Eqe Reviewer With Answer 2s271i

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (ALGEBRA) Choose the capital letter that corresponds to the correct answer in each of the following. 1. The equation whose roots are the reciprocal of the roots of the equation 2x 2 − 3x − 5 = 0 is: A. 3𝑥 2 + 5𝑥 − 5 = 0

B. 5x 2 + 3x − 2 = 0

C. 2x 2 − 5x + 3 = 0

D. 5x 2 − 3x + 2 = 0

2. If the roots of the equation are -1, 2 and 4, what is the equation? A. x 2 − 5x 2 + 2x + 8 = 0

B. x 3 − 4x 2 + 3x + 8 = 0

C. x 3 − 5x 2 − 3x + 6 = 0

D. x 3 − 4x 2 + 2x + 6 = 0

C. 56𝑎3 𝑏 5

D. 448𝑎3 𝑏 5

3. Find the 6th term in the expansion of (a + 2b)8 . A. 1792𝑎3 𝑏 5

B. 1792𝑎5 𝑏 3

4. The remainder when 2x 4 − kx − 15x 2 − 3x − 2 is divided by (x-3) is 4. What is the value of k? A. 4

B. 7

C. 3

D. 5

5. If log 2=x and log 3=y, find log 1.2 in of x and y. A. 2x + y - 1

B. 3x + 2y - 1

C. 2x – y +1

D. 2x – 3y - 1

6. Find the sum of the first 100 positive odd integers. A. 10000

B. 9899

C. 5000

D. 8910

7. A rubber ball is made to fall from a height of 50 ft and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner? A. 420 ft

B. 271 ft

C. 343 ft

D. 250 ft

8. How many 4-digit number less than 4000 can be formed from the digits 2, 3, 5, 6, 7 and 9 if each digit must be used only once? A. 120

B. 40

C. 20

D. 80

9. In how many ways can 18 points, no three of which are collinear, be connected to form a triangle? A. 720

B. 540

C. 144

D. 816

10. Given that "w" varies directly as the product of x and y and inversely as the square of z, and that w=4, when x=2, y=6, and z=3. Find the value of w when x=1, y=4 and z=2. A. 2

B. 3

C. 4

D. 5

11. A father is four times as old as his son now. Six years ago, he was 7 times as old as his son during that time. Find their present ages. A. 8, 41

B. 12, 48

C. 10, 41

D. 12, 45

12. Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration in the mixture? A. 19.54%

B. 15.3%

C. 11.4%

D. 5%

13. A farmer can plow the field in 8 days. After working for 3 days, the son s him and together they plow the field in three more days. How many days will it require for the son to plow the field alone? A. 6 days

B. 12 days

C. 11 days

D. 9 days

14. At what time after 12 o'clock will the hour hand and the minute hands of a clock form an angle of 120° for the first time? A. 12:21.818

B. 12:18.818

C. 12:22.818

D. 12:24.818

15. The sum of the digits of a certain two-digit number is 10. If the digits are reversed, a new number is formed which is one less than twice the original number. Find the original number. A. 19

B. 37

C. 82

D. 64

 2 3 3 and B    , then AB is equal to   1 1   4

16. If A  

A.

 6  7   

B.

 6

 7

C.

6 9   4  4  

D.

 6  12  3  4   

17. If x varies inversely as y and when x = 2, y = 5, what is the value of y2 when x = 1/3. A. 900

B. 1/900

C. 30

D. 1/30

18. In a class of 40 students, 27 like Differential Calculus and 25 like Gen. Chemistry 1. How many students like both subjects? A. 8

B. 10

C. 12

D. 14

19. Find the product of two numbers such that twice the first added to the second equals 19-and three times the first is 21 more than the second. A. 24

B. 32

C. 18

D. 20

20. A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take the second jogger catch the first? A. 20 min

B. 21 min

C. 22 min

D. 18 min

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (TRIGONOMETRY) Choose the capital letter that corresponds to the correct answer in each of the following. 1. The measure of 2.25 revolutions clockwise is: A. -835°

