8. What Is the Greatest Possible Number of Points of Intersection of a Triangle and A

1BeesDay 1Start UpsMath A Regents January 2002 8. What is the greatest possible number of points of intersection of a triangle and a circle? (1) 6 (2) 2 (3) 3 (4) 4 2Day 2Start UpsMath A Regents June 2001 22. In the accompanying diagram, parallel lines AB and CD are intersected by transversal EF at points X and Y, and mFYD = 123. Find mAXY.E X A BY C D 123 FMath A Regents January 2002 29. In the accompanying diagram, AB and CD intersect at E. If m AEC = 4x – 40 and mBED = x + 50, find the number of degrees in AEC.C B E (4x – 40) ( x + 50 )A D 3Day 3Start UpsMath A Regents January 2001 2. In right triangle ABC, mC = 3y – 10, mB = y +40, and mA = 900.What type of triangle is triangle ABC?(1) scalene (2) isosceles (3) equilateral (4) obtuseMath A Regents January 2002 23. Vertex angle A of isosceles triangle ABC measures 200 more three times m B. Find mC. 4Day 4Start UpsMath A Regents January 2002 16. In the accompanying diagram, ABCD is a straight line, and angle E in triangle BEC is a right angle. What does a0 + d0 equal? A (1) 135 B a0 (2) 160 b0(3) 180(4) 270 E d0 CD 5Day 5Start UpsMath A Regents June 2000 27. Hersch says that if a triangle is an obtuse triangle, then it cannot also be an isosceles triangle. Using a diagram, show that Hersch is incorrect, and indicate the measures of all the angles and sides to justify your answer.Math A Regents January 2001 28. In the accompanying figure, two lines intersect, m3 = 6t +30, and m2 = 8t –60. Find the number of degrees in m 4.3 1 24 6Day 6Hint: Supply students with geo-paper for HW 6Start UpsMath A Regents August 2001 9. The sum of the measures of the interior angles of an octagon is (1) 180 0 (2) 3600 (3) 5400 (4) 10800Worksheet: Math A Questions 7Day 6.5 Hint: Take an additional calendar day for “Special Right Triangles”Start UpsMath A Regents June 2001 7. In isosceles triangle DOG, the measure of the vertex angle is three times the measure of one of the base angles. Which statement about triangle DOG is true? (1) Triangle DOG is a scalene triangle (2) Triangle DOG is an acute triangle (3) Triangle DOG is a right triangle (4) Triangle DOG is an obtuse triangle“Special Right Triangles” Objective: To discover the special properties of 30-60-90 and 45-45-90 right triangles Materials needed: protractors, rulers, graph paperActivity IHave students draw a right triangle with two equal legs. (Use graph paper or rulers to measure sides.) Have students measure the angles and sides. Have students come up with conjectures about an isosceles right triangle. Students should discover that:  hypotenuse = leg times  2 and hypotenuse  each leg = 2Activity IIHave students draw a right triangle in which one leg is twice as long as the other leg. Have students measure the sides and angles Have students arrive at conjectures concerning 30-60-90 triangles State the special properties of a 30-60-90 right triangle.Worksheet: Special Right Triangles 8Day 7Start UpsIn the diagram, mACD = 1300, and mB = 250 What is the mA?AD B CMath A Regents June 1999 12. In the accompanying diagram of A B C, is extended to D, exterior angle C B D measures 145°, and mC = 75.What is mC A B?( 1 ) 35 ( 3 ) 110 ( 2 ) 70 ( 4 ) 220Worksheet: Parallelograms and Trapezoids - MATH A QUESTIONS 9Day 7.5 Hint: Take an additional day for Properties of Parallelograms and TrapezoidsStart UpsMath A Regents June 1999 16. In the accompanying figure, ACDH and BCEF are rectangles, AH = 2, GH = 3, GF = 4, and FE = 5. What is the area of BCDG?(1) 6 (2) 8 (3) 10 (4) 20OBJECTIVE: Properties of parallelograms and trapezoidsACTIVITY I What is special about parallelograms? Hand out graph paper and have students draw parallelograms of various sizes. Why is a figure called a parallelogram? Have students measure the sides, angles and diagonals. What conjectures can they make?ACTIVITY II What is special about trapezoids? Have students draw different trapezoids. Have the students measure the sides, angles and diagonals of a trapezoid What seems to be true about trapezoids ? ACTIVITY III What is special about isosceles trapezoids? Have each student draw different isosceles trapezoids Have students measure the sides, angles, and diagonals of the trapezoids. What seems to be true about isosceles trapezoids have? 10Day 8Hint: Draw triangles for HW 8 in class.Start UpsMath A Regents January 2002 22. A 12-foot tree casts a 16-foot shadow. How many feet tall is a nearby tree that casts a 20-foot shadow at the same time?Math A Regents June 2001 34. The plan of a parcel of land is represented by trapezoid ABCD in the accompanying diagram. If the area of triangle ABE is 600 square feet, find the minimum number of feet of fence to completely enclose the entire parcel of land, ABCD.11Day 9Start UpsMath A Regents June 2001 24. If a girl 1.2 meters tall casts a shadow 2 meters long, how many meters tall is a tree that casts a shadow 75 meters long at the same time?Math A Regents June 2001 7. In isosceles triangle DOG, the measure of the vertex angle is three times the measure of one of the base angles. Which statement about triangle DOG is true?