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Example Items Geometry Geometry Example Items are a representative set of items for the ACP. Teachers may use this set of items along with the test blueprint as guides to prepare students for the ACP. On the last page, the correct answer and content SE is listed. 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 ACP. None of these Example Items will appear on the ACP. Teachers may provide feedback with the form available on the Assessment website: assessment.dallasisd.org. First Semester 2016–2017 Code #: 1101 (Version 2 : 12/02/16) ACP Formulas Geometry/Geometry PAP 2016–2017 Perimeter and Circumference Square: Circle: P = 4s C = 2r C = d Rectangle: P = 2l + 2w Arc Length: x 2 r 360 Triangle: A 1 bh 2 Regular Polygon: A 1 aP 2 Circle: A = r Sector of a Circle: A x 360 1 P 2 Area Square: Rectangle: A = s2 A=lw Parallelogram: Rhombus: A = bh A = bh A 1 d1d2 A = bh 2 A Trapezoid: 2 r2 1 (b1 b2 )h 2 Lateral Surface Area Prism: L = Ph Pyramid: L Cylinder: L = 2rh Cone: L = rl Total Surface Area Prism: S = Ph + 2B Cylinder: S = 2rh + 2r Sphere: S = 4r2 2 1 P B 2 Pyramid: S Cone: S = rl + r Area of a Sector: A x 360 2 r2 Volume Rectangular Prism: V = l wh Cube: V = s3 Prism: V = Bh Pyramid: V Cylinder: V = r 2h V = Bh Sphere: V Cone: V 1 Bh 3 1 Bh 3 4 3 r 3 Polygons Interior Angle Sum: S = 180(n – 2) Measure of Exterior Angle: 360 n V 1 2 r h 3 ACP Formulas Geometry/Geometry PAP 2016–2017 Coordinate Geometry Midpoint: y y2 x x2 M 1 , 1 2 2 Distance: d (x2 x1 )2 (y2 y1 )2 Slope of a Line: m Slope-Intercept Form of a Line: y = mx + b Point-Slope Form of a Line: y – y1 = m(x – x1) Standard Form of a Line: Ax + By = C Equation of a Circle: (x – h)2 + (y – k)2 =r y2 y1 x2 x1 2 Trigonometry Pythagorean Theorem: Trigonometric Ratios: a2 + b2 = c2 sin A opposite leg hypotenuse cos A adjacent leg hypotenuse tan A opposite leg adjacent leg Special Right Triangles: sin A sin B sin C a b c Law of Sines: Law of Cosines: 45 - 45 - 90 30 - 60 - 90 a2 b2 c 2 2bc cos A b2 a2 c 2 2ac cos B c 2 a2 b2 2ab cos C Probability Permutations: n Pr n! (n r )! Combinations: n Cr n! (n r )! r ! HIGH SCHOOL Page 1 of 13 EXAMPLE ITEMS Geometry, Sem 1 1 CT has a midpoint at (–1, 0). If C is located at (–7, –3), what is the location of point T ? A (–13, –6) B (–4, –1.5) C (2, 1.5) D (5, 3) Dallas ISD - Example Items Page 2 of 13 EXAMPLE ITEMS Geometry, Sem 1 2 The graph of AB is shown. Which equation represents a line parallel to AB that passes through the point (0, 4)? 3 4 x4 3 A y B y 3 x4 4 C y 3 x4 4 D y 4 x4 3 During Geometry class, Clarence and Alicia wrote the conditional statement shown. If two angles are acute, then they are congruent. Which statement represents the inverse of the conditional? A If two angles are not acute, then they are not congruent. B If two angles are congruent, then they are acute. C If two angles are not congruent, then they are acute. D If two angles are not congruent, then they are not acute. Dallas ISD - Example Items Page 3 of 13 EXAMPLE ITEMS Geometry, Sem 1 4 A geometry student concluded the statement shown. Supplementary angles form a linear pair Which diagram represents a counterexample to this student’s conclusion? A 1 2 1 = 12° B 2 = 168° 3 4 3 = 25° 4 = 155° 6 C 5 7 5 = 90° 6 = 40° 7 = 50° D 5 The statement is true, therefore there is no counterexample. Euclid’s Fifth Postulate (Parallel Postulate) states “If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.” Is this also true in Spherical geometry? A No, there are no parallel lines in Spherical geometry. B No, there are many lines that pass through the point that are parallel to the given line. C Yes, there is exactly one line through the point that is parallel to the given line. D Yes, all postulates and facts are the same for Spherical and plane geometry. Dallas ISD - Example Items Page 4 of 13 EXAMPLE ITEMS Geometry, Sem 1 6 The figures shown are regular polygons. 