Volume/Surface Area
Locus
Transformations
Circles
Miscellaneous
100
The volume of a rectangular prism is 400 cm3, and the area of the base is 25 cm. What is the altitude of the prism?
V = Bh ; 400 = 25h ; Answer: 400/25 = 16 cm
100
What is the equation of the locus of points 4 units from the origin?
x^2 + y^2 = 16
100
What is the image of point P( 3, -4 ) after R90?
Rule: (x, y ) --> ( -y, x ); Answer: ( 4, 3 )
100
Two chords intersect at point P. The chords intercept arcs of 60 and 100 degrees. What is the measure of acute angle P?
( 60 + 100 ) / 2 = 80 degrees
100
What is the name of a statement that is logically equivalent to the original if -then statement?
contrapositive
200
A sphere has a radius of 12 inches. What is the total surface area of the sphere in terms of pi?
4 x pi x 12^2 = 576 pi in^2
200
What is the total number of points that are equidistant from two parallel lines and also equidistant from two points on one of the lines?
1 point. ( The intersection of the perpendicular bisector of the line segment containing the points and a line midway between the parallel lines. )
200
P'( 3, -6 ) is the image of P after a D3. What are the coordinates of P, the pre-image of P'?
Working backwards the opposite of multiplying by 3, divide each coordinate by 3. Answer: ( 1, -2 )
200
Point P lies outside the circle. Two tangent lines from point P intercept a major arc of 260 degrees. What is the measure of angle P?
(260 - 100) / 2 = 80 degrees
200
In triangle ABC, the exterior angle of a triangle at angle C is 6x. If angle A is represented by x, and angle B is represented by 100, find the measure of interior angle C.
6x = x + 100; 5x = 100; x = 20; Ext angle at C = 6(20) = 120; Answer: Angle C = 60 degrees
300
A cone has a slant height of 10 meters, and a diameter that is twice the slant height. What is the lateral area of the cone to the nearest hundredth?
LA = Pi x r x l = Pi x 10 x 10 = 314.16 meters^2
300
Describe fully the locus of points equidistant from the x & y axis.
A pair of angle bisectors that bisect the angles formed by the x & y axis. ( the line y = x and the line y = -x )
300
Name an opposite isometry.
Reflection or Glide Reflection. Their orientation changes.
300
A circle has an inscribed angle of 32 degrees. What is the measure of its intercepted arc?
32 x 2 = 64 degrees
300
The measure of an exterior angle of a regular polygon is 24 degrees. How many sides does the polygon have?
360 total for the sum of the exterior angles of ANY polygon. 360 / 24 = 15 equal exterior angles --> 15 sides.
400
The lateral area of a cylinder is 188.5 cm^2. The altitude of the cylinder is 6 cm. What is the length of the radius to the nearest whole number?
LA = 2(pi)rh ; 188.5 = 2(pi)(r)(6) ; Answer: 188.5 / ( 2 x pi x 6 ) = 5 cm
400
At Holland Town Park, a statue and a tree are 20 feet apart. If a prize is buried 15 feet from the statue, and is equidistant from both the tree and the statue, how many locations could the prize be buried in?
Two locations. ( The intersection of a perpendicular bisector of the tree and statue, and a circle with radius 15 )
400
Name a transformation that is not an isometry.
A dilation. ( Isometries preserve distance. )
400
A secant from point P has a length of 12 cm. The part of the secant that lies outside the circle has a length of 5 cm. In simplest radical form, what is the length of the tangent line drawn from point P?
Whole secant x outside piece = tangent^2. 12 x 5 = x^2. 60 = x^2. x = sqrt 60. x = 2 radical 15
400
The median of a trapezoid is 12 and the larger base is 18. What is the length of the shorter base?
A median of a trapezoid will have a length equal to 1/2( sum of both parallel bases ). 12 = 1/2( 18 + n ); 24 = 18 + n; Answer: n = 6
500
A sphere's great circle has a diameter of 25 feet. What is the volume of the sphere to the nearest cubic foot?
V = 4/3(pi)r^3 ; V = 4/3(pi)(12.5)^3 ; V = 8181 cubic feet
500
In the coordinate plane, point A(3,5 ) and point B( 7, 5 ). How many points are equidistant from both A & B and 5 units from the y-axis?
an infinite number of points on the line x = 5.
500
The coordinates of point A are (2,5 ). Using the composition T(x-4,y+2) o r y=x , what are the coordinates of A', the image of A?
(x, y ) --> ( y, x ) for r y= x ( 2, 5 ) --> ( 5, 2 ) ......... ( x, y ) --> ( x -4, y + 2 ) for T(x-4, y+2 ) ............... (5,2 ) --> ( 5-4, 2+2 ) = ( 1,4 ) Answer: (1,4 )
500
Chords AB and CD intersect at point P. AP = 5, DP = 2, and BP = 6. Find the measure of CP.
CP = 15 AP x BP = CP x DP. 5 x 6 = n x 2. 30 = 2n Answer: n = 15
500
Right triangle ABC with right angle at B. Altitude BD is drawn to the hypotenuse and measures 9 cm. AD = 27, find the measure of CD.
Proportion: 9:x = 27:9; 81 = 27x; Answer: x = 3
M
e
n
u