6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 1/6

1

x+1

DiagnosticExamination

1. Theequation,4x26x+10=0,has(a) threerealsolutions(b) tworealsolutions(c) norealsolutions(d) onerealsolution(e) fourrealsolutions

2. Simplify[a44a2+4]1/2

(a) |a22|(b) a22(c) |a2+2|(d) a2+2(e) a2+2a+2

3. Simplify

x+1

(x22x3)

x3

x+1

(a)

(b) (x+1

x3) (

x22x3

x+1)

x+1

6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 2/6

(c)(x3)2

(d)1

x3

(e) 12

4. Theareaofarighttrianglewithsides3,4,and5is(a) 6(b) 12(c) 10(d) 15(e) 20

5. Thelineperpendiculartothelinex=5hasslope(a) 1(b) 0(c) 2(d) 1(e) 2

6. Howmanypointsareintheintersectionofy=x2+3x+1andy=2x+5?(a) 3(b) 0(c) 1(d) infinitelymany(e) 2

7. If3x+6=12,whatisx?(a) x=4(b) x=2(c) x=0(d) x=2(e) Alloftheotheranswersareincorrect.

8. Ifx=3,findthesmallestvalueofywhichsatisfiesy2x+3yx2+54=0.(a) 0(b) 3(c) Thereisnosmallestvalue.

6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 3/6

(d) 3(e) 6

9. Findthelargestsolutionofx3+4x2+3x=0.(a) x=2(b) x=0(c) x=3(d) x=1(e) x=1

10. Iff(x)=2x,findf(3).(a) 6(b) Alloftheotheranswersareincorrect.(c) 2(d) 9(e) 8

11. log(x)

6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 4/6

(a) Theinterval[1,1](b) Thesetofallnumbersxsuchthat11(d) x2(c) Alloftheotheranswersareincorrect.(d) x>1(e) x1

19. If4xy=1and2x+y=5,findxandy.

6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 5/6

(a) x=0andy=3(b) x=1andy=5(c) x=1andy=3(d) x=4andy=1(e) x=0andy=6

20. If5x6y=4and3x+4y=10,thenx/yis(a) 2(b) 3(c) 0(d) 1(e) Cannotbedetermined

21. Ify+3x+2=0andy=x2,thenthereisasolutionwithxgivenby(a) x=2(b) x=0(c) x=1(d) Cannotbedetermined(e) x=1

22. Arighttrianglehassidesoflength3,4,and5.Whatisthecosineofitssmallestangle?(a) 5/3(b) 4/3(c) 3/5(d) 3/4(e) 4/5

23. Whichofthefollowingiscorrect?(a) sin(.1)

6/11/2015 DiagnosticExamination

http://diagnostic.math.berkeley.edu/exam.php 6/6

(e) 0

Gradeyourexam