w hole + ½ partial = 10u + (½ )(10u )

Size: px
Start display at page:

Download "w hole + ½ partial = 10u + (½ )(10u )"

Transcription

1 MATH 10 MEASURE Self-Test ANSWERS (DETAILED answ ers start on NEXT PAGE.) 1. a. (½) (4u) + [(8u) (u) ] = (4 + 64)u (see diagram ) 1a. Perimeter = 4u + 8u + ½ (u) = (8 + 16)u (½) (u) b. 7.5 u [ ½ 1 ½ 6 ½ = 7.5 ] (w ork from outside in) (½) (u) Perimeter = ( ) units (Use the Pythagorean theorem.) (½) (4u) (8u) That c. w hole + ½ partial = 10u + (½ )(10u ) = 15u d. l w h = 8lwh = 8 (original volume) (6+ 1)(8+ 1)(7+ 1) ! It s b a. h (a + b)/ b. r c. (x/60) r d. C = r e. V = 4 r f. SA = 4 r ))))))) ) 4. a u = 4 5 units.. 1/ b. D[( 1,4),(,0)] = 5; D[(,0),(, )] = 5; D[( 1,4),(, )] = 50. Yes: d + d = d Area in square Area in circle = (1 cm) (6 cm) = (144 6 )cm 6. V of prism or cylinder = (Area of base) (Height) = 8000 m 7. a. (a) (0 cm) 0 cm = 6000 cm Volume of pyramid or cone = (1/) (area of base)(height) b. (a) (80 cm ) 0cm = 1600/ cc. ( cc is an alternate abbreviation for cm cubic centimeters) 8. a. V = (a) (5 cm) 5cm = 65 / cm lateral SA = (1/) (10 cm)(5 6 cm) = 5 6 cm b. V = (5 cm) 5cm = 65 cc BTW: Total SA = ( ) cm lateral SA = (10cm) 5cm = 50 cm BTW: Total SA = ( ) cm radial face part of Circumference 9a. SA = top+ bottom + radial faces + strip of C V = one-sixth of the V of the original w heel SA = (15cm cm) + (1/6) (15cm) + 0 cm /6 V = (1/6) (15cm) cm = 5 /cm 9b. SA = (15cm cm) + (0/60) (15cm) + (1/1) 0 cm V = (0/60) (15cm) cm = 5 /4 cm 0 is 1/1 of the circle, so V is half V of part a 10. SA = (1/) 4 (5cm) + (1/) (10cm) 1cm = 115 cm V = V + V = (1/) (4/) (5cm) + (1/) (5cm) (1cm) = (550 /)cm hemisphere cone o o 11. The relationship betw een C and F is a line going from (0,) to (100,1); o o o o o o that makes a rise of 100 C equal to a rise of 180 F: i.e. 100 C = 180 F, so ( 100 C/180 F ) = 1!. o o o o o o o o o o o 100 C/180 F reduces to 5 C/9 F. And, yes, 5 C/9 F = 1 also. So C = (5 C/9 F) ( F F). o o o (Notice F must be adjusted dow n to 0 before multiplying, so that F w ill end up being 0 C.). 5 o o o o 9 9 o o 5 C = ( / )(F ) a. 7 F = C (18 Reaumur) c F = 7 C F = ( / )C + b. 0 C = 86 F 1. a. cm b. cm c. m d. km e. kg f. g g. g (actually mg, but that' s not in the list) h. t i. ml or cc j. L k. ml or cc l. kl kl = 1000 L = ml = 10 ml = 10 cc = 6 10 g = 1000 kg = 1 metric ton. OR: 1 kl = 1 kl 1000L 1000 ml 1 cc 1 g* 1 kg 1 metric ton = 1 metric ton 1 kl 1 L 1mL cc 1000g 1000 kg valid ONLY for w ater at 4 C 14. a. Carpet costs $/yd ; wood costs $4/ft = $4/ft ft/yd ft/yd = $6/yd ; carpet is cheaper. b. 1 ft = (1 in) = 144 in ; 1 yd = ( ft) = 9 ft (Use the method show n in #1.) c. (1 ft) = (1 in) = 178 in ; (1 yd) = ( ft) = 7 ft ; 1 yd = 7 ft = in = in d. 1 m = (100 cm) = cm ; (see #1) = ml e. (see #1; the conversion at * is valid for w ater only!) f..1 dal g. 00 dam g. 00 cm = 00 cm 1m 1 m =.0m h. 8dl = 8dl 100ml 1cc = 800 cc = 000 m 100cm. 100cm dl ml = cm 15. ½ Just barely not. The longest dimension in a 4" x7" x7" box is the extreme diagonal, (674) 5.96" 16. New area = 100cm.5.5 = 65 cm

