1 Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition defining mathematical terms to correspond with physical objects inferring a general truth by examining a number of specific examples 2 In the diagram below,! 1 "!4. SG00185 3 onsider the arguments below. I. Every multiple of 4 is even. 376 is a multiple of 4. Therefore, 376 is even. II. number can be written as a repeating decimal if it is rational. Pi cannot be written as a repeating decimal. Therefore, pi is not rational. Which one(s), if any, use deductive reasoning? I only II only both I and II neither I nor II SG00552 l m 3 4 1 2 4 Theorem: triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in!,! and! are both obtuse. Which theorem will Eduardo use to reach a contradiction? t Which of the following conclusions does not have to be true?!3 and!4 are supplementary angles. Line l is parallel to line m.! 1 "!3! 2 "!3 If two angles of a triangle are equal, the sides opposite the angles are equal. If two supplementary angles are equal, the angles each measure 90. The largest angle in a triangle is opposite the longest side. The sum of the measures of the angles of a triangle is 180. SG00025 SG10066
5 Use the proof to answer the question below. Given:!; is the midpoint of Prove:!!! Statement Reason 1.!; is the midpoint of 1. Given 2.! 2. efinition of Midpoint 3.! 3. Reflexive Property 4.!!! 4.? What reason can be used to prove that the triangles are congruent? S S SS SSS SG10068
6 In the figure below,!. If we assume that m! " m!, it follows that ". This contradicts the given statement that!. What conclusion can be drawn from this contradiction? m!! m! m! " m! m!! m! m! " m! SG00524
7 Use the proof to answer the question belowġiven:! 2 "! 3 Prove:! 1 "! 4 2 1 l 4 3 m t Statement Reason 1.! 2 "! 3 1. Given 2.! 1 "! 2;! 3 "! 4 2.? 3.! 1 "! 4 3. Transitive Property What reason can be used to justify statement 2? omplements of congruent angles are congruent. Vertical angles are congruent. Supplements of congruent angles are congruent. orresponding angles are congruent. SG10069
8 Two lines in a plane always intersect in exactly one point. Which of the following best describes a counterexample to the assertion above? coplanar lines parallel lines perpendicular lines intersecting lines 11 conditional statement is shown below. If a quadrilateral has perpendicular diagonals, then it is a rhombus. Which of the following is a counterexample to the statement above? SG00320 9 Which figure can serve as a counterexample to the conjecture below? If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram. rectangle rhombus square trapezoid SG10194 10 Given: TRP is an isosceles trapezoid with diagonals RP and T. Which of the following must be true? SG20216 RP! T RP!T RP " T RP bisects T SG00260
12 Which triangles must be similar? two obtuse triangles two scalene triangles with congruent bases two right triangles two isosceles triangles with congruent vertex angles 14 Parallelogram is shown below. E SG00578 13 Which of the following facts would be sufficient to prove that triangles and E are similar? Which pair of triangles can be established to be congruent to prove that! "!?! and!!e and!e! and!!e and!e SG10146 E 15 If! and!xyz are two triangles such that!, which of the following would XY YZ be sufficient to prove the triangles are similar? E and E are congruent.!e is a right angle. and E are parallel.! and! are congruent.! "! X! "!Y! "!Z! X "!Y SG10218 SG00544
16 In parallelogram FGHI, diagonals IG and FH are drawn and intersect at point M. Which of the following statements must be true? FGI must be an obtuse triangle. HIG must be an acute triangle. FMG must be congruent to HMG. GMH must be congruent to IMF. 18 Which of the following statements must be true if!ghi "!JKL? G H I K 17 Which of the following best describes the triangles shown below? SG00559 J L 30 8 8 The two triangles must be scalene. The two triangles must have exactly one acute angle. t least one of the sides of the two triangles must be parallel. The corresponding sides of the two triangles must be proportional. SG20074 60 both similar and congruent similar but not congruent congruent but not similar neither similar nor congruent SG00478 12 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