(1) Triangle DOG is a scalene triangle. (2) Triangle DOG is an acute triangle. (3) Triangle DOG is a right triangle. (4) Triangle DOG is an obtuse triangle.12Day 10Start UpsMath A Regents August 2001 33. A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 500. The distance between the ship on the surface and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is the ship on the surface? 13Day 11Start UpsHints: 1) Complete Tri-Square Rug Games in 1 day and have students observe patterns that form right, obtuse, and acute triangles 2) Formalize no later than next day 3) Start recording impossible rugs in class 4) Start recording Pythagorean triples ex: 3,4,5; 5,12,13; 8,15,17Math A Regents June 2001 32. Keesha wants to tile the floor shown in the accompanying diagram. If each tile measures 1 foot by 1 foot and costs $2.99, what wil be the total cost, including an 8% sales tax for tiling the floor?3 ft.10 ft.4 ft.7 ft.Test: Mid Unit Assessment 14Day 12Start UpsMath A Regents Test 1 # 25 A ramp has to be constructed for a new public building. The ramp should have an incline of exactly 150. The building is located 45 feet from the road. What is the length of the ramp to the nearest tenth of a foot? ramp15 45 feet Worksheet: Pythagorean Theorem Worksheet 15Day 13Start UpsMath A Regents June 2001 15. A woman has a ladder that is 13 feet long. If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?(1) 8 (2) 9 (3) 11 (4) 12 16Day 14Start UpsMath A Regents January 2002 27. The plot of land illustrated in the accompanying diagram has a perimeter of 34 yards. Find the length, in yards of each side of the figure. Could these measures actually be the measures of the sides of a triangle? Explain your answer.3x – 1 x + 34xQuiz: Pythagorean Theorem 17Day 14.5 Hint: Take an additional calendar day to teach Properties of a Rectangle, Rhombus and SquareStart UpsMath A Regents Aug. 2001 21. Triangle ABC, with side AC extended to D, is shown in the accompanying diagram. If m ABC = 63 and mBCD = 92, what is mBAC?BA 920 C DPROPERTIES OF A RECTANGLE, A RHOMBUS, AND A SQUAREWhat are the properties of rectangles? Hand out graph paper to students and have students draw different rectangles. Have students measure the sides, angles, and diagonals of the rectangle. What conjectures can be made about rectangles?What is the definition of a rhombus? Have students draw different rhombuses. Have students measure the sides, angles, and diagonals of the rhombus. Ask students to measure the angles formed by the crossing diagonals. What conjectures can be made about rhombuses?What are the properties of a square? Have each students draw different squares. Have students measure the sides, angles, and diagonals of the square. What conjectures can be made about squares?Have student draw a Venn Diagram or Tree Diagram for QuadrilateralsWorksheet: QUADRILATERALS Math A-like Questions – Day 14.5 18Day 15 Start UpsMath A Regents June 2002 31. As seen in the accompanying diagram, a person can travel from New York City to Buffalo by going north 170 miles to Albany and then west 280 miles to Buffalo.Buffalo 280 miles Albany170 miles x New York City a. If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x, would she need to build the highway? Find the angle to the nearest degree. b. To the nearest mile, how many miles would be saved by traveling directly from New York City to Buffalo rather than by traveling first to Albany and then to Buffalo? 19Day 16Hints: 1) Start HW 16 in class. 2) Define aesthetic 3) Verbalize how to get length from widthStart UpsMath A Regents August 2001 3. Which expression is rational? ______(1)  (2)  (1/2) (3)  3 (4)  (1/4) 20Day 17Start UpsMath A Regents January 2000 12. The expression 93 is a number between(1) 3 and 9 (2) 8 and 9 (3) 9 and 10 (4) 46 and 47 21Day 18Hints: 1) Copy pentagon on p.134 and distribute to class 2) Make triangle on p.135 out of cardboard and then rotate it 3) More Opinions About Corrals p. 137 Have students write in a neat, organized fashion Go over each step and post on Chart paperStart UpsMath A Regents January 2000 2. Which number has the greatest value? 