egular plygn has five mre sides than regular plygn egular plygn has half the number f sides as regular plygn The perimeter f plygn is twenty mre than the perimeter f regular plygn, when bth are in centimeters A: has ne exterir angle that is 8 degrees, and ne side length f 8 cm The perimeter f in cm is equal t a 0 Give the value f a in cm B: Give the degree measure f ne interir angle f plygn c 0 C: lygn has ne central angle f degree measure Give the value f c 5 (Nte: The central angle is an acute angle frmed by tw cnsecutive radii f the plygn) D: lygn has ne side with length 0 cm, and plygn has apthem length cm Give the area in square cm f plygn March eginal 08 egular plygn has five mre sides than regular plygn egular plygn has half the number f sides as regular plygn The perimeter f plygn is twenty mre than the perimeter f regular plygn, when bth are in centimeters A: has ne exterir angle that is 8 degrees, and ne side length f 8 cm The perimeter f in cm is equal t a 0 Give the value f a in cm B: Give the degree measure f ne interir angle f plygn c 0 C: lygn has ne central angle f degree measure Give the value f c 5 (Nte: The central angle is an acute angle frmed by tw cnsecutive radii f the plygn) D: lygn has ne side with length 0 cm, and plygn has apthem length cm Give the area in square cm f plygn
een in the picture: T VW, with, T, U cllinear, and V, W and N cllinear m = (8x + ) = (0 0) m UTW y = ( + + 9) m TWN x y (8x + ) T U (0 y 0) A = the value f x (x + y + 9) B = the value f y V W N C = m T m T in degrees D = WN if the area f VN is five times the area f WV WV March eginal 08 een in the picture: T VW, with, T, U cllinear, and V, W and N cllinear m = (8x + ) = (0 0) m UTW y = ( + + 9) m TWN x y (8x + ) T U (0 y 0) A = the value f x (x + y + 9) B = the value f y V W N C = m T m T in degrees D = WN if the area f VN is five times the area f WV WV
A right circular cne has base B shwn, with radius 6 and height 5 Call this the larger cne The smaller right circular cne shwn has base B, which is parallel t B The tw bases are a distance 5 apart A = the lateral area f the larger cne in square inches B = the lateral area f the smaller cne in square inches C = the vlume f the larger cne in cubic inches D = the vlume f the part f the larger cne that is belw the smaller cne, in cubic inches (That is, the vlume f the frustum f the cne, that has parallel bases B and B ) ut yur answer fr part D in fractin frm B B 0 5 March eginal 08 A right circular cne has base B shwn, with radius 6 and height 5 Call this the larger cne The smaller right circular cne shwn has base B, which is parallel t B The tw bases are a distance 5 apart A = the lateral area f the larger cne in square inches B = the lateral area f the smaller cne in square inches C = the vlume f the larger cne in cubic inches D = the vlume f the part f the larger cne that is belw the smaller cne, in cubic inches (That is, the vlume f the frustum f the cne, that has parallel bases B and B ) ut yur answer fr part D in fractin frm B B 0 5
U is the altitude t the hyptenuse f right GU G, U, and are cllinear; U, and are cllinear GU=U G= U= G A = the length f U nt drawn t scale B: If U= ( U ) then give the value f U C = the length f D = a + b + c if the perimeter f quadrilateral G is a + b c fr c a psitive prime number, and a and b psitive integers March eginal 08 U is the altitude t the hyptenuse f right GU G, U, and are cllinear; U, and are cllinear GU=U G= U= A = the length f G U nt drawn t scale B: If U= ( U ) then give the value f U C = the length f D = a + b + c if the perimeter f quadrilateral G is a + b c fr c a psitive prime number, and a and b psitive integers
