8/13/2019 Diag Exam

1/9

Diagnostic Test - Mathematics

1. The altitude of a cone is equal to half the diameter of the sphere circumscribed about it. How manytimes is the volume of the sphere greater than that of the cones?

a.

b. !c. "

d. #

!. Determine the volume of the spherical segment given its altitude equal to " cm and the radius of thebase circle equal to $ cm.

a. !%!p&' cm'

b. '"!p&' cm'

c. '"!p&' cm

'

d. "1(p&' cm'

'. ) ball whose radius is equal to '* cm is provided with a cylindrical hole bored along its diameter.+ompute the volume of the remaining portion if the radius of the cylindrical hole is equal to 1$ cm.

a. !*, %$!p cm'

b. 1%, '!%p cm'

c. 1$, "'!p cm'

d. !1, 1%'p cm'

". The edge of a cube is equal to a. ind the radius of the circumscribed sphere.

a. &!

b. !a

c. a/'&!

d. "/!a

%. The perimeter of a rectangle is !!. 0f one of the rectangles is doubled and the other tripled, theperimeter would be '! more than the perimeter of the original rectangle. hat are the sides of therectangle?

a. ( and %

b. $ and 2

c. 1* and

d. 1! and 11

(. if a polygon has %" diagonals, then it must have,

a. 1! sides

8/13/2019 Diag Exam

2/9

b. 1* sides

c. 11 sides

d. 1' sides

2. ) trench is constructed so that its cross section is a trape3oid the area of which is !1 sq.ft. if theshorter base is ! times its height and the longer base is % ft longer than its height. ind the length of the

shorter base.a. '

b. "

c. %

d. (

$. if the acute angles of a right triangle are in the ratio 14!, then the number of degrees in the smallangles is4

a. '*

b. !*c. "%

d. *

. The length of a wire fence around a circular flowerbed is 1*p feet. The area of the flowerbed in sq.ftis

a. 1**p

b. %*p

c. !%p

d. %p

1*. The perimeter of rectangle is !$m and its diagonal is 1* m. find the area of the rectangle.

a. "$ sq.m

b. '$ sq.m

c. 1* sq.m

d. !$ sq.m

11. ind the distance between 5", ', !6 and 5-', -!, 16.

a. '/'

b. "/'

c. %/'

d. (/'

1!. ind the distance from the origin to 5", -', !6.

8/13/2019 Diag Exam

3/9

a. /!

b. /!2

c. /1'

d. /'1

1'. ind the radius of the sphere 7!8y

!83

!-!78(y8!3-1" 9 *.

a. a. "

b. %

c. (

d. '

1". The triangle with vertices 5', %, -"6, 5-1, 1, !6 and 5-%, -%, -!6 is

a. right

b. isosceles

c. equilaterald. scalene

1%. ind the direction numbers of the line through :15-', !, "6 and :!5!, %, -!6.

a. ;%, ', (

b. %, -', (

c. %, ', -(

d. %, ', (

1(. ind the angle between the line