B. 805°

C. -810°

D. 810°

2. A certain angle has an explement 5 times the supplement. Find the angle. A. 67.5°

B. 108°

C. 135°

D. 58.5°

3. A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower? A. 76.31 m

B. 73.31 m

C. 73.16 m

D. 73.61 m

4. One leg of a right triangle is 20 cm and the hypotenuse is 10 cm longer than the other leg. Find the length of the hypotenuse. A. 10 cm

B. 15 cm

C. 25 cm

D. 20 cm

5. In a triangle ABC, find the side c if angle C=100°, side b=20 and side a=15. A. 28

B. 27

C. 29

D. 26

6. A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower are 13° and 35° respectively. The height of the tower is 50 m. Find the height of the monument. A. 33.51 m

B. 37.58 m

C. 47.30 m

D. 30.57 m

7. Given a right triangle ABC. Angle C is right angle, BC=4 and the altitude to the hypotenuse is 1 unit . Find the area of the triangle. A. 2.065 s.u.

B. 3.065 s.u.

C. 1.065 s.u.

D. 4.065 s.u.

8. In a given triangle ABC, the angle C is 34°, side a is 29 cm, and side b is 40 cm. Solve for the area of the triangle. A. 324.33 sq cm

B. 344.15 sq cm

C. 317.15 sq cm

D. 343.44 sq cm

9. A right triangle is inscribed in a circle such that one side of the triangle is the diameter of a circle. If one of the acute angles of the triangle measure 60° and the side opposite that angle has length 15, what is the area of the circle? A. 175.15 s.u.

B. 223.73 s.u.

C. 235.62 s.u.

D. 228.61 s.u.

10. Two triangles have equal bases, the altitude of one triangle is 3 cm more than its base while the altitude of the other is 3 cm less thanits base. Find the length of the longer altitude if the areas of the triangle differ by 21 square centimeters. A. 10 cm

B. 20 cm

C. 14 cm

D. 15 cm

11. If sec 2A= 1/(sin 13A), determine the angle A in degrees. A. 5°

B. 6°

C. 3°

D. 7°

12. Simplify the expression 4cos y sin y[1 - 2(sin y)2]. A. sec 2y

B. cos 2y

C. tan 4y

D. sin 4y

13. If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x. A. 0.265

B. 0.256

C. 0.562

D. 0.625

14. If arctan 2x + arctan 3x = 45°, what is the value of x? A. 1/6

B. 1/3

C. 1/5

D. 1/4

B. A + 2B = 30°

C. A + B = 180°

D. None of these

15. If sin 3A = cos 6B, then, A. A + B = 90°

16. A circle has a radius of 7 cm. What is the arc length contained in a central angle of 135o? A. 21π/4 cm

B. 3π/28 cm

C. 4π/3 cm

D. 3π/4 cm

17. Which of the following cases on oblique triangles is the ambiguous case? A. Two angles and a side given

B. Two sides and an excluded angle given

C. Two sides and an included angle given

D. Three sides given

18. Which of the following sets of numbers is a Pythagorean triple having an area of 60 square units for the associated triangle? A. (6, 8, 10)

B. (3, 4, 5)

C. (8, 15, 17)

D. (9, 40, 41)

C. [0, +∞)

D. [ -1, 0]

19. What is the range of y  sin x A. ( -∞ , +∞)

B. [ -1, 1]

20. In the given equation below solve for x.

x  (tan   cot  )2 sin 2   tan 2  A. 1

B. sin θ

C. 2

D. cos θ

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (ANALYTIC GEOMETRY) Choose the capital letter that corresponds to the correct answer in each of the following. 1. The line segment connecting (x,6) and (9,y) is bisected by point (7,3). Find the value of x and y. A. 5, 0

B. 4, 0

C. 5, 2

D. 4, 1

2. Find the inclination of the line ing through (5,3) and (10,7). A. 33.88°

B. 33.66°

C. 38.66°

D. 36.88°

3. Find the equation of a line with slope 3 and y-intercept of 1. A. 3x - y + 1 = 0

B. 3x + y + 1 = 0

C. 3x - y - 1 = 0

D. 3x + y - 1 = 0

4. What is the equation of the line that es through (-3,5) and is parallel to t line 4x - 2y + 2 = 0? A. 4x - 2y + 22 = 0

