Example Items Geometry Geometry Example Items are a representative set of items for the P. Teachers may use this set of items along with the test blueprint as guides to prepare students for the P. On the last page, the correct answer, content SE and SE justification are listed for each item. The specific part of an SE that an Example Item measures is NOT necessarily the only part of the SE that is assessed on the P. None of these Example Items will appear on the P. Teachers may provide feedback regarding Example Items. () ownload the Example Feedback Form and email it. The form is located on the homepage of the ssessment website (assessment.dallasisd.org). OR () To submit directly: Login to the ssessment website. Under News in the left-hand column, click on Sem Example Items ownload. bove the subjects, click on Example Feedback Form. Second Semester 07 08 ode #: 0
P Formulas Geometry/Geometry PP 07 08 Perimeter and ircumference Square: P = 4s Rectangle: P = l + w ircle: = r = d rc Length: x r 60 rea Square: = s Triangle: Rectangle: = l w = bh Regular Polygon: bh ap Parallelogram: = bh ircle: = r Rhombus: dd = bh Sector of a ircle: x 60 r Trapezoid: ( b b ) h Lateral Surface rea Prism: L = Ph Pyramid: L P ylinder: L = rh one: L = rl Total Surface rea Prism: S = Ph + Pyramid: S P ylinder: S = rh + r one: S = rl + r Sphere: S = 4 r rea of a Sector: x 60 r Volume Rectangular Prism: V = l wh ube: V = s Prism: V = h Pyramid: V h ylinder: V = r h V = h one: V h V r h 4 Sphere: V r Polygons Interior ngle Sum: S = 80(n ) Measure of Exterior ngle: 60 n
P Formulas Geometry/Geometry PP 07 08 oordinate Geometry Midpoint: M x x y y, istance: d ( x x ) ( y y ) Slope of a Line: Slope-Intercept Form of a Line: y y m x x y = mx + b Point-Slope Form of a Line: y y = m(x x) Standard Form of a Line: x + y = Equation of a ircle: (x h) + (y k) =r Trigonometry Pythagorean Theorem: a + b = c Trigonometric Ratios: sin cos opposite leg hypotenuse adjacent leg hypotenuse opposite leg tan adjacent leg Special Right Triangles: 0-60 - 90 45-45 - 90 sin sin sin Law of Sines: a b c Law of osines: a b c bc cos b a c ac cos c a b ab cos Probability Permutations: n P r n! ( n r)! ombinations: n r n! ( n r)! r!
EXMPLE ITEMS Geometry, Sem composite figure is shown on the coordinate grid. What is the total area of this composite figure? 6 square units 84 square units 0 square units 04 square units ircle V is shown. ased on the information in the diagram, what is the measure of QS? 40 7.5 75 9.5 allas IS - Example Items
EXMPLE ITEMS Geometry, Sem KM and JL are chords of circle P. ased on the information in the diagram, what is the length of JL? Record the answer and fill in the bubbles on the grid provided. e sure to use the correct place value. 4 plane intersects a three-dimensional figure and is perpendicular to its base. If the intersection is a rectangle, which three-dimensional figure is intersected by the plane? one ylinder Sphere Square pyramid allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 5 Tamika is making a flag design in the shape of a parallelogram. Which x- and y-values must she use in order to guarantee that the flag is in the shape of a parallelogram? x y x y x y x y 6 Matt has a standard deck of 5 playing cards. What is the probability that Matt draws two face cards without replacement? 676 9 69 allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 7 regular hexagonal pyramid is shown. ased on the information in the diagram, what is the total surface area of the pyramid to the nearest hundredth of a square inch? Record the answer and fill in the bubbles on the grid provided. e sure to use the correct place value. allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 8 In rectangle,, F, F, and are congruent. What is the probability that a point chosen at random lies the shaded region? 8 4 9 Jaxon drew a regular hexagon as shown. ased on the information in the diagram, what is the approximate area of Jaxon s hexagon? 7.8 cm 5.6 cm 54.0 cm 9.5 cm allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 0 ircle M is shown on the coordinate grid. Which equation represents circle M? ( x 4) ( y ) 5 ( x 4) ( y ) 5 ( x ) ( y 4) 5 ( x ) ( y 4) 5 Francesca has a bag that contains blue marbles, 6 purple marbles, 4 green marbles, and 5 orange marble. What is the probability that Francesca draws a green marble, and then an orange marble, without replacement? 0 8 5 8 0 5 79 5 allas IS - Example Items