5 is issceles with ==0 The length f 0 0 is an integer fr all parts belw A = the number f distinct pssible triangles with the infrmatin abve B = the number f distinct pssible triangles with the infrmatin abve, if altitude frm t side is als an integer C = the sum f the areas f all distinct pssible triangles with the infrmatin abve, and with the altitude frm t side als an integer D = p + q + r if the area f is p q fr p, q r and r are relatively prime and has the greatest pssible integer length March eginal 08 5 is issceles with ==0 The length f is an integer fr all parts belw 0 0 A = the number f distinct pssible triangles with the infrmatin abve B = the number f distinct pssible triangles with the infrmatin abve, if altitude frm t side is als an integer C = the sum f the areas f all distinct pssible triangles with the infrmatin abve, and with the altitude frm t side als an integer D = p + q + r if the area f is p q fr p, q r and r are relatively prime and has the greatest pssible integer length
6 Cnsider the statements belw : A triangle with sides cm, cm, 5 cm has ne angle that is 0 degrees : A rhmbus with perimeter 60 cm and ne diagnal with length 8 cm has area 08 sq cm : A sphere with vlume 6π cubic units has surface area 6π square units : A triangle can have an area f k square cm, and perimeter f p cm, fr k < p A = the number f statements, frm,, and abve, which are true B: list the statements frm,, and abve which are true C: Give the greatest psitive integer length that an equilateral triangle s side can have t als have an area less than 00 D: Give the least psitive integer length that a regular hexagn s side can have s that its area is greater than 00 March eginal 08 6 Cnsider the statements belw : A triangle with sides cm, cm, 5 cm has ne angle that is 0 degrees : A rhmbus with perimeter 60 cm and ne diagnal with length 8 cm has area 08 sq cm : A sphere with vlume 6π cubic units has surface area 6π square units : A triangle can have an area f k square cm, and perimeter f p cm, fr k < p A = the number f statements, frm,, and abve, which are true B: list the statements frm,, and abve which are true C: Give the greatest psitive integer length that an equilateral triangle s side can have t als have an area less than 00 D: Give the least psitive integer length that a regular hexagn s side can have s that its area is greater than 00
7 Tw buildings are 00 meters apart L Bth buildings are 80 meters tall 80 m 50 m W A wire is 50 m abve grund between the tw buildings, as shwn AT NOON: A tightrpe walker at pint W is 0 m frm pint The walker at W is mving tward at 05 m per minute A spt light at L causes the tip f the walker s shadw, G, t mve alng the grund T G U A: At nn, tell hw far pint G n the grund is frm pint T at the base f the left building, in meters Write yur answer in fractin frm B: At :0 M tell hw far G is, frm T at the base f the left building, in meters C: At :00 M Tell hw far abve grund pint G (the tip f the shadw) is, n the rightmst building, in meters D: At what time (M) is the pint G exactly at pint U, the base f the rightmst building? March eginal 08 7 Tw buildings are 00 meters apart L Bth buildings are 80 meters tall 80 m 50 m W A wire is 50 m abve grund between the tw buildings, as shwn AT NOON: A tightrpe walker at pint W is 0 m frm pint The walker at W is mving tward at 05 m per minute A spt light at L causes the tip f the walker s shadw, G, t mve alng the grund T G U A: At nn, tell hw far pint G n the grund is frm pint T at the base f the left building, in meters Write yur answer in fractin frm B: At :0 M tell hw far G is, frm T at the base f the left building, in meters C: At :00 M Tell hw far abve grund pint G (the tip f the shadw) is, n the rightmst building, in meters D: At what time (M) is the pint G exactly at pint U, the base f the rightmst building?