B. 4x + 2y -11 = 0

C. 2x + y + 10 = 0

D. 2x - y + 11 = 0

5. What is the distance between the line x + 2y + 8 = 0 and the point (5,-2)? A. 4.20 units

B. 4.44 units

C. 4.02 units

D. 4.22 units

6. Determine the acute angle between the lines y - 3x = 2 and y - 4x = 9. A. 4.39°

B. 5.35°

C. 3.75°

D. 2.53°

7. Find the equation of the circle whose center is at (3,-5) and whose radius is 4. A. x2 + y2 - 6x + 10y +18 = 0

B. x2 + y2 - 6x - 10y +18 =0

C. x2 + y2 + 6x + 10y +18 = 0

D. x2 + y2 + 6x - 10y +18 = 0

8. What is the center of the curve x2 + y2 - 2x - 4y - 31 = 0? A. (-1,-2)

B. (-1,2)

C. (1,-2)

D. (1,2)

9. Compute the length of the latus rectum of the parabola y2 + 8x - 6y + 25 = 0. A. 8

B. 64

C. 16

D. 4

10. The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. the distance from the center to the directrix is: A. 6.05 units

B. 6.53 units

C. 6.61 units

D. 6.22 units

11. Find the eccentricity of the curve 9x2 - 4y2 - 36x + 8y = 4. A. 1.8

B. 1.7

C. 1.9

D. 1.6

12. How far is the center of the ellipse x2/16 + y2/9 = 1 from each of its directrices? A. 7√7/7

B. 9√7/7

C. 5√7/7

D. 16√7/7

13. Determine B such that 3x + 2y - 7 = 0 is perpendicular to 2x - By + 2 = 0. A. 2

B. 3

C. 4

D. 5

14. In Cartesian coordinates, the coordinates of the vertices of quadrilateral are (1,1), (0,8), (4,5), and (-3,4). What is the area? A. 25 s.u.

B. 20 s.u.

C. 18 s.u.

D. 14 s.u.

15. A line with an inclinationof 45° es through (-5/2,-9/2). What is the coordinate of a point on the line if its correspondiing y-coordinate is 6? A. 4

B. 8

C. 7

D. -2

16. The axis of a hyperbola perpendicular to the latera recta is called the A. directrix

B. major axis

C. conjugate axis

D. transverse axis

17. What is the area of the right triangle formed by the line 5x - 3y =15 with the coordinate axes? A. 7.5 s.u.

B. 15 s.u.

C. 20 s.u.

D. 5 s.u.

( x  2) ( y  1)   1? 25 36 2

18. What is the eccentricity of the hyperbola defined by

A.

61 36

B.

61 25

C.

2

61 6

D.

61 5

19. What is the equation of the circle tangent to the line 3 x  4 y  4 and with center (–2, 3)? A.

B.

C.

( x  2)  ( y  3)  4

( x  2)  ( y  3)  4 2

2

2

20. A triangle has vertices at A(2, 4), B(4,

D.

( x  2)  ( y  3)  2 2

2

( x  2) 2  ( y  3) 2  2

-2), and C( -2, 6). What is the length of the median drawn from the

vertex A to the side BC ? A. 3√7 units

B. √37 units

C. √13 units

D. √5 units

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (SOLID MENSURATION) Choose the capital letter that corresponds to the correct answer in each of the following. 1. How many sides has a polygon if the sum of its interior angles equals twice the sum of its exterior angles? A. 7

B. 6

C. 4

D. 5

2. How many diagonals can be drawn from a dodecagon? A. 66

B. 48

C. 54

D. 36

3. A regular octagon is inscribed in a circle whose radius is 12. Find the area of the octagon. A. 521.31 s.u.

B. 351.27 s.u.

C. 407.29 s.u.

D. 351.25 s.u.

4. Find the area of a trapezoid whose median is 32 cm and whose altitude is 6 cm. A. 150 sq cm

B. 142 sq cm

C. 164 sq cm

D. 192 sq cm

5. A rhombus is formed by two radii and two chords of a circle of radius 10 m. What is the area of the rhombus? A. 86.6 sq m

