Sample Diagnostic Test

for Mathematics Arithmetic Elementary Algebra College Level Math

WHAT IS THE PURPOSE OF THIS BOOKLET? Most students who enroll at Merced College have not had a math course for at least two years. The purpose of this booklet is to review math problems to help you improve your test score for course placement. You will save time and money. Before you register for an English and/or math course, you must take the Merced College assessment test, called Accuplacer. The assessment process determines your current skill level in reading, sentence skills, and math. Your Merced College counselor will use the results from this test plus other measures, such as prior coursework and grades to determine your initial course placement. It is important to take the time you need to do your best on the test so that your score reflects your skill level. This means you will be more likely to be successful in the math course in which you enroll and progress in the math sequence more quickly to achieve your educational goal. ACCUPLACER ASSESSMENT INFORMATION FOR MATHEMATICS: • • • • • • •

TEST QUESTIONS ARE MULTIPLE-CHOICE. TEST RESULTS ARE AVAILABLE IMMEDIATELY. TEST IS NOT TIMED. NO CALCULATOR PERMITTED. THERE ARE 17 QUESTIONS ON THE ARITHMETIC TEST. THERE ARE 12 QUESTIONS ON THE ELEMENTARY ALGEBRA TEST. THERE ARE 20 QUESTIONS ON THE COLLEGE-LEVEL TEST.

THE LEVEL OF THE MERCED COLLEGE MATH CLASS IS WRITTEN NEXT TO EACH QUESTION INDICATING WHERE A STUDENT MIGHT FIRST ENCOUNTER THE CONCEPT.

[MATH 90] [MATH 91] [MATH 80] [MATH A] [MATH C] [MATH 26] [MATH 25]

= Whole Numbers = Decimals and Fractions = Pre-Algebra = Elementary (Beginning) Algebra = Intermediate Algebra = College Algebra = Trigonometry

NOTE: COUNSELOR EVALUATION OF TEST SCORES AND OTHER MEASURES, SUCH AS PRIOR ACADEMIC WORK AND GRADES DETERMINE INITIAL PLACEMENT FOR ENROLLMENT IN YOUR FIRST MATH COURSE AT MERCED COLLEGE.

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ARITHMETIC OPTION This test covers the basic arithmetic operations and verbal problems that involve fundamental arithmetic concepts. (I) Operations with whole numbers and fractions Simplify or solve the following problems and choose the best answer from the choices given. [1]

6 9

[MATH 91]

(a) 1

(b) 2 3

3

(d) 9 6

(c) − 6 9

[2] 3 of 36

[MATH 91]

4

(a) 27

[3] 3

(b) 43

[5]

+

3 2 ÷ 11 5 1 (a) 11

(b)

1 3

(c)

7 8

(d)

5 8 [MATH 91]

(b)

15 22

(c)

1 2

(d)

22 15

1 2 3 −2 3 5 (a) 1

[6]

(d) 146

[MATH 91]

1 8 4 1 (a) 2

[4]

(c) 108

1 2

[MATH 91]

(b)

5,031 – 1,286 (a) 3,855

1 15

(c)

14 15

(d) 1

1 15

[MATH 90] (b) 4,855

(c) 3,745

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(d) 4,775

ARITHMETIC OPTION (II) Operations with decimals and percents [1] Which of the following is the largest? (a) 0.558 (b) 0.09 (c) 0.598

[MATH 91] (d) 0.155

[2] You scored 85% on a 60-question exam. How many questions did you miss? (a) 10 (b) 9 (c) 8 (d) 51 [MATH 91] [3] Evaluate: 35.2 − 3.31 (a) 3.199 (b) 32.01

(c) 31.89

(d) 32.13

[4] Evaluate: 142 . + 9.02 + 8.001 (a) 18.441 (b) 9.045

(c) 15.829

(d) 17.4

[MATH 91]

[MATH 91]