2 M ATH 1 0 Self-Test M EASURE extended solutions w ith comments 1a. We assume arcs are semi-circular. Perimeters are show n on page )))) 8mm We view this as a half-circular region[i] (with diameter 8mm) 8mm joined to a rectangular region [II] (8mm by 8mm) )))) 6mm from w hich two small semicircular regions [III] have been removed radius of the small circles must be the difference 8mm 6mm= mm. (And must also be ½ of 8mm/.) Area I: radius is ½ of 8mm, or 4mm. Area of half-circular disc is (½ ) (4mm) Area II: area of 8m by 8mm square is 64mm 8mm Area III: area of tw o half-circular cutouts [diameter = 4mm]... is ½ (mm) Thus Total Area of figure is (½ ) (4mm) + 64mm ½ (mm) = (4 + 64)mm 1b We start w ith the smallest vertical-horizontal bounded rectangle that contains the polygon given (w hich happens to be a triangle, but that s not important, this w orks for any polygon w ith vertices on lattice pts) Area w ithin polygon = area of rectangle areas of take-aw ay parts: (4u)(6u) ½ (4u)(u) ½ (u)(1u) ½ (6u)() = 4 / = 7.5 u 1c We cover the region w ith squares We count the squares w hich lie entirely w ithin the region outlined We count the squares w hich lie partially w ithin the region outlined We then make the ESTIMATE: Area w ithin outline 10u + (½ )(10)u = 15u (approximate area) 1d. 8m 6m (This is based on the assumption that the squares w hich are partially enclosed average half inside, half outside) The volume of the box is (area of base)(height) = length w idth height 7m = (6m 8m) 7m = 6 m Doubling all the dimensions, w e can compute: NEW V= (1m 16m) 14m = 688 m... that is, 8 6 m In fact, w e could have anticipated this, since V = l w h = 8 l w h = 8 (original volume) If each dimension is increased by 1m, is the volume increased by 1m? Explain. 8m + 1m 7m 6m NO! The increase in volume is much, much greater than that! Just consider, first, the effect of increasing just ONE dimension e.g. increase the length from 8m by 1m to 9m. As illustrated at left, this w ould add a 1m by 6m by 7m slab to one end of the box. That alone, then, adds 4m of volume to the box. Here w e illustrate the addition of a 1m extension to the depth of the box. Just for the old box, this extension results in an additional 1m 8m 7m or 56m, and that does not even take into account the extension of the length from 8m to 9m! To account for that, w e need another 1m by 1m by 7m piece in the corner! Extending the height an additional 1m, from 7m to 8m results in a new slab added to the top of the box, 1m by 6m by 8m to cover the original box, but 1m x 7m x 9m to cover the box w ith its new extended length and depth. Picture it (draw the top extension in) yourself! Here s the entire difference, found algebraically: Original volume, V = l w h, After each dimension is increased by amount a: NEW V = (l+a)( w+a)(h+a) = l w h + l w a + l a h + a w h + l a a + a w a + h a a + a a a Difference: l w a + l a h + a w h + l a a + a w a + h a a + a a a

3 4. a. Sketch the points ( 4,5) and (4,1) in the plane. Find the distance betw een the points. (-4,5) The change in x = 5 1 = The change in y = 4 ( 4) = = c (4,1) c = c = 8 0) = = 4 5 (Units) b. Do points ( 1,4), (,0), (, ) lie at the vertices of a right triangle? How do you know? The solution is based on the Pythagorean Theorem: the sum of the squares of the tw o short legs is equal to the square of the hypotenuse if, and ONLY if, the triangle is a right triangle. So find the distances betw een the three pts. They are 5, 5, and sqrt(50). We find the pythagorean relationship holds true (5 + 5 = 5 0 ). So the triangle must be a right triangle. 5. Area inside the square is (1cm). D of the circle = 1cm, so A = (6cm). Now subtract! 6. No matter w hat shape the base of a prism is, the Volume of the prism is just the product: (Area of base) (Height) 7. No matter w hat shape the base of a pyramid is, the Volume of the pyramid is just (one third) the volume of the corresponding prism (See #6 note above!) These ideas apply to cylinders and cones as well. 8a. Volume of cone = ( a) (Area of Base)(Height) [see note above!] Finding the surface area of cone is similar to surface of pyramid. Pyramids have lateral faces that are triangular. The area of each triangle is (½ )(base length)(height)... When these are added up around the pyramid, the total (for lateral surface area) is (½ ) (Perimeter of base) (slant height). [See more details on the answ ers to the Surface Area Quiz).] Similarly, the lateral surface area of a cone is (½)(Perimeter of Base of cone)(slant height of cone) 9. The entire wheel of brie has the shape of a right circular cylinder, with height of only cm. A w edge w hich is one-sixth of the w heel has volume = one-sixth of the w heel. A w edge w ith a central angle of contains only one-tw elfth of the w heel, since 60 = 1. The Surface Area consists of three parts: The top and bottom of the w edge are surfaces in the shape of a sector of a circle (radius 15cm). Thus the area is (PART) (15cm) In part a, this is (1/6) (15cm). The bottom has the same area. The remaining surface of the w edge might be covered w ith a strip of paper cm high. The length w ould be ((radius) + (1/6) (Circumference) cm Part of Circumference ((15cm) + (1/6) ( (15cm) ) So the total lateral area is (cm) ((15cm) + (1/6) ( (15cm)) 15cm The total surface area of the 1/6-w heel w edge of brie is: (1/6) (15cm) + (cm) ((15cm) + (1/6) ( (15cm)) (For the 0 w edge of brie, replace (1/6) w ith (1/1) in all parts!)