19 In the figure below,! F and "!". 20 Given: and intersect at point E; " 1!"2 F 1 3 E 4 2 Which additional information would be enough to prove that!!!ef?! E!! EF! E E SG00517 Which theorem or postulate can be used to prove!e "!E? SSS S SS SG10074 21 In the figure below, n is a whole number. What is the smallest possible value for n? n n 15 1 7 8 14 SG00295 13 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 22 Which of the following sets of numbers could represent the lengths of the sides of a triangle? 2, 2, 5 3, 3, 5 4, 4, 8 5, 5, 15 24 What values of a and b make quadrilateral MNOP a parallelogram? N 21 O 3a 2b 13 SG10041 23 In the accompanying diagram, parallel lines l and m are cut by transversal t. t 1 l M 4a + b P a!1, b! 5 a! 5, b!1 2 m Which statement about angles 1 and 2 must be true?! 1 "!2.!1 is the complement of!2.!1 is the supplement of!2.!1and!2 are right angles. SG00579 11 34 a!, b! 7 7 34 11 a!, b! 7 7 SG10163 25 Quadrilateral is a parallelogram. If adjacent angles are congruent, which statement must be true? Quadrilateral is a square. Quadrilateral is a rhombus. Quadrilateral is a rectangle. Quadrilateral is an isosceles trapezoid. SG20048 14 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 26 For the quadrilateral shown below, what is m! a! m! c? 28 right circular cone has radius 5 inches and height 8 inches. 95 o c o a o 53 137 180 233 32 o 8 in. 5 in. What is the lateral area of the cone? (Lateral area of cone "!rl, where l " slant height ) l SG10162 27 If is a parallelogram, what is the length of segment? 40! sq in. 445! sq in. 5! 39 sq in. 5! 89 sq in. SG00053 7 5 E 6 10 11 12 14 SG20236 15 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 40 The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the areas of the two squares? 43 The sum of the interior angles of a polygon is the same as the sum of its exterior angles. What type of polygon is it? 2 to 3 4 to 9 16 to 27 16 to 81 quadrilateral hexagon octagon decagon SG00013 SG00305 41 Lea made two candles in the shape of right rectangular prisms. The first candle is 15 cm high, 8 cm long, and 8 cm wide. The second candle is 5 cm higher but has the same length and width. How much additional wax was needed to make the taller candle? 320 cm 3 640 cm 3 960 cm 3 1280 cm 3 SG20116 42 Two angles of a triangle have measures of 55 and 65. Which of the following could not be a measure of an exterior angle of the triangle? 115 120 125 130 SG00571 44 What is m! x? 35 60 85 95 x 60 25 SG20086 45 If the measure of an exterior angle of a regular polygon is 120!, how many sides does the polygon have? 3 4 5 6 SG20204 19 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 50 What is the measure of an exterior angle of a regular hexagon? 30! 60! 120! 180! SG00570 51 diagram from a proof of the Pythagorean theorem is pictured below. a b 52 right triangle s hypotenuse has length 5. If one leg has length 2, what is the length of the other leg? 3 21 29 7 SG00566 53 new pipeline is being constructed to re-route its oil flow around the exterior of a national wildlife preserve. The plan showing the old pipeline and the new route is shown below. c 60 miles NEW PIPELINE OL PIPE LINE 32 miles Which statement would not be used in the proof of the Pythagorean theorem? 1 The area of a triangle equals ab. 2 The four right triangles are congruent. The area of the inner square is equal to half of the area of the larger square. The area of the larger square is equal to the sum of the areas of the smaller square and the four congruent triangles. bout how many extra miles will the oil flow once the new route is established? 