If Rick takes chemistry this year, then Jesse will be Rick's lab partner. If Jesse is Rick's lab partner, then Rick will get an A in chemistry.

Transcription

1 G1 State the law of logic that is illustrated? If possible, use that law to write a new conditional statement that follows from the pair of true statements. If Rick takes chemistry this year, then Jesse will be Rick's lab partner. If Jesse is Rick's lab partner, then Rick will get an A in chemistry. G1 The Venn diagram below shows the types of novels a book club read during the year. Suspense Romance Directions: Circle all the correct answers 14 Which of the following is supported by the information in the Venn diagram above. A. 35 members read a romance novel B. 12 members read both a suspense novel and a romance novel C. 16 members read all three types of novels D. 32 members read only a suspense novel or a mystery novel G2 Given: All 8 horizontal lines are parallel. If m1 82 find m2 m3 m4 m5 m6 m7 If m8 74 find m9 Reason : Mystery

2 G3 Over what line was triangle ABC reflected? B B Answer: A C C A G4 Given triangle ABC and A C. Check all answers that are applicable. A. Isosceles B Acute C. Equilateral D. Scalene G5 Susie had some friends over at her house who wanted to go play basketball. Using the information in map shown, which basketball court is the closest to Susie s house? Sherwood Park 58 W N S Susie s House 62 Rosetree Park

3 G6 Which additional piece of information is necessary to prove that triangle ABC is congruent to triangle DEF using SAS? Given: ACB DFE ; AC DF A B F C E D G7 If the perimeter of two similar parallelograms, ABCD and MNOP, is 24 inches and 8 ft respectively, then the ratio, IN SIMPLEST FORM, of NO to BC is : : G7 A surveyor wanted to approximate the width of a river. He placed poles at point A and point B to represent the average width of the river and at points C, D and E along the riverbank. The surveyor measured the distances as shown in the diagram below. Given this diagram, what was the width of the river in feet, from point A to point B? A River B E C 80 D Directions: Type your answer(s) in the box

4 G8 As Jill stood at B, the foot of a six meter pole, he asked Jack how far it was across the pond from B to C. Jack got his carpenter s square and climbed the pole. Using his line of sight, he set up the figure shown. When Jill found AB=3m, Jack knew the answer. What was it? G9 Given the points A (-4,3), B (-1,5), and C (2,1); what must be the coordinate of point D to make ABCD a parallelogram? Point D = (, ) G10 The area of the annulus (shaded region) is 32π cm 2. What is the length of the inner radius r? 18

5 G11 2 Given that the shaded area is 12 cm, find the radius of the circle below: a) 3cm b) 4cm c) 5cm d) 6cm G12 Given the center of a circle at (9,6) and a point on the circle (3,2) write the equation of a circle. G13 A rectangular cake pan has a base of 10 cm by 12 cm and a height of 8 cm. If 810 poured into the pan, how far up the side will the batter come? 3 cm of batter is G14 Two cylinders both have a height of 8 cm. The volume of the first cylinder is 200π 3 cm and the volume of the second cylinder is 800π 3 cm. What is the ratio of the radius of the small cylinder to the big cylinder? :

6 Reasoning, Lines, and Transformations G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) using deductive reasoning. G.2 The student will use the relationships between angles formed by two lines cut by a transversal to a) determine whether two lines are parallel; b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and c) solve real-world problems involving angles formed when parallel lines are cut by a transversal. G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include a) investigating and using formulas for finding distance, midpoint, and slope; b) applying slope to verify and determine whether lines are parallel or perpendicular; c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. G.4 The student will construct and justify the constructions of a) a line segment congruent to a given line segment; b) the perpendicular bisector of a line segment; c) a perpendicular to a given line from a point not on the line; d) a perpendicular to a given line at a given point on the line; e) the bisector of a given angle, f) an angle congruent to a given angle; and g) a line parallel to a given line through a point not on the given line. Triangles G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will a) order the sides by length, given the angle measures; b) order the angles by degree measure, given the side lengths; c) determine whether a triangle exists; and d) determine the range in which the length of the third side must lie. These concepts will be considered in the context of real-world situations. G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs. G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs. G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.

7 Polygons and Circles G.9 The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems. G.10 The student will solve real-world problems involving angles of polygons. G.11 The student will use angles, arcs, chords, tangents, and secants to a) investigate, verify, and apply properties of circles; b) solve real-world problems involving properties of circles; and c) find arc lengths and areas of sectors in circles. G.12 The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Three-Dimensional Figures G.13 The student will use formulas for surface area and volume of three-dimensional objects to solve real-world problems. G.14 The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, and volumes; b) determine how changes in one or more dimensions of an object affect area and/or volume of the object; c) determine how changes in area and/or volume of an object affect one or more dimensions of the object; and d) solve real-world problems about similar geometric objects.