. Find the area of the interior region of this figure: = + in interval notation (with 8 6-7. Let f ( ) =. If f ( a) f ( a ) Topic VI Trigonometr 8. Find cos(θ) in the given triangle. = +, then a = Θ w 9. Use this triangle to find cotθsinθ. w 9 a Θ 6. Evaluate: cos( Θ + π ) 6. Verif this identit: secθ cosθ = tanθsinθ b 6. Graph the function: = cos
6. Graph: = sin 6. In the figure shown, find cscθ. Θ (, ) 6. Epress º in radians. 66. Which trig functions are even? 67. Find 68. Find sin. π cos. Topic VII Logarithmic and Eponential Functions 69. Solve for b: log a b = 7. Solve for : = 7. Evaluate: 7. Evaluate: 7. Simplif: 7. Solve for : log 6 6 9 6 log9 7 log log + log ab a b = log = 7. Solve for : ( )
76. Graph: = 77. Graph: = log ( + ) Topic VIII Word Problems 78. A baker has a special on peanut butter cookies and chocolate chip cookies. There are dozen cookies on special. If there are % more chocolate chip cookies than peanut butter cookies, how man chocolate chip cookies are there? 79. A w b 6L inch poster is enlarged so that its length is ft. What is its width? 8. The circumference of a circle is quadrupled. How much is the area increased? 8. The sum of two numbers is 79½. Si times the first number minus seven times the second number is 778. Find the numbers. 8. The cube root of a number is squared and the result is 6. What is the number? 8. The price of an airplane ticket is decreased 6% to $9.. What was the original price? 8. If the radius of a circle is decreased b %, what is the percent decrease in the area of the circle? 8. What is the surface area of the given triangular prism? 86. Find the area of the given figure to the nearest tenth. 7 87. How long does it take something to travel meters at meters per second? 88. A tree twent-five feet tall casts a shadow that is feet long. If the shadow of a nearb building is 9 feet long, how tall is the building? 6
Answers to the Calculus Readiness Sample Test Questions..... 6. + + ( ) v 7u ( + )( ) 7. 8. 9. + + 9b ( + b)( b )( b) ab ( ) ab or a a b b a b + m m 7. 9 =. ( a+ b) a b. + 6 + 9z. 6.. 6. 7. bc a a b m 8. 6 9.. m. 8.. = 7. a a or b a a b. a = 8 6. = 7. =, = 9 9 8. =, = 9. 7. + =.. The line formed b the points is =. This line intersects the -ais at,, so the base of the 8 right triangle is = units in length. The area is then 6. =,. ±. = or 6. Add 9 to both sides. 7. = 7 ( doesn t work) 8. + 7 9. 8 a > 7 sq units. 7
. < 6 or > 7... 6. Vertical: =, = Horizontal: = 7. 8. 9. ( + ) +. = 9. a) b)... -.. domain: 6 or + 6 ( ) ( ) range: g( ) - - 8
. domain: 9,+ 9 range:, 9 + + 8 + 6 = a = 6. ( ) ( ) ( ) ( ) 7. 8. cosθ = 9. b a + b 6. cosθ 6. 6. w 9 w secθ cosθ = cosθ cosθ cos Θ = cosθ sin Θ = cosθ sinθ = sinθ cosθ = tanθsinθ 6. 9 6. 9π 66. cosine and secant 67. π or 6 68. 69. b = a 7. log ln = or log ln 7. 6 7. 9 7. ab log 7. = 7. = 7 76. - - - - 6 6. 77. - - - -6 6 9
78. p +.p = ; 7 dozen chocolate chip cookies 79. inches 8. 6 times 8. 6 and 8. 8. ± 6 $ 8. 7.7% 8. 7 + 86. 7.6 87..9 sec 88. 8 ft.