24 68 92 160 SG10016 SG10192 21 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 29 Figure is a kite. 10 cm 10 cm 6 cm 8 cm 8 cm 17 cm 15 cm 17 cm 31 sewing club is making a quilt consisting of 25 squares with each side of the square measuring 30 centimeters. If the quilt has five rows and five columns, what is the perimeter of the quilt? 150 cm 300 cm 600 cm 900 cm SG20111 32 The four sides of this figure will be folded up and taped to make an open box. 5 centimeters What is the area of figure, in square centimeters? 120 154 168 336 SG20157 30 If a cylindrical barrel measures 22 inches in diameter, how many inches will it roll in 8 revolutions along a smooth surface? 121! in. 168! in. 176! in. 228! in. SG00564 What will be the volume of the box? 50 cm 3 75 cm 3 100 cm 3 125 cm 3 SG00299 16 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 33 classroom globe has a diameter of 18 inches. 34 The rectangle shown below has length 20 meters and width 10 meters. 4 m 4 m 4 m 4 m 4 m 4 m 4 m 4 m Which of the following is the approximate surface area, in square inches, of the globe?!surface rea " 4!r 2 # 113.0 226.1 254.3 1017.4 SG20238 If four triangles are removed from the rectangle as shown, what will be the area of the remaining figure? 136 m 2 144 m 2 168 m 2 184 m 2 35 If RSTW is a rhombus, what is the area of!wxt? SG00012 R W X 60 o 12 S T 18 3 36 3 36 48 SG00227 17 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 36 What is the area, in square units, of the trapezoid shown below? y (0, 5) (8, 5) 38 What is the area, in square meters (m), of the trapezoid shown below? 12 m 5 m 5 m 6 m 0 (12, 0) 37.5 42.5 50 100 37 The figure below is a square with four congruent parallelograms inside. x SG20226 28 36 48 72 SG10047 39 What is the area, in square inches (in.), of the triangle below? 10 in. 10 in. 5 3 12 10 in. What is the area, in square units, of the shaded portion? 60 84 114 129 25 25 3 50 50 3 SG10048 SG20225 18 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 46 In the figure below,!. (x + 40)º (x 40)º 48 What is m"1? 36 o 88 o What is the value of x? 40 50 80 90 SG00244 47 The measures of the interior angles of a pentagon are 2x, 6 x, 4 x! 6, 2 x!16, and 6x! 2. What is the measure, in degrees, of the largest angle? 28 106 170 174 1 34 56 64 92 49 What is m " WZX? V 132º SG20179 SG10028 W Z 52º Y 80! 90! 100! 110! X SG30022 20 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 54 Marsha is using a straightedge and compass to do the construction shown below. 55 Given: angle What is the first step in constructing the angle bisector of angle? P Which best describes the construction Marsha is doing? a line through P parallel to line l a line through P intersecting line l a line through P congruent to line l a line through P perpendicular to line l l!!!" raw ray. raw a line segment connecting points and. From points and, draw equal arcs that intersect at. From point, draw an arc that intersects the sides of the angle at points and. SG10131 SG00526 22 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 56 Scott is constructing a line perpendicular to line l from point P. Which of the following should be his first step? P P l l 57 Which triangle can be constructed using the following steps?!"#!"#$#%&$#'($)*$#%&$+),(-..$)/$()'/#$!0$ $"# 1(&/$#%&$+),(-..$.)$#%-#$#%&$(&/+'2$#'($ '.$)/$()'/#"#0$ %"# 34-5$-/$-4+$-6)7&$. &"# 8'#%)"#$+%-/9'/9$#%&$)(&/'/9:$("#$#%&$,&#-2$#'($)/$()'/#"#"-/;$;4-5$-/$-4+$ '/#&4.&+#'/9$#%&$*'4.#$-4+$-#$()'/#"$0$ '"# 34-5$ -/;$. P l right P obtuse scalene l equilateral SG10135 SG00308 23 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 58 The diagram shows!. y 59 Figure O is a parallelogram. y (a, b) (a + c, b) x O (c, 0) x Which statement would prove that! is a right triangle? What are the coordinates of the point of intersection of the diagonals?!slope "!slope " =1!slope "!slope " =!1 distance from to = distance from to distance from to =! (distance from to ) SG00475 " & a b, ' 2 2 #$ % " & c b, ' 2 2 #$ % " # & a# c, ' 2 2 $% " & a # c a #, ' 2 2 # $% SG20101 24 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 60 What type of triangle is formed by the points (4, 2), (6,!1), and (!1, 3 )? right equilateral isosceles scalene 63 In the figure below, sin $ 07.. 