[5] Round to the nearest hundredth: 89.348 (a) 89 (b) 89.3 (c) 89.34

(d) 89.35

[MATH 91]

[6] 56 is 80 percent of what number? (a) 0.70 (b) 1.43

(d) 70

[MATH 91] (c) 90

ARITHMETIC OPTION (III) Applications, problem solving, and estimation [1] Jimmy purchased a math book for $125. The sales tax rate is 7%. What is the total price of the book including the tax? Estimate to the nearest dollar. (a) $132

(b) $195

(c) $134

(d) $118

[MATH 91]

[2] Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for one-half of his time to the project and a second person for one-third of her time, what part of the third worker’s time should be budgeted to this project?

(a)

1 3

(b)

3 5

(c)

1 8

(d)

1 6

[MATH 80]

[3] During one month, your total gasoline bill was $84 and the car was driven 560 miles. What was the cost per mile for gasoline? (a) $0.15

(b) $0.50

(c) $0.25

(d) $1.50

[MATH 80]

[4] At a cost of $0.31 per mile, how much does it cost to operate a car during a year in which the car is driven 23,000 miles? [MATH 91] (a) $713

(b) $7820

(c) $7130

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(d) $8100

ELEMENTARY ALGEBRA OPTION

This test covers basic algebraic operations involving algebraic polynomials, algebraic equations, and solving word problems. (I)

[1] Evaluate:

Operations with integers and rational numbers; order of operations

− 13 − (2 − 3) ⋅ 23

(a) − 276

(b)

276

[MATH 80] (c)

− 36

(d)

− 10

(e)

[2] Any nonzero real number divided by zero is (a) 0

(b) a real number

[MATH 91]

(c) undefined

(d) 1

[3] Arrange the following numbers from smallest to largest:

1 0.002 , − , 3 (a) (b) (c)

1 − 3, − , 3 1 − 3, − , 3 1 , − 3, 3

(d) (e)

10

[MATH 80]

1 , − 3, 0.51 2

1 , 0.51 2 1 0.002, 0.51, 2 1 , 0.51, 0.002 2 1 1 0.002, 0.51, , − , −3 2 3 1 1 0.002 , − , , − 3, 0.51 3 2

[4] Evaluate:

(a) 3

0.002,

32 − 6 + 9 ÷ 3 (b) 4

[MATH 91]

(c) 0

(d) 6

[5] Evaluate: − 16 − ( −2)

[MATH 80]

4

(a) − 7

2

(b) − 13

(c) − 2

2

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(d) − 3

ELEMENTARY ALGEBRA OPTION (II) Algebraic expressions: evaluate and simplify [1] Simplify: 8( x − 3) + 9 − 2( x + 3) (a)

15 x − 3

[MATH 80]

(b) 6 x − 21

(c) 6 x − 9

(3x + 1)(3x + 2)

[2] Multiply and simplify:

(b) 9 x 2 + 2

(a) 9 x 2 + 9 x + 2

(d) 17 x + 27 [MATH A]

(c) 6 x 2 + 9 x + 2

(d) 6 x 2 + 6 x + 2

[3] Multiply and simplify: (3 x 2 + x + 1)( 2 x − 1) (a)

6x + 2x − 1 3

(b)

6x + x + 6x − 1 3

2

(c)

[4] Factor completely: x 2 − x − 12 (b) ( x − 3)( x + 4) (a) ( x + 3)( x − 4) [5] Simplify:

[MATH A]

6x − x − x − 1 3

2

(d) 6 x 3 − x 2 + x − 1 [MATH A] (d) ( x − 2)( x + 6)

(c) ( x + 2)( x − 6)

3 2+ 8

(a) 5 2

[MATH C]

(b) 3 10

(c) 12

(d) 30

ELEMENTARY ALGEBRA OPTION (III) Translate written phrases; solving equations and inequalities [1] Which of the following inequalities denotes the expression: “x is greater than 3 but not more than 5” (a)

3≤ x≤5

(b)

3< x