Measurement and Geometry MEASUREMENT AND GEOMETRY

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1 MEASUREMENT AND GEOMETRY The following ten California mathematics academic content standards from the strand are assessed on the CAHSEE b 17 test questions and are represented in this booklet b 5 released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the CAHSEE. GRADE 7 MEASUREMENT AND GEOMETRY Standard Set 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement sstems to solve problems: 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement sstems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 1.2 Construct and read drawings and models made to scale. 1. Use measures epressed as rates (e.g., speed, densit) and measures epressed as products (e.g., person-das) to solve problems; check the units of the solutions; and use dimensional analsis to check the reasonableness of the answer. Standard Set 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. The know how perimeter, area and volume are affected b changes of scale: 2.1 Use formulas routinel for finding the perimeter and area of basic twodimensional figures and the surface area and volume of basic threedimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and clinders. 2.2 Estimate and compute the area of more comple or irregular two- and threedimensional figures b breaking the figures down into more basic geometric objects. 2. Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied b a scale factor, the surface area is multiplied b the square of the scale factor and volume is multiplied b the cube of the scale factor. 2. Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 1 square inches or [1 ft 2 ] = [1 in 2 ], 1 cubic inch is approimatel 16.8 cubic centimeters or [1 in ] = [16.8 cm ]). 2

2 Standard Set.0 Students know the Pthagorean theorem and deepen their understanding of plane and solid geometric shapes b constructing figures that meet given conditions and b identifing attributes of figures:.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.. Know and understand the Pthagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empiricall verif the Pthagorean theorem b direct measurement.. Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures One millimeter is A B 1 of a meter of a meter. 100 C 100 meters. D 1000 meters A bo is two meters tall. About how tall is the bo in feet (ft) and inches (in.)? ( 1 meter 9 inches) A 5 ft 0 in. B 5 ft 6 in. C 6 ft 0 in. D 6 ft 6 in. M020 M00276

3 111. Juanita eercised for one hour. How man seconds did Juanita eercise? A 60 B 120 C 60 D, In Sacramento, the temperature at noon was 5 Celsius (C). What was the temperature in degrees Fahrenheit (F)? 9 F= C If Jill is driving at 65 miles per hour, what is her approimate speed in kilometers per hour? 1 mile 1.6 kilometers ( ) A 16 B 1 C 10 D 17 M007 A 5 B 6 C 67 D The actual width (w) of a rectangle is 18 centimeters (cm). Use the scale drawing of the rectangle to find the actual length (l). M0269 M cm w l.6 cm A 6 cm B 2 cm C 6 cm D 5 cm M02087

4 115. The scale drawing of the basketball court shown below is drawn using a scale of 1 inch (in.) = 2 feet (ft) in. in. What is the length, in feet, of the basketball court? A 90 ft B 10 ft C 11 ft D 120 ft M022 5

5 116. Javier is using a ruler and a map to measure the distance from Henle to Sailport A scale drawing of a horse is shown below. Mt. Roger Seaside Henle Burton Sailport Centimeters (cm)? in. The actual distance from Henle to Sailport is 120 kilometers (km). What scale was used to create the map? A 1cm = 6km B 1cm = 12km C 1cm = 15km D 1cm = 20km M21169 = 8 inches What is the actual height of the horse, in inches (in.), from the hoof to the top of the head? A 56 B 6 C 72 D 80 M Sit miles per hour is the same rate as which of the following? A 1 mile per minute B 1 mile per second C 6 miles per minute D 60 miles per second M027 6

6 119. Beverl ran si miles at the speed of four miles per hour. How long did it take her to run that distance? B C A B 2 hr 1 1 hrs 2 C hrs D 6 hrs 120. Marcus can tpe about 2 words per minute. If he tpes at this rate for 0 minutes without stopping, about how man words will he tpe? A 1260 B 2100 C 2520 D 200 M0201 A 122. In the figure above, the radius of the inscribed circle is 6 inches (in.). What is the perimeter of square ABCD? A 12π in. B 6π in. C 2 in. D 8 in. D M0226 M A landscaper estimates that landscaping a new park will take 1 person 8 hours. If people work on the job and the each work 6-hour das, how man das are needed to complete the job? A 2 B C 6 D 8 M feet 12. The largest possible circle is to be cut from a 10-foot square board. What will be the approimate area, in square feet, of the remaining board (shaded region)? ( A= πr 2 andπ 1). A 20 B 0 C 50 D 80 M000 7

7 9 in in. 5 in. 12. What is the area of the triangle shown above? 15 A square units B 60 square units C 88 square units D 120 square units M What is the volume of the shoebo shown above in cubic inches (in. )? A 29 B 75 C 510 D What is the area, in square units, of trapezoid QRST shown below? 1 A= h( b1+ b2) 2 M ft 68 ft 105 ft R 6 S 8 26 ft 125. A rectangular pool 2 feet b 68 feet is on a rectangular lot 105 feet b 26 feet. The rest of the lot is grass. Approimatel how man square feet is grass? A 2,100 B 2,800 C 21,000 D 28,000 Q V A 68 B 10 C 208 D T M12087 M0011 8