21 SG10235 61 The point!!3, 2" lies on a circle whose equation is! x # 3" 2 #! y # 1" 2 $ r 2. Which of the following must be the radius of the circle? 3 10 9 10 SG30048 5 62 In the figure below, if sin x $, what are cos x and tan x? 13 What is the length of? 14.7 21.7 30 32 SG00432 x cos = 12 5 x and tan x = 13 12 cos = 12 12 x and tan x = 13 5 cos = 13 5 x and tan x = 12 12 cos = 13 13 x and tan x = 12 5 SG00493 25 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 64 pproximately how many feet tall is the streetlight? 65 Right triangle is pictured below. 10.6 32º 8.2 h Which equation gives the correct value for? 40º sin 32!" 82. 20 ft cos 32!" 10. 6 12.8 sin 40!! 0.64 cos 40!! 0.77 tan 40!! 0. 84 82 tan 58!". sin 58!" 10. 6 15.4 SG10210 16.8 23.8 SG20047 26 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 66 In the accompanying diagram, m!! 32" and! 10. Which equation could be used to find x in!? 67 The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 53 " angle with the wall. Which is closest to the distance up the wall the ladder reaches? x 53 32 10 8 ft? x!10 sin 32" x!10 cos 32" sin 53 0.80 cos 53 0.60 tan 53 1.33 x!10 tan 32" 3.2 ft 10 x! cos32" 4.8 ft 6.4 ft SG00555 9.6 ft SG00342 27 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 68 Triangle JKL is shown below. K 69 What is the approximate height, in feet, of the tree in the figure below? 24 o L 100 ft J 28 Which equation should be used to find the length of JK? JK sin 24!" 28 28 sin 24!" JK JK cos 24!" 28 28 cos 24!" JK SG20031 64.3 76.6 119.2 130.5 50 sin 50!! 0. 766 cos 50!! 0. 643 tan 50!! 1. 192 SG20126 70 If a! 3 3 in the right triangle below, what is the value of b? a b c 28 9 6 3 12 3 18 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education. SG10052
LI FOR N I ST N R S TE ST 71 What is the value of x in the triangle below? x 10 x 73 square is circumscribed about a circle. What is the ratio of the area of the circle to the area of the square? 1 4 1 2 5 5 2 10 3 20 2!! 4 SG10056 SG00585 72 What is the value of x, in inches? 74 In the circle below, and are chords intersecting at E. 7 in. E 30 o x 7 3 14 14 3 21 If E! 5, E! 12, and E! 6, what is the length of E? SG20099 7 9 10 13 SG00022 29 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 75!" R ## is tangent to a circle, whose center is, at point. is a diameter. R 76 In the figure below,! ### "!##" is tangent to circle O at point, secant intersects circle O at points and, m $ = 70!, and m $ = 110!. 70 o 25º O 110 o What is m! R? 50 65 90 130 SG20186 What is m!? 20 40 55 70 SG10257 30 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 77 In the circle shown below, the measure of! PR! 140" and the measure of! RPQ! 50". 79 If triangle is rotated 180 degrees about the origin, what are the coordinates of "? 140º R O 50º What is the measur! e of PQ? 50! 60! 70! 120! P Q SG10003 78 The vertices of are (2, 1), (3, 4), and (1, 3). If is translated 1 unit down and 3 units to the left to create EF, what are the coordinates of the vertices of EF? (0, 1), E(1, 2), F(1, 3) (0, 1), E(0, 3), F( 2, 2) ( 2, 2), E(0, 3), F( 1, 0) ( 1, 0), E(0, 3), F( 2, 2) y 7 6 5 4 3 2 1-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7-1 -2-3 "! 5,! 4# "!5, 4# "!4, 5# "! 4,! 5# -4-5 -6-7 x SG10096 SG00317 31 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.
LI FOR N I ST N R S TE ST 80 Trapezoid below is to be translated to trapezoid!!!! by the following motion rule.! x, y " #! x # 3, y"4" y 9 8 7 6 5 4 3 2 1-9 -8-7 -6-5 -4-3 -2-1 0-1 1 2 3 4 5 6 7 8 9-2 -3-4 -5-6 -7-8 -9 x What will be the coordinates of vertex!?!1,! 3"!2, 1"! 61",!8,!3" SG10214 32 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 2008 alifornia epartment of Education.