B. 92.1 sq m

C. 143.1 sq m

D. 220.1 sq m

6. Find the volume of a right circular cylinder of radius 4 cm inscribed in a right circular cone of height 14 cm and radius 7 cm. A. 96 cm3

B. 96π cm3

C. 100 cm3

D. 128π cm3

7. The volume of the sphere is increased by how much if its radius is increased by 20 %? A. 32.6 %

B. 33.5 %

C. 44 %

D. 72.8 %

8. A rectangular bin 4 ft long, 3 ft wide, and 2 ft high is solidly packed with bricks whose dimensions are 8 in by 4 in by 2 in. The number of bricks in the bin is: A. 386

B. 956

C. 68

D. 648

9. When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. Find the radius of the ball bearing. A. 0.6 cm

B. 1 cm

C. 1.2 cm

D. 2 cm

10. What is the area of a lune whose angle is 85° on a sphere of radius 30 cm? A. 1670.45 cm2

B. 2670.35 cm2

C. 2570.53 cm2

D. 1670.35 cm2

11. The volume of a truncated prism with an equilateral triangle as its horizontal base is equal to 3600 cm3. The vertical edges at each corner are 4, 6 and 8 cm respectively. Find one side of the base. A. 37.22 cm

B. 15.64 cm

C. 25.34 cm

D. 30.52 cm

12. A polygon is said to be ________ when no side, when extended, will through the interior of the polygon. A. Eccentric

B. Isoperimetric

C. Circumscribed

D. Convex

13. Seven regular hexagons, each with 6-cm sides are arranged so that they share the same sides and the centers of the six hexagons are equidistant from the seventh central hexagon. Determine the ratio of the total area of the hexagons to the total outer perimeter enclosing the hexagon. A. 7/2

B. 7√3/2

C. 3√3/2

D. 3/7

14. The volume of a right prism is 234 cu.m. with an altitude of 15 m. If the base of the prism is an equilateral triangle, find the length of the base edge. A. 5 m

B. 10 m

C. 6 m

D. 8 m

15. A cone and a cylinder have the same height and the same volume. Find the ratio of the radius of the cone to the radius of the cylinder. A. 1/3

B. 1/√3

C. √3

D. 3

16. What is the volume of the frustum of a cone whose upper base is 15 cm in diameter and lower base 10 cm in diameter with an altitude of 25 cm? A. 3018.87 cu.cm.

B. 3108.87 cu.cm.

C. 3180.87cu.cm.

D. 3081.87 cu.cm.

17. The angle of a sector is 30 deg and the diameter is 30 cm, what is the area of the sector? A. 3375 cm2

B. 58.9 cm2

C. 35.81 cm2

D. 235.62 cm2

18. The sides of a cyclic quadrilateral are a=3 cm, b=3 cm, c=4 cm, and d=4 cm. Find the radius of the circle that can be inscribed in it. A. 2.71 cm

B. 3.10 cm

C. 1.51 cm

D. 1.71 cm

19. The diameters of two spheres are in the ratio 2:3. If the sum of their volumes is 1,260 cu.m., the volume of the larger sphere is: A. 927 cu.m.

B. 972 cu.m.

C. 856 cu.m.

D. 865 cu.m.

20. Spherical balls 1.5 cm in diameter are packed in a box measuring 6 cm by 3 cm by 3 cm. If as many balls as possible are packed in the box, how much free space remains in the box? A. 25.73 cc

B. 29.87 cc

C. 20.47 cc

D. 28.41 cc

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (DIFFERENTIAL CALCULUS) Choose the capital letter that corresponds to the correct answer in each of the following. 1. What is the rate of change of the volume of a right circular cylinder with respect to the height if the radius is fixed at 2 cm. A. π cm3/cm

2. Find

d 100 y dx100

B. 2π cm3/cm

C. 3π cm3/cm

D. 4π cm3/cm

B. cos x

C. -sin x

D. -cos x

C. -0.25

D. -0.875

if y = sin x.