8 128. One-inch cubes are stacked as shown in the drawing below. 10. What is the area of the shaded region in the figure shown below? 2 cm 1 in. { { {1 in. 1 in. 2 cm 2 cm 2 cm What is the total surface area? A 19 in. 2 B 29 in. 2 C 2 in. 2 D 8 in. 2 A cm 2 B 6 cm 2 C 8 cm 2 D 16 cm 2 M0281 M A right triangle is removed from a rectangle as shown in the figure below. Find the area of the remaining part of the rectangle. 2 in. 2 in In the figure shown above, all the corners form right angles. What is the area of the figure in square units? A 67 B 7 C 78 D 91 M in. 8 in. 6 in. A 0 in. 2 B in. 2 C 8 in. 2 D 52 in. 2 M0209 9

9 12. In the figure below, ever angle is a right angle What is the area of the shaded figure below? 8 8 What is the area, in square units, of the figure? A 96 B 108 C 120 D 1 6 M10790 = 1 square centimeter (cm 2 ) A 8 cm 2 B 9 cm 2 C 10 cm 2 D 12 cm 2 M

10 1. The short stairwa shown below is made of solid concrete. The height and width of each step is 10 inches (in.). The length is 20 inches. 16. Gina is painting the rectangular tool chest shown in the diagram below. 2 in. 10 in. 10 in. 12 in. 10 in. 20 in. 10 in. What is the volume, in cubic inches, of the concrete used to create this stairwa? A 000 B 000 C 6000 D 8000 If Gina paints onl the outside of the tool chest, what is the total surface area, in. 2, she will paint? in square inches ( ) A 68 B 68 C 1296 D 2880 M206 M Bonni has two similar rectangular boes. The dimensions of bo 1 are twice those of bo 2. How man times greater is the volume of bo 1 than the volume of bo 2? A B 6 C 8 D 9 M

11 17. The object below is made of ten rectangular prisms, each with dimensions of 5 centimeters (cm) b cm b 2 cm. What is the volume, in cubic centimeters, of the object? A 100 B 150 C 250 D 00 5 cm cm 2 cm M The width of the rectangle shown below is 6 inches (in.). The length is 2 feet (ft). 19. One cubic inch is approimatel equal to 16.8 cubic centimeters. Approimatel how man cubic centimeters are there in cubic inches? A 5.6 B 1.8 C 19.8 D A rectangular field is 6 feet long and 20 feet wide. How man acres is the field? (1 acre =,560 square feet A 2 B C D 5 ) M02700 M in. 2 ft What is the area of the rectangle in square inches? A 12 B 16 C 60 D 1 M02 52

12 0 R S T 11. Which of the following triangles R S T is the image of triangle RST that results from reflecting triangle RST across the -ais? A C T T 0 R S 0 R S B D S 0 R T S 0 R T M

13 12. The points (1, 1), (2, ), (, ), and (5, 1) are the vertices of a polgon. What tpe of polgon is formed b these points? A Triangle B Trapezoid C Parallelogram D Pentagon M The graph of rectangle ABCD is shown below. B 2 C A D What is the area, in square units, of rectangle ABCD? A 6 B 10 C 12 D 1 1. A clothing compan created the following diagram for a vest. D E F C B 2 1 A To show the other side of the vest, the compan will reflect the drawing across the -ais. What will be the coordinates of C after the reflection? A ( 27, ) B ( 72, ) C ( 2, 7) D ( 2, 7) M1060 M016 5

14 15. Which graph shows the figure below reflected across the -ais? A C B D M

15 16. What is the value of in the right triangle shown below? N km 5 feet 1 feet km A 8 feet B 12 feet C 18 feet D 2 feet M0181 Home 17. The club members hiked kilometers north and kilometers east, but then went directl home as shown b the dotted line. How far did the travel to get home? A km B 5 km C 6 km D 7 km M

16 19. In the drawing below, the figure formed b the squares with sides that are labeled,, and z is a right triangle What is the value of in the triangle shown above? A 11 B 1 C 17 D M026 Which equation is true for all values of,, and z? A + = z z B = z 2 C 2 2 i = z 2 D 1 = z 2 M

17 150. The size of a television screen is measured along its diagonal. A 25-inch (in.) television screen is shown below. 20 in Which figure is congruent to the figure shown above? 25 in.? A If the television screen shown above is 20 inches wide, what is the height, in inches, of the screen? A 5 B 90 B C C 10 D 15 6 M21 D M

18 152. In the diagram below, heagon LMNPQR is congruent to heagon STUVWX. 15. If triangles EFG and JKL are congruent, then which two segments MUST be congruent? L M E F R N Q P S T X U W V G Which side is the same length as MN? A NP B TU C UV D WX M1069 L A EF and JK B EF and JL C FG and JK D FG and JL J K M

19 Question Number Correct Answer Standard School Year of Eam 109 A 7MG D 7MG D 7MG C 7MG D 7MG D 7MG C 7MG D 7MG C 7MG A 7MG B 7MG A 7MG A 7MG D 7MG A 7MG B 7MG C 7MG D 7MG B 7MG D 7MG A 7MG A 7MG B 7MG C 7MG A 7MG C 7MG C 7MG C 7MG D 7MG D 7MG D 7MG A 7MG B 7MG B 7MG C 7MG A 7MG C 7MG B 7MG B 7MG

20 Question Number Correct Answer Standard School Year of Eam 18 B 7MG B 7MG D 7MG B 7MG B 7MG A 7MG