1. The position at time t in seconds, of an object moving along a line is given by s(t) = 3 t^3 - 40.5 t^2 + 162 t for t belongs to [0, 8]. When is the object stationary?

t = 6 & t = 3 seconds

t = 6 & t = 4 seconds

t = 3 & t = 4 seconds

None of the above

2. What are the Critical number (s ) of the function f(x) = - 5x^2 + 20 x + 2?

3

2

4

1

3. What are the Critical number (s ) of the function f(x) = 2 x^3 - 24 x

3 & -3

2 & -2

4 & -4

1 & -1

4. What are the Critical number (s ) of the function f(x) = 6 x^2 + 16 x - 40

a) -1 /3

c -2 / 3

c) -1

d) - 4 /3

5. Where is the function f(x) = x / ( x -2) , undefined?

a) 2

b) 0

c) - 2

d)None

6. What are the interval (s ) of increase or decrease of the function f(x) = - 5x^2 + 20 x + 2?

Increase when x > 2 & Decrease when x < 2

Increase when x > 3 & Decrease when x < 3

Increase when x < 2 & Decrease when x > 2

None

7. What are he intervals of increase and decrease of the function f(x) = 2 x^3 - 24 x ?

Increase when x< -2 & x > 2 ; Decrease when x > -2 & x< 2

Decrease when x< -2 & x > 2 ; Increase when x > -2 & x< 2

Increase when x< 2 & x > -2 ; Decrease when x > 2 & x< -2

None of the above

8. What are he intervals of increase and decrease of the function f(x) = 6 x^2 + 16 x - 40 ?

Increase when x < 4/3 & Decrease when x > 4/3

Increase when x < - 4/3 & Decrease when x > - 4/3

Increase when x > - 4/3 & Decrease when x < - 4/3

None of the above

9. What are the horizontal, vertical or oblique Asymptotes of the function f(x) = 8 / ( x^2 - 9)

HA; y = 1, VA's; x = 3 ; x = -3 & OA - None

HA; y =0, VA's; x = 3 ; x = -3 & OA - None

HA; y = 1, VA's; x = 3 ; x = -3 & OA; y = x - 3

None of the above

10. What is the point of intersection between the line L: (x, y, z) = (-1, 3, 4) + p(6, 1, -2) & plane P: x + 2 y - z + 29 = 0

( 12, 9, 10)

(-19, 0, 10)

Infinite points of intersections

11. What is the point of intersection between the lines? : L1: vector r = (3,7,2) + m( 1, -6, 0) ; m belongs to R &L2: vector r = (-3, 2, 8) + s( 7,-1, -6) ; s belongs to R

No POI - Lines are skew

(4, 1, 2)

Infinite solutions - Lines are parallel & coincident

No POI - Lines are parallel & distinct

12. State whether the two planes intersect, if they do, specify if their intersection is a line or plane? p1: x + y + z = 1 ; p2: 2 x + 2y + 2 z = 2

Yes ; plane

No

Yes ; line

13. State whether the two planes intersect, if they do, specify if their intersection is a line or plane? p1: x - y + 2z - 2 = 0 ; p2: x + y + 2 z + 2 = 0

Yes ; plane

No

Yes ; line

14. What is the distance between the point P(-1, 1, 6) to the line with the equation (x,y,z) = (1, 2, -1) + s( 0, 1, 1) ? ; s belongs to R

5

6

4

7

15. What is the distance from S(-1, 2, -4) to the plane with the equation 8 x - 4 y + 8 z + 3 = 0?

3.75

4.75

5.75

6.75

16. Skew lines are those lines which are not parallel and do not have any POI.

True

False

17. Two planes intersect in a line when ratio of their normals A, B, C is proportional.

True

False

18. Two planes intersect in a line if ration of their normals A, B, C are not proportional.

True

False