A. sin x

3. Find the second derivative of y = x-2 at x = 2. A. 0.96

B. 0.375

4. Determine the derivative of

( x  1)3 x A. B.

3( x  1) ( x  1)3  x x2 3( x  1) 2 ( x  1)3  x x2

C. D.

(3x  1) 2 ( x  1)3  x x2 x  1 ( x  1) 2  x x2

5. Find the limit of the function (x3 – 5x2)/(x3 + 2x2) as x approaches 0. A. 2/5

B. 5/2

C. -5/2

D. -2/5

6. Find the maximum area of a rectangle inscribed in a semicircle of radius 5 inches if its base lies along the diameter of the semicircle. A. 15 sq in

B. 25 sq in

C. 50 sq in

D. 10 sq in

7. Given the function y = x3 - 5x2 - 8x + 3. Determine the maximum point, minimum point and point of inflection. A. (-0.67,5.81), (4,-45), (1.67,-19.65)

B. (0.67,5.81), (-4,45), (-1.67,19.65)

C. (-0.78, 6.74), (4,45), (1.67,19.65)

D. (5.81,0.67), (45,-4), (1.67,-19.65)

8. A painting of height 3 ft hangs on the wall of a museum, with the bottom of the painting 6 ft above the floor. If the eyes of an observer are 5 ft above the floor, how far from the base of the wall should the observer stand to maximize his angle of vision? A. 3 ft

B. 5 ft

C. 2 ft

9. Determine the derivative of the logarithm of (2x – 1). log e A. 2x 1 log 2 B. 2x 1

D. 4 ft

C. D.

2 log e 2x 1 log 2e 2x 1

10. Which of the following functions satisfies the Laplace’s equation

 2u x 2



 2u y 2

A. u  ln( x  y )

C.

u  x 2  2y 2

u  e  x cos y

D.

u  x 3  3xy2

B.

 0?

11. Find the radius of the largest right circular cylinder inscribed in a sphere of radius 5. A. 4.08 units

B. 1.25 units

C. 5.14 units

D. 8.12 units

12. Find the volume of the largest cylinder that can be inscribed in a right circular cone of radius 3 inches and whose height is 10 inches. A. 41.888 cu. in.

B. 24.878 cu. in.

C. 48.178 cu. in.

D. 43.228 cu. in.

13. A man whose height is 1.8 m is walking directly away from a street light at a constant rate of 1.2 m/s. If the street light is 12 m above the ground, find how fast his shadow lengthens. A. 0.51 m/s

B. 0.31 m/s

C. 0.21 m/s

D. 0.71 m/s

14. A boat is being pulled into the dock by a rope that es through a ring on the bow of the boat. The dock is 8 ft higher than the bow ring. How fast is the boat approaching the dock when the length of the rope between the dock and the boat is 10 ft, if the rope is being pulled at the rate of 3 ft per second? A. 3 ft/s

B. 7 ft/s

C. 5 ft/s

D. 9 ft/s

15. Find the radius of curvature of the equation y = 3x3 at (3,1). A. 9844

B. 9944

C. 9484

D. 9448

16. Find the slope of the curve y = 2x3 - 3x2 - x + 5 at (2,-1). A. 11

B. -11

C. 35

D. 64

17. Two particles have positions at time t given by the equations s1 = t3 + 6t2 - 7t and s2 = 2t3 - 3t2. Find their positions when they have the same acceleration. A. s1 =27, s2 =60

B. s1 =60, s2 =27

C. s1 =36, s2 =23

D. s1 =53, s2 =24

18. Divide 120 into two parts so that the product of one and the square of the other is maximum. Find the numbers. A. 60, 60

B. 100, 20

C. 80, 40

D. 50, 70

19. Given the function f(x) = x3 -2x + 1, find the value of the first derivative at x=4, f'(4). A. 48

B. 46

C. 40

D. 43

20. Find the angle that the curve y = 1 - 3x3 cut the x-axis. A. 77°

B. 79°

C. 120°

D. 75°

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (INTEGRAL CALCULUS) Choose the capital letter that corresponds to the correct answer in each of the following.