EXMPLE ITEMS Geometry, Sem The composite figure is created by combining a rectangular prism with a semi-cylinder. ased on the information in the diagram, what is the volume of this composite figure to the nearest cubic centimeter? Record the answer and fill in the bubbles on the grid provided. e sure to use the correct place value. allas IS - Example Items
EXMPLE ITEMS Geometry, Sem In circle O, m O. ased on this information, what is the length of, in terms of? 6 units 859 80 units units 4 90 units 4 Michelle built a triangular garden in her yard as shown in the diagram. The fence that runs from the greens section to the onions section is 40 feet long and forms a 7 angle with the fence connecting the tomatoes and onions. bout how long is the tomatoes-onions fence? 4 feet 0 feet feet 50 feet allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 5 rectangular prism is shown. If the prism is dilated by a scale factor of, 4 which statement is true? The surface area of the new prism is 64 the surface area of the original prism. The surface area of the new prism is 6 the surface area of the original prism. The surface area of the new prism is 8 the surface area of the original prism. The surface area of the new prism is 4 the surface area of the original prism. 6 pizza was cut into 8 equal slices as shown. Leslie ate 5 slices. 45 If the diameter of the pizza was 6 inches, what was the area of the pizza that Leslie ate? 5. square inches 78.5 square inches 5.7 square inches 0. square inches allas IS - Example Items
EXMPLE ITEMS Geometry, Sem 7 rectangular television screen has a diagonal measurement of inches. ased on the information in the diagram, what are the approximate length, x, and width, y, of the television? x = 7.7 inches y = 6.0 inches x =.6 inches y = 6.0 inches x = 8.5 inches y = 4.9 inches x = 5. inches y = 0.7 inches 8 In circle Z, E = x, E = (x + 0), E = (x + 4), and E = (x + 5). ased on this information, what is the length of? 0 0 49 50 allas IS - Example Items
EXMPLE ITEMS Geometry Key, Sem Item# Key SE SE Justification G. G.5 4 G. 4 G.0 5 G.6E 6 G. 7 9.5 G. etermine the area of composite two-dimensional figures comprised of a combination of triangles, [and] regular polygons. Investigate patterns to make conjectures about geometric relationships, including special angles of circles. pply theorems about circles, including relationships among chords to solve non-contextual problems. Identify the shapes of two-dimensional cross-sections of cylinders. Prove a quadrilateral is a parallelogram using diagonals and apply these relationships to solve problems. ompute the probability of the two events occurring together without replacement. pply the formulas for the total surface area of threedimensional figures, including pyramids to solve problems using appropriate units of measure. 8 G. etermine probabilities based on area to solve problems. 9 G. 0 G.E G. 9 G. G. 4 G.9 5 G.0 6 G. 7 G.9 8 G.5 pply the formula for the area of regular polygons to solve problems using appropriate units of measure. etermine the equation for the graph of a circle with radius r and center (h, k), (x - h) + (y - k) = r. ompute the probability of two events occurring together without replacement. pply the formulas for the volume of three-dimensional figures, including composite figures to solve problems using appropriate units of measure. pply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems. etermine the lengths of sides by applying the trigonometric ratios cosine to solve problems. escribe how changes in the linear dimensions of a shape affect its surface area. pply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems. pply the relationships in special right triangles 0-60 -90 to solve problems. Investigate patterns to make conjectures about geometric relationships, including special segments of circles.