120° 90° 72° 60° There is a pattern formed by the number of sides in the polygon and the measure of each exterior angle of the polygon. If this pattern continues, what is the measure of each exterior angle, in degrees, of a regular polygon with 40 sides? Record the answer and fill in the bubbles on the grid provided. Be sure to use the correct place value. Dallas ISD - Example Items Page 5 of 13 EXAMPLE ITEMS Geometry, Sem 1 7 The diagram shows the arcs and segments used to construct SR, given Based on this construction, which term describes SR ? 8 A Median B Altitude C Angle bisector D Perpendicular bisector In ABC, AC = 13 and BC = 18 as shown. Which inequality describes all possible lengths of AB ? A 13 x 18 B 13 x 18 C 5 x 31 D 5 x 31 Dallas ISD - Example Items PQR. Page 6 of 13 EXAMPLE ITEMS Geometry, Sem 1 9 In the diagram, a b. Based on the information in the diagram, what is m1? A 48° B 75° C 153° D 201° Dallas ISD - Example Items Page 7 of 13 EXAMPLE ITEMS Geometry, Sem 1 10 Line l, line m, line p, line q, and ray t are coplanar. Given: m1 = 7x + 3.5 m2 = 2x + 10 What value of x makes the information in this diagram true? Record the answer and fill in the bubbles on the grid provided. Be sure to use the correct place value. Dallas ISD - Example Items Page 8 of 13 EXAMPLE ITEMS Geometry, Sem 1 11 In the figure, RA NA and R N . R N A E Which triangle congruence theorem is used to prove 12 A AAS (Angle–Angle–Side) B ASA (Angle–Side–Angle) C SAS (Side–Angle–Side) D SSA (Side–Side–Angle) In the diagram, PQR G RAE NAG ? YWX. Based on the information in the diagram, what is the length of XY ? A 2 B 5 C 7 D 13 Dallas ISD - Example Items Page 9 of 13 EXAMPLE ITEMS Geometry, Sem 1 13 In JKL, C is the centroid and QC 4. What is the length of QL ? A 6 B 8 C 12 D 32 Dallas ISD - Example Items Page 10 of 13 EXAMPLE ITEMS Geometry, Sem 1 14 Isosceles triangle PLM is shown. L (7x – 9) P (3x – 2) (5x – 6) What is the length of PM , to the nearest hundredth? Record the answer and fill in the bubbles on the grid provided. Be sure to use the correct place value. Dallas ISD - Example Items M Page 11 of 13 EXAMPLE ITEMS Geometry, Sem 1 15 In the figures, pentagon ABCDE and pentagon LMNOP are drawn with the dimensions shown. B 20 C M 18 (4y – 2) (2x – 1) A D E If pentagon ABCDE is similar to pentagon LMNOP, what is the value of x ? 5.83 B 6.25 C 7.25 D 15.5 Dallas ISD - Example Items O L 16 A N 12 P Page 12 of 13 EXAMPLE ITEMS Geometry, Sem 1 16 Triangle ABC is shown. Based on the information in the diagram, what is the length of BM ? Record the answer and fill in the bubbles on the grid provided. Be sure to use the correct place value. Dallas ISD - Example Items Page 13 of 13 EXAMPLE ITEMS Geometry, Sem 1 17 Triangle FGH is shown. Based on the information in the diagram, what is the area of Record the answer and fill in the bubbles on the grid provided. Be sure to use the correct place value. Dallas ISD - Example Items FGH ? EXAMPLE ITEMS Geometry, Sem 1 Answer SE Process Standards 1 D G.2B G.1B, G.1C, G.1D, G.1E 2 D G.2C G.1B, G.1C, G.1D 3 A G.4B G.1B, G.1D, G.1F, G.1G 4 A G.4C G.1B, G.1C, G.1D, G.1F, G.1G 5 A G.4D G.1C, G.1D, G.1F, G.1G 6 9 G.5A G.1B, G.1C, G.1D 7 A G.5C G.1B, G.1C, G.1D, G.1F 8 C G.5D G.1B, G.1C, G.1D 9 B G.6A G.1B, G.1C 10 8.5 G.6A G.1B, G.1C, G.1D, G.1F 11 B G.6B G.1B, G.1C, G.1D, G.1E, G.1F 12 D G.6C G.1B, G.1C, G.1F 13 C G.6D G.1B, G.1C, G.1D 14 2.75 G.6D G.1B, G.1C, G.1D, G.1F 15 C G.7A G.1B, G.1C, G.1D, G.1F 16 7 G.8A G.1B, G.1C, G.1D, G.1E 17 150 G.8B G.1B, G.1C, G.1D, G.1E Dallas ISD - Example Items