2 1. Evaluate the indefinite integral:  (1  cos  ) csc  d



A.

cot   csc  C

B.

 cot   csc  C

C.

 cot   csc  C

D.

cot   csc  C

2. Find the area bounded by the curve y  e x the line x = ln 3, and the coordinate axes. A. 2

s.u.

B. e - 1

s.u.

C. 1

s.u.

D. 2e s.u.

3. The region enclosed by the curve y = x3, the y-axis, and the line y = 1 is revolved about the y-axis. What is the volume generated? A. 3π/10

cu. units

B. 3π/5

cu. units

C. π/5

cu. units

D. 7π/10

cu. units

1 3𝑥

4. Integrate: ∫0 ( 𝑥 ) 𝑑𝑥 𝑒

A. B.

1.510 1.051

C. D.

1.105 1.501



5. Evaluate the indefinite integral:  (1  cos  ) csc 2  d A. cot   csc  C C.  cot   csc  C



B.  cot   csc  C D. cot   csc  C

6. Evaluate the integral of sin5x cos3x dx with an upper limit equal to A. B.

1/24 1/36

π /2 and a lower limit of 0.

C. D.

1/48 1/12

C. D.

6.67 6.33

7. Find the area bounded by the curves y2 = 4x and x2 = 4y. A. B.

5.67 5.33

8. Find the moment of inertia of the area bounded by the curve x2 = 4y, the line x – 4 = 0 and the x-axis, with respect to the y-axis. A. 51.2 C. 52.1 B. 25.1 D. 21.5 9. Evaluate the double integral of r sin u dr du, the limits of r is 0 and cos u and the limits of u are 0 and pi. A. 1

B. 1/2

C. 0

D. 1/3

10. The area formed by the boundaries y=1, x=2, and y = e-x is closest to: A. 3.54

B. 1.14

C. 1.59

D. 2.77

11. Find the length of the curve given its parametric equations x = t3 - 3t and y = 3t2 from t = 0 to t = 1. A. 2

B. 3

C. 4

D. 5

12. Find the centroid of the plane area bounded by the equations y2 = 4x, x = 1 and the x-axis on the first quadrant. A. 1/3, 4/3

B. 3/5, 3/4

C. -1, 2/3

D. 3/4, -2/3

13. Determine the surface area generated if the line segment intercepted by the coordinate axes is revolved about the y-axis. Assume the equation of the line to be 3x + 4y -12 = 0. A. 10π sq. units

B. 20πsq. units

C. 15π sq. units

D. 25πsq. units

log x 14. Evaluate:   3 2 dx 

6log 2 x C ln 6 (6 log 2 x ) ln 2 B. C ln 6 A.

C. D.

4

2

B. 4

C. 5

(3log 2 x ) ln 2 C ln 6

(6log2 x ) ln 3  C (6log2 x ) ln 3  C

15. If f is continuous and   f ( x)dx  10 , find   f (2 x)dx  10 . 0 0 A. 0

D. 10

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (COLLEGE PHYSICS 1) Choose the capital letter that corresponds to the correct answer in each of the following. 1. A convenient means of representing physical quantities that have magnitude and direction.

A. scalars

B. vectors

C. tensors

D. none of the above

C. cross product

D. unit scalar

2. It is sometimes called the scalar product.

A. dot product

B. vector product

3. Determine the dot product of the two vectors A = 8i - 6j + 4k and B = 3i +7j + 9k.

A. 12

B. 14

C. 16

D. 18

4. A bus moving at a speed of 20 m/s begins to slow at a rate of 3 m/s each second after seeing a red light at the intersection. Find how far it goes before stopping.

A. 56.7 m

B. 66.7 m

C. 75.6 m

D. 86.4 m

5. A body projected upward from a level ground at an angle of 50° with the horizontal has an initial velocity of 40 m/s. How far from the starting point will it strike?

