Bryn Mawr College Department of Physics Mathematics Readiness Examination for Introductory Physics

Transcription

1 Brn Mawr College Department of Phsics Mathematics Readiness Eamination for Introductor Phsics There are 7 questions and ou should do this eam in two and a half hours. Do not use an books, calculators, or computers.. If, then + (C) 4. A clinder has a circular cross section of diameter 4 cm (centimeters) and length 5 cm. The volume is approimatel 600 cm 60 cm (C) 6,000 cm 0.6 cm 6 cm. If, then (C) 7 4. The area under this line between and 5 is about (C)

2 Introductor Phsics Mathematics Readiness Eamination 5. ( )( 6) 4 (C) 6. ( ) (C) ( )(4 + ) (C) C (C) A. + + (C) ( +0) ( 0) (C) ( + 0)( 0) ( 50)( 50) ( )( 50). ( )6 ( 0 ) (C)

3 Introductor Phsics Mathematics Readiness Eamination. ( + ) ( ) (C) If A and B in the following triangle, then C A 0 90 C a / / (C) 5 B 4. If of a number is 8, then what is 4 of the number? 6 (C) If and 5, then 40 0 (C) If there are about three feet in a meter, 5 meters is about 8 feet 75 feet (C) 450 feet 4.5 feet 0.45 feet 7. ( + ) ( 5 ) (C)

4 Introductor Phsics Mathematics Readiness Eamination (C) ( )( + ) ( )( ) (C) ( )( + ) ( + )( ) ( )( ) 0. ln( ab) 0 ab e ab (C) e ( a+b) ln( a)+ln( b) a ln(b) (C) (C) The bo pictured below has a square base and a closed top. Epress its surface area in terms of and h. h (C) + 4h 8 + 4h 4 + h h + 4h

5 Introductor Phsics Mathematics Readiness Eamination 5 4. If 4 and 7, then (C) 8 5. If f () is a function whose graph is the parabola sketched below, then f ( ) < 0 whenever < 0 < (C) > < or > < < 6. If mone in a bank doubles ever 5 ears, then b what factor does it increase over a 0 ear period? 4 8 (C) Definition: A function is even if f ( ) f ( ) for each in the domain of f. Which of the functions whose graphs are shown is even? (C)

6 Introductor Phsics Mathematics Readiness Eamination 6 8. If , then 6 5 (C) ( 0)( 5)( )() (C) The -coordinate of the intersection of the graphs of 6 and + is (C) (C) (7). 7 9 (C) Which of the following best resembles the graph of +? (C) 4. If log ( + ), then 5 6 (C) 7 8 log

7 Introductor Phsics Mathematics Readiness Eamination 7 5. ( )( )( ) 6 (C) Which of the following curves best resembles the graph of f ( )? (C) ( + )( ) 7. If 0, then ( + ) or or (C),, or or,, or 8. a 5b a + b b a b (C) 4a 7b a a +b b 9. The smbol means "is approimatel equal to." Given that 7 000, then 4 4,000 40,000 (C) 400,000 4,000,000 8,000

8 Introductor Phsics Mathematics Readiness Eamination In the given figure, the distance between points A and C is 8 0 (C) 4 6 A(,) C(5,8) B(5,) If f ( ), then f (a + ) + 5 a + 8 a + 4 (C) a + 0 a + 4 a + 6 a + a + 6 a The graph of the equation 5 + is a horizontal line (C) a vertical line not a line a line rising to the right a line falling to the right 4. If a + b and a 0, then b + a b a (C) b a b b 44. The quantit a + b is a factor of how man of the following: a b a + b a b a + b 0 (C) p > p + is equivalent to p > p > (C) p > 4 p > 6 p > 5

9 Introductor Phsics Mathematics Readiness Eamination In the triangle shown, tan( a) A 0 90 B C a A/B B/A (C) B/C A/C C/A 47. A ab A a+b ba a (C) A a A b ( A a ) b A a A b 48. The area of the rectangle pictured below is (C) f ( ) Suppose the sides of a rectangle with length and width are each doubled. The area of the rectangle now is (C) (4 raised to the zeroth power) 0 (C) 4 0.5

10 Introductor Phsics Mathematics Readiness Eamination ( + 5) 7 (C) 5. In the triangle shown, sin( b) 4 b d D c.. (C) is equivalent to (C) 54. / / 0 4/9 (C) 9/ The length of a certain rectangle is meters more than twice its width. If the perimeter of the rectangle is 90 meters, then the width of the rectangle is 6 m m (C) 4 m 6 m 9 m 56. 4( s + ) ( ) 4 s s + 6 (C) 4 s + s s /4 /7 7/8 5/8 (C) /4 /47 /4

11 Introductor Phsics Mathematics Readiness Eamination 58. If 5 <, then < 5 > (C) 5 < > 5 5 > Definition: A function f () has a minimum value at the number c if f ( c) f ( ) for ever in the domain of f (). If the domain of the function whose graph appears on the right is[ 0,4], at which number does the function have a minimum value? 0 (C) The side D in this triangle is 4 b d D c 5 5 (C) ( ) ( 6) 8 8 (C) sin θ cos θ cos θ (C) cos θ csc θ cos( θ ) 6. If f ( ) cos(), then f ( 6)

12 Introductor Phsics Mathematics Readiness Eamination 0 (C) 64. The circumference of a circle of radius R is R R (C) R R R 65. Which of the following best represents the graph of sin for between and (C) 66. sin θ tanθ csc θ tan θ sin θ cos θ (C) sin θ tan θ sec θ 67. For which value of is tan not defined? (C) 0 4

13 Introductor Phsics Mathematics Readiness Eamination 68. The area of a circle of radius R is R R (C) R R R 69. The angle a in this triangle is A 0 90 B C a (C) The slope of line A is (C) A If there are (5/8) mile per km (kilometer) and 60 seconds in a minute, then 00 km/minute is about miles/second 4,000 miles/second (C) 6 miles/second 0. miles/second mile/second