8 H, J and M are midpints f the sides f GNL as shwn GM, NH and LJ intersect at K G GH = 5, HN= GN=, KM=55 LK= 7, LM=6 H 5 K J A = the sum f the lengths 7 f the three medians f GNL 55 B = the perimeter f KLN in fractin frm C = the area f GLN L 6 M N D = the perimeter f quadrilateral GJKH, in fractin frm 8 H, J and M are midpints f the sides f GNL as shwn GM, NH and LJ intersect at K March eginal 08 G GH = 5, HN= GN=, KM=55 LK= 7, LM=6 H 5 K J A = the sum f the lengths 7 f the three medians f GNL 55 B = the perimeter f KLN in fractin frm C = the area f GLN L 6 M N D = the perimeter f quadrilateral GJKH, in fractin frm
9 ~ UT,, and T are cllinear The diagram is nt drawn t scale T, and intersects U at pint X =6 ==UT= 6 X U A = the length f T, written as a fractin T B = sin( U) + cs( ) + tanu, written as a fractin C = the distance that X is frm (the height frm X f the triangle X) D = the length f side U, in UT, in fractin frm March eginal 08 9 ~ UT,, and T are cllinear The diagram is nt drawn t scale T, and intersects U at pint X =6 ==UT= 6 X U A = the length f T, written as a fractin T B = sin( U) + cs( ) + tanu, written as a fractin C = the distance that X is frm (the height frm X f the triangle X) D = the length f side U, in UT, in fractin frm
0 ight rectangular pyramid is similar t right rectangular pyramid The base f has dimensins cm by 6 cm The base f has perimeter 0 cm A = the length f ne diagnal f the base f, in cm B = the vlume in cubic cm f if the vlume f in cubic cm is 80 C = the altitude f pyramid if the vlume f pyramid in cubic cm is 80 D= the ttal surface area f in square cm, if the surface area f is 70 sq cm March eginal 08 0 ight rectangular pyramid is similar t right rectangular pyramid The base f has dimensins cm by 6 cm The base f has perimeter 0 cm A = the length f ne diagnal f the base f, in cm B = the vlume in cubic cm f if the vlume f in cubic cm is 80 C = the altitude f pyramid if the vlume f pyramid in cubic cm is 80 D= the ttal surface area f in square cm, if the surface area f is 70 sq cm
Chrds,, and T are shwn in circle W T intersects at U Arcs, and T have degree measures 80, and 70 respectively 80 Circle W has radius 6 cm (and center W) A = m U U B = m if arc has half the degree measure f arc T C = m + n if the length f chrd is D = m U + m UT msin( n ) T 70 March eginal 08 Chrds,, and T are shwn in circle W T intersects at U Arcs, and T have degree measures 80, and 70 respectively 80 Circle W has radius 6 cm (and center W) A = m U U B = m if arc has half the degree measure f arc T C = m + n if the length f chrd is D = m U + m UT msin( n ) T 70
hwn are three cncentric circles with center The circles have radii, and 8, althugh the diagram is nt drawn t scale is a chrd f the largest circle, and is tangent t the secnd largest (medium) circle T is a chrd f the medium circle, and tangent t the smallest circle is parallel t T T A = the length f B = the length f T C = the distance between and T at their respective midpints D = the area f the segment f the circle (shaded) bunded by and minr arc March eginal 08 hwn are three cncentric circles with center The circles have radii, and 8, althugh the diagram is nt drawn t scale is a chrd f the largest circle, and is tangent t the secnd largest (medium) circle T is a chrd f the medium circle, and tangent t the smallest circle is parallel t T T A = the length f B = the length f T C = the distance between and T at their respective midpints D = the area f the segment f the circle (shaded) bunded by and minr arc
Circles and are tangent t at pints and respectively = and =6 The circles are tangent t each ther A = the length f B = the length f C = the length f D = the area f quadrilateral March eginal 08 Circles and are tangent t at pints and respectively = and =6 The circles are tangent t each ther A = the length f B = the length f C = the length f D = the area f quadrilateral
T is a right triangle and tw sides have lengths 9 and The tw pssible lengths f the third side are A and B, fr A > B Fr parts A and B, give the values f A and B XYZ is a right triangle and has ne side length All sides f XYZ have integer lengths, and the hyptenuse length is less than 0 C = the perimeter f XYZ if the hyptenuse has the least pssible length D = the perimeter f XYZ if the hyptenuse has the greatest pssible length March eginal 08 T is a right triangle and tw sides have lengths 9 and The tw pssible lengths f the third side are A and B, fr A > B Fr parts A and B, give the values f A and B XYZ is a right triangle and has ne side length All sides f XYZ have integer lengths, and the hyptenuse length is less than 0 C = the perimeter f XYZ if the hyptenuse has the least pssible length D = the perimeter f XYZ if the hyptenuse has the greatest pssible length
5 A: Give the vlume in cubic inches f the sphere which has surface area 50π sq inches B: Give the perimeter in inches f a regular hexagn with area 5 square inches C: Give the area in square inches f an equilateral triangle with perimeter 9 inches D: Give the value f x if the angle measures f the angles f a pentagn are 0, ( x), ( x ), ( x + 0) and x March eginal 08 5 A: Give the vlume in cubic inches f the sphere which has surface area 50π sq inches B: Give the perimeter in inches f a regular hexagn with area 5 square inches C: Give the area in square inches f an equilateral triangle with perimeter 9 inches D: Give the value f x if the angle measures f the angles f a pentagn are 0, ( x), ( x ), ( x + 0) and x