A. 171 m

B. 161 m

C. 195 m

D. 152 m

6. A type of force acting on a body caused by the friction between the body and the ground.

A. load

B. shear

C. bear

D. mass

7. A horizontal force of 140 N is needed to pull a 60 kg box across the horizontal floor at constant speed. What is the coefficient of friction between the floor and the box?

A. 0.238

B. 0.322

C. 0.342

D. 0.521

8. A 2 kg brick is moving at a speed of 6 m/s. How large a force F is needed to stop the brick in a time of 7 seconds?

A. 1.87 N

B. -1.87 N

C. -1.71 N

D. 1.71 N

9. A 0.5 kg object travelling ast 2 m/s east collides with a 0.3 kg object at 4 m/s west. After collision, the 0.3 kg object is travelling at 2.0 m/s east. What is the magnitude and direction of the velocity of the first object?

A. 1.6 m/s west

B. 1.8 m/s east

C. 2.1 m/s west

D. 1.2 m/s east

10. How long does a bicycle with an acceleration of 0.8 m/s2 take to go from 4 m/s to 12m/s?

A. 6.4 s

B. 10 s

C. 15 s

D. 26 s

11. A car has an acceleration of 1.2 m/s2. If its initial velocity is 10 m/s, the distance the car covers in the first 5 sec after the acceleration begin is

A. 15 m

B. 25 m

C. 35 m

D. 65 m

12. To raise a 20 kg steel beam to a height of 10 m on a bridge being built requires work of

A. 2000 J

B. 1000 J

C. 1960 J

D. 9800 J

13. A ball is thrown vertically upward at 19.6 m/s. The ball comes to a momentary stop in approximately

A. 0.5 s

B. 1.0 s

C. 1.5 s

D. 2.0 s

14. A 250 N box hangs from a rope. If the box is pushed with a horizontal force of 145 N, the angle between the rope and the vertical is approximately

B. 45°

C. 60°

D. 75°

A. 30° 15. A car has wheels of radius 30 cm. It starts from rest and accelerates uniformly to a speed of 15 m/s in a time of 8 seconds. Find the number of rotations one wheel makes in this time.

A. 23 revs

B. 25 revs

C. 32 revs

D. 45 revs

16. Find the gravitational force between an electron and a proton, 1 meter apart.

A. 1.02 x 1057 N

B. 1.02 x 10-57 N

C. 1.02 x 10-67 N

D. 1.02 x 1067 N

17. Which of the following is true about centripetal force? A. B. C. D.

It is directed toward the center of the circular path. It appears to act outward on a body. It is directly proportional to the radius of the circular path. It is inversely proportional to the square of the tangential velocity

18. A 0.50 kg ball with a speed of 20 m/s strikes and sticks to a 70 kg block resting on a frictionless surface. Find the block's velocity after the collision.

A. 1.42 m/s

B. 14.2 m/s

C. 142 m/s

D. 0.142 m/s

19. When a bullet of mass 10 grams strikes a ballistic pendelum of mass 2 kg, the center of gravity of the pendelum is observed to rise a vertical distance of 10 cm. The bullet remains embedded in the pendelum. Calculate the velocity of the bullet.

A. 280 m/s

B. 320 m/s

C. 295 m/s

D. 350 m/s

20. At her highest point, a girl on the swing is 7 ft above the ground, and at her lowest point, she is 3 ft above the ground. What is the maximum velocity?

A. 10 fps

B. 16 fps

C. 12 fps

D. 14 fps

ADAMSON UNIVERSITY PHYSICS SOCIETY OF ADAMSON UNIVERSITY ENGINEERING QUALIFYING EXAM REVIEW MATHEMATICS AREA (COLLEGE PHYSICS 2) Choose the capital letter that corresponds to the correct answer in each of the following.

1. A certain capacitor having a capacitance of 12 microfarad is charged to a potential difference of 100V. What is the charge in the capacitor?

A. 1.20x 10-7 C

B. 12.0x10-7 C

C. 1.20x10-4 C

D. 12.0x10-4 C

2. A charge of + 1 x 10-6C is placed at each corner of a cube 10 cm on one side. Find the electric field at the center of the cube?

