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Unformatted text preview: Name: Mathematics 131 Final Exam Instructor: Noah Kieserman December 17, 2007 There are twenty (20) problems and ten (10) pages, including this one. Cross out
any incorrect work and give only one answer. Bahati Njema  Good Luck! H
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cm 1. (3.2 #9) In AABC, AD bisects [BAG Find ZACB. 2. (2.3 #10, 11) In general, how many lines of symmetry do each of the following ﬁgures have? (a) isosceles triangle
(b) kite (c) rectangle (d) parallelogram
(e) square (f) circle (g) In general, does a parallelogram have rotational symmetry of order 2? of order 4? 3. (3.2 #3) Write a Teacher’s Solution to the following problem. In the ﬁgure, AB ED. Calculate
a: + y + z. (Hint:Draw a line through C parallel to BA.) 4. (4.1 #6) Give an Elementary Proof. Exposition counts  be clear. In the ﬁgure a = b. Prove that c i d. Q Y 5. (4.1 #8) Give an Elementary Proof. Exposition counts — be clear. In the ﬁgure, prove that d = a + b + c. 6. (7.1 #5 — #7) The quadrilateral DEFG is a rectangle. How many similar triangles can you ﬁnd in the
ﬁgure? Name them all. ~ 8. (7.2 #6 ~ #2) A ground plan of a house is drawn on a scale of 1 cm to 2 m. Express the scale of the
plan in the form 1171/, in particular without any reference to units. Find also the length and breadth of
the plan of a room, 2.5 In by 1.5 m. 9. (Worksheet #20, Give three different ways of ﬁnding the unknown side. 10. (Worksheet #19, #3e) The trigonometric functions sin 9, cos 0, and tan 0 are deﬁned in terms of the sides of a triangle. The angle 9 may belong to triangles of many different sizes. Why does it not matter
what size triangle we’re talking about? 11. (Worksheet #19, #3defg) (a) ‘Give an equation describing a line that passes through (—1,—1) and is perpendicular to the line
y = ~.5w + 1. ‘ (b) Give an equation describing a line whose slope is zero. (0) Give an equation describing the line through the points (3,2) and (3,4). (d) Are there any lines in the plane that can’t be described by an equation? 12. (Worksheet #19, #5a) Give a Teacher’s Solution to the following problem. Let A 2‘ (3,1), B '= (1,2),
and C = (2,4). Is AABC' aright triangle? 13. (a) (8.2 #7) A machine part is made by bending a metal strip into a circular arc according to the
design below. How many such parts can be made from a metal strip 2 meters long? Leave your
answer in terms of the symbol 7r. 59¢"?
<1): 80° (b) (8.3 #6) Find the area of the shaded region between two concentric circles with radii 4 cm and 6
cm. Leave your answer in terms of the symbol 7r. Which is larger, the area of the shaded region,
or the area of the smaller circle? 14. (6.3 #ﬁace) Find the following: S 6ﬁ. Q (a) RS (b) QT
(c) The area of ARST. 15. (a) (8.1 #9) In the ﬁgure below, E and E are straight line segments. If the area of AABC’ is 30
cm2, What is the area of ACDE? 9cm B A ‘l (b) (Worksheet #21, #3d) Are the following triangles similar? What is the length of the unknown
side? What is the unknown area? ’ 16. '(9.1 #9—#4) A rectangular container, 15 'cm long and 10 cm wide, contains water to a depth of 4 cm.
When a stone of volume 300 cm3 is put in, the water level rises. Find the height of the new water
level. (Assume that the stone is completely under water.) 17. (9.2 #2b, 2a, 3c, 1b, Worksheet #21, #1e) Do the following unit conversions: (a) 2,867 g = ? kg (b) 2.6 cm2 = ? mmz. ((3) 58,300 mm3 = ? cm3 (d) 200 gazillion em2 = ? mm2 18. (Worksheet #24, #1'ab)
(a) What is the volume of a 25cm x 40cm x 60cm ﬁshtank in liters? (b) A typical Nalgene bottle is approximately 20 cm high, and holds 1 l. What is its cross—sectional
area? How high will 400 ml come in the container? 19. (Worksheet #22, #2b) Prove that for similar triangles with scale factor k, the area scales as k2. 20. (9.3 #16) A cylindrical piece of cheese of radius 6 cm and thickness 4 cm stands on a horizontal table
top. 71 of the whole piece is removed by cutting vertically downwards through the radii 0X and CY as
shown in the diagram. Find the volume of the remaining piece of cheese. Leave your answer in terms of the symbol 7r. ...
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This note was uploaded on 08/08/2008 for the course MATH 131 taught by Professor Allprofs during the Fall '07 term at Wisconsin.
 Fall '07
 ALLPROFS

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