Math 113 Sample Exam III: Systems of Linear Equations & Geometry = 2.) 4.) 6.) 8.) 10.)

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1 1 Math 11 Sample Eam III: Sstems of Linear Equations & Geometr Section I Sstem of Linear Equations Solve each sstem of linear equations using substitution 1.) 9 1.) 1.) 5 0 s r s r.) 1 Solve each sstem of linear equations using elimination 5.) ) ) ) 6 5 Solve the sstem of linear equations b an method 9.) 0 0 z z z 10.) 1 z z z

2 Determine if the following sstems of linear equations have (a.) one solution. (b.) infinitel man solutions, or (c.) no solutions 11.) ) ) Section II Geometr 1.) Find the complement of a angle.) Find the supplement of a 5 angle.) Given <AOC 15 and <BOC 60, find the measure of <AOB. A B C O

3 .) Given that <MOZ is a right angle, let <MOY and <YOZ 0 find the eact measure of <YOZ. X M Y O Z 5.) Find ) Given l 1 is parallel to l, <1 and <6 60, find. 1 l l 7

4 7.) Given l 1 is parallel to l, < and <7 0, find. 1 l l Name one pair of Vertical Angles Corresponding Angles Alternate Interior Angles Alternate Eterior Angles.) Given < 55, find <a and <b a b

5 9.) Classif the triangles as acute, obtuse, or right. a.) b.) c.) 10.) Find the perimeter and area of the following figures. All measurements are in centimeters. a.) Rectangle ABCD b.) Rhombus LNMP A B L N c.) C 1 D P M c.) Triangle ABC d.) Trapezoid JACK ) What is the perimeter of a. A regular pentagon with a side inches b. A regular heagon with a side 5 inches 1 c. A regular decagon with a side inches 5

6 1.) What is the circumference and area of a circle with (use eact values) a. A radius.5 inches b. A radius 10 cm c. A diameter inches d. A diameter mm 1.) A field is shaped like a parallelogram with a base 5 d. and a side 1 d. what is the required ards of fencing to surround the field? 1.) If carpeting costs $5/d, how much will it cost to carpet the room shown below (hint 9ft 1 d ) : 10ft 0ft 15ft 5ft 6

7 15.) What is the area of the shade section if the inner circle has a radius of 10 inches and the outer circle has a radius of inches? (use π.1, round to nearest hundredth) 16.) A window has the shape shown below, what is the perimeter and area of the window? (use π.1, round to nearest hundredth) ft ft 17.) Given triangle ABC and triangle DEF are similar triangles, find the perimeter of triangle DEF. B E 1m m m A 16m C D F 7

8 1.) In the figure below MO is parallel to LP, MO measures in., LP measures 6 in., and LN measures 1 in. Find the length of ML. N M O L P 19.) In the figure below NK is parallel to SE, SN 6ft, KE ft, and NA 6 ft., find the length of AE A N K S E

9 0.) In the figure below AE and ST intersect at N, AS 9mm, SN 1mm, NT mm, and AE 5mm, find NE A T S N E 1.) Given triangle ABC and triangle XYZ do the conditions <A <X, <B <Y, and AB XY guarantee that triangle ABC and triangle XYZ are congruent? If the are congruent b what theorem are the congruent?.) Given triangle ABC and triangle XYZ do the conditions BC XY, <A <Z, and AC ZY guarantee that triangle ABC and triangle XYZ are congruent? If the are congruent b what theorem are the congruent? 9

10 .) The triangle shown below is a right triangle, find. 6.) The triangle shown below is a right triangle, find ) If I travel 9 miles East and then 9 miles South, how far am I from m starting point? 6.) Find the volume of a rectangular solid that has a length of.5m, a width of m, and a height of 1.5m. 7.) What is the length of a side of a cube that has a volume of 51cm? 10

11 .) Find the volume of a sphere that has a radius of 6 inches. (use π.1, round to nearest hundredth) 9.) The height of a cube is cm. The diameter of the cone is 16cm. Find the volume of the cone. Round to the nearest hundredth of a cubic centimeter. 0.) A storage tank in the shape of a clinder is ¾ full of eggnog. The height of the storage tank is 5m and the diameter is m. Find the volume of the storage tank that IS NOT FILLED with eggnog. (use π.1, round to nearest hundredth) 1.) The width of a rectangular solid is 5 in., the length is 0 in., and the height is 10 in. What is the surface area of the solid? 11

12 .) The diameter of a ball is 16ft. A can of paint will cover 00 ft of surface, how man cans of paint do I need to completel cover the ball in paint? (use π.1, round to nearest hundredth).) The side of the base of a regular square pramid is 1mm, and the pramid s slant height is 15 mm, find the surface area..) If the surface area of a cube is 9 in what is the length of a side of the cube? 5.) A can of soup has a height of 5 inches and a diameter of inches, what is the surface area of the LABEL for the can of soup? (use π.1, round to nearest hundredth) 1