A. 9x105 N/C

B. 4.5x105 N/C

C. 3.6x106 N/C

3. A parallel plate capacitor has a capacitance plates are 1.0mm apart. What is the area of the plates?

A. 11.30 m2

B. 113.0 m2

C. 1.130 m2

4. A 4 Ώ resistor is connected in series resistors. The current through the 4 Ώ the 3 Ώ resistor?

A. 6 A

B. 8 A

D. Zero of

10

microFarad

the

D. 1130 m2

with the parallel assembly of 3 resistor is 12 A. What is the

C. 4 A

and

Ώ and 6 Ώ current through

D. 10 A

5. A certain wire draws a current of 5A when connected to a 30 V source. What is the current drawn by a similar wire that is doubled in diameter?

B. 6 A

C. 45 A

D. 24 A

A. 20 A 6. Given: R1=10Ώ, R2=3Ώ, R3=6Ώ. Which connection scheme can best be substituted in the absence of a 12Ώ resistor. A. B. C. D.

R1 in series with the parallel combination of R2 and R3 R2 in series with the parallel combination of R1 and R3 R3 in series with the parallel combination of R1 and R2 All resistors in parallel

7. One gram of stream of 100°C causes a more serious burn thhan one gram of water at 100°C because the stream A. B. C. D.

is less dense strikes the skin with greater force has a higher specific heat capacity contains more internal energy

8. What is the power required to transfer 97000 coulombs of charge through the potential rise of 50 V in one hour?

A. 1.3 kW

B. 0.9 kW

C. 0.5 kW

D. 2.8 kW

9. A ray of light is incident on a plane surface separating two transparent substances of indeces 1.60 and 1.40. The angle of incidence is 30 deg and the ray originates in the medium of higher index. Compute the angle of refraction.

A. 30°

B. 45°

C. 25°

D. 35°

10. A small blaked aoli copper sphere of radius 2 cm is placed in an evacuated enclosure whose walls are kept at 100 deg Celsius. At what rate must energy be supplied to the sphere to keep its temperature constant at 127 deg Celsius?

A. 1.76 W

B. 2.54 W

C. 1.56 W

D. 2.45 W

C. magnetic domains

D. moving electric charges

11. All magnetic fields originate in

A. stationary charged particles

B. permanent magnets

12. How much oil at 200 deg Celsius must be added to 50 g of the same oil at 20 deg Celsius to heat it to 70 deg Celsius?

A. 12.39 g

B. 29.12 g

C. 19.23 g

D. 23.91 g

13. If a conductor's cross-sectional area is doubled and its length is halved, the value of its resistance will

A. double

B. quadruple

C. decrease by a factor of two

D. decrease by a factor of four

14. A 100 meter long wire with a cross-sectional area of 10-3 m2 has a resistance of 10 Ώ. Determine the resistivity of the wire.

A. 10-2 Ώ-m

B. 10-3 Ώ-m

C. 10-4 Ώ-m

D. 10-5 Ώ-m

15. Determine the force between two 4 microcoulomb charges separated by 0.1 m in air.

A. 1.44 N

B. 14.4 N

C. 144 N

D. 1440 N

16. A 33 kΏ resistor is connected in series with a parallel combination made up of a 56 kΏ resistor and a 7.8 kΏ resistor. What is the total resistance of these three resistors?

A. 63.77 kΏ

B. 49.07 kΏ

C. 95.81 kΏ

D. 39.85kΏ

17. Cobalt is an example of ______________ material.

A. diamagnetic

B. ferromagnetic

C. paramagnetic

D. magnetic

18. What lens is commonly used to correct nearsightedness?

A. magnifying lens

B. convergent lens

C. divergent lens

D. microscopic lens

19. What refers to the defect in lenses which causes unequal refraction of the different colors?

A. chromatic diffraction

B. chromatic polarization

C. chromatic aberration

D. chromatic dispersion

20. A converging lens of focal length 20 cm is placed 37 cm in front of a screen. At what distance that the object be placed so that its image appears on the screen?

A. 43.5 cm

B. 35.7 cm

C. 27.6 cm

D. 50.7 cm