2  (1) 1 (2) 2 (3) (4) 1.5 3 2 22Day 19Start UpsMath A Regents August 2001 1. The perimeter of an equilateral triangle varies directly as the length of a side. When the length of a side is doubled, the perimeter of the triangle is(1) halved (2) doubled (3) multiplied by 3 (4) divided by 3 23Day 20Start UpsMath A Regents June 2002 Regents 8. Two triangles are similar. The lengths of the sides of the smaller triangle are 3, 5, and 6, and the length of the longest side of the larger triangle is 18. What is the perimeter of the larger triangle?(1) 1 (2) 18 (3) 24 (4) 42Math A Regents January 2002 12 What is the area of a square whose perimeter is represented by 12x? (1) 6x  2 (2) 9 x2 (3) 12 x3 94) 144 x2 We have 300 feet of fencing material. Determine the side of a regular a) triangle b) square c) pentagon Quiz: RADICALS1. Math A Regents August 2000 # 16The expression 2 5  2 is equivalent to(1) 2 48 (2) 10 (3) 9 2 (4) 49 2 2. Math A Regents Jan. 2001 # 2 If x  0, the expression ( x)( 2x ) is equivalent to ______(1)  2 x (2) 2x (3) x2  2 (4) x  23. Math A Regents August 2001 # 2 Which expression is rational ? ______(1)  (2)  1 / 2 (3)  3 (4)  1 / 4 ______4. Math A Regents June 1999 # 20 The expression  27 +  12 is equivalent to ______(1) 5  3 (2) 13  3 (3) 5  6 (4)  39 24Day 21Start UpsHints: Distribute special enlarged graph paper for HW 21 POW 10 Possible Patches – Optional (if time permits)Math A Regents January 2002 2. If the lengths of a right triangle are 5 and 7, what is the length of the hypotenuse? ______(1)  2 (2) 2  3 (3) 2  6 (4)  74 25Day 22Start UpsMath A Regents June 2001 9. Factor completely: 3x 2 - 27 (1) 3 ( x – 3 )2 (2) 3 ( x2 - 27 ) (3) 3 (x + 3 ) (x – 3)(4) ( 3x + 3) ( x – 9) 26Day 23Hint: Have students develop shortcut for A Voluminous Task (top = bottom; front = back; left side = right side)Start UpsMath A Regents August 1999 27. A person standing on level ground is 2000 feet away from the foot of a 420-foot-tall building as shown is the accompanying diagram. To the nearest degree what is the value of x ?420 x 2,000 ft 2,000 ft. 27Day 24Start UpsMath A Regents August 1999 34. Mr. Gonzalez owns a triangular plot of land BCD with DB = 25 yards and BC = 16 yards. He wishes to purchase the adjacent plot of land in the shape of right triangle ABD, as shown in the accompanying diagram, with AD = 15 yards. If the purchase is made, what will be the total number of square yards in the area of the plot of land, triangle ACD?D15 yd 25yd A B 16 yd C 28Day 25Start UpsMath A Regents August 2001 5. In the accompanying diagram, a circle with radius 4 is inscribed in a square. What is the area of the shaded region?4 29Day 26Start UpsMath A Regents June 2002 28. As shown in the accompanying diagram, radio station KMA is increasing its radius from 40 miles to 50 miles. How many additional square miles of listening area, to the nearest tenth, will the radio station gain? Station KMA 30Day 27Start UpsMath A Regents June 1999 27. The dimensions of a brick, in inches, are 2 by 4 by 8. How many such bricks are needed to have a total volume of exactly 1 cubic foot?31Day 28Hint: Remind students that HW 28 is a required part of PortfolioStart UpsMath A Regents January 2002 27. In the accompanying diagram, a rectangular container with the dimensions 10 inches by 15 inches by 20 inches is to be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. What is the maximum number of full cups of water that can be placed into the container without the water overflowing the container?Radius ( 2 in)20 in 5 in10 15 in 32Day 29 Start UpsMath A Regents January 2001 23. A cardboard box has length x – 2, width x + 1, and height 2x. a) Write an expression, in terms of x, to represent the volume of the box. b) If x = 8 centimeters, what is the number of cubic centimeters in the volume the box?Day 30 BEES END OF UNIT CUMULATIVE TESTDay 31Start UpsMath A Regents January 2000 30. The volume of a rectangular pool is 1080 cubic meters. Its length, width, and depth are in the ratio 10: 4: 1. Find the number of meters in each of the three dimensions of the pool.

8. What Is the Greatest Possible Number of Points of Intersection of a Triangle and A

Details

Download

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

Support