4 10. Finding the total surface area and volume of an ice cream cone, topped w ith a hemisphere of ice cream, given the diameter of the top of the cone is 10 cm. and the height of the cone is 1 cm. Volume = V + V = (½) ( /) (r) + (a) (r) (h) = (½) ( /) (5cm) + (a) (5cm) (1cm) = (550 /)cm hemisphere 4 cone 4 Surface Area = SA hemisphere + Lateral SA cone = (½) 4 r + (½ ) r (h) = (½) 4 (5cm) + (½ ) (5cm) (1cm) 11. Was/w ill be discussed in class. 1. Don t be intimidated by the number of steps here. See how each multiplication just gives you new units. 1 kl = 1 kl 1000L 1000 ml 1 cc 1g* 1 kg 1 metric ton 1 kl 1 L 1mL cc 1000g 1000 kg = 1 metric ton For instance, if w e pause right here, w e see that w e now have L (liters) and since w e know a conversion from milliliters (ml) to cc to grams*, we continue by converting the liters to milliliters. Then w e need, at THIS POINT, to get from grams to kilograms, then to tons. 1g = 1cc...valid ONLY for w ater at 4 C 14. b. 1 ft = (1 in) = 144 in Using dimensional analysis: 1 ft = 1 ft 1 in 1 in = 144in )))) )))) 1 ft 1 ft * One foot * Using common sense : This 1-foot by 1-foot square is a square foot. One ft 1 1 (ie 144) square inches are required to cover this square foot! ONE square inch 1a. PERIMETER: 1a. We have a semi-circular arc of a circle with D= 8mm, and a full circle with diameter 4mm, 8mm )))) In addition to tw o straight sides of length 8mm each. So the full perimeter is 8mm )))) 6mm P = (½) 8mm + (4mm) + 8mm + 8mm = (8 + 16) mm 1b If the sides w ere horizontal and vertical, w e could just count the units of length on each side. But none of the sides are horizontal or vertical, So w e must compute the length of each side, using the Pythagorean thm Each side of the given triangle is the hypotenuse of a right triangle w ith horizontal & vertical sides. For instance, the upper left side of the given triangle is the hypotenuse of the shaded triangle. The shaded triangle is 4 units high & units w ide, so its hypotenuse must be... 5units long. For the upper right side: + 1 = c, so c = 1 0 P = units.

5 15. Find the longest diagonal inside a 4" by 7" by 7" right rectangular prism. (BOX!) The diagonal on the base of the box: (4") + (7") = c 576 in + 49in 65 in = c 7" D 5 in = c 4" c + (7in) = D (5in) + 49in = c 7" 674in = D in D 16. Explain w hy the answ er to #16 is NOT just.5 times the old area! The scale factor applies to both dimensions that contribute to area: height and w idth. The scale factor is the ratio of new lengths to old, so the ratio of (New height)/(old height)=.5 and the ratio of (New w idth)/(old w idth) is also.5. New Area = (Old Area) (Ratio of New height to Old height) (Ratio of New w idth to Old w idth) = (Old area) (scale factor) (scale factor) If you think in terms of the simplest area (think rectangle), this is obvious. D x by y.5x by.5y It becomes even more obvious when scaled up by a factor which is a whole number, say : x by y x by y: Area is 9 times as great.

MATH 310 TEST Measure April Answers

MATH 310 TEST Measure April Answers MATH 310 TEST Measure April 25 2007 Answers 1. Use t he draw ing below to illust rat e the relat ionship betw een cubic yards and cubic f eet. 2. Show the dimensional analysis for the conversion of 2 cubic

More information

1 yd 2 1 yd 2 3 ft 3 ft = ))))) x ))))) x ))))) = 9 sq. ft yd yd. 60 yd 2 60 yd 2 3 ft 3 ft = ))))) x ))))) x ))))) = 540 ft 2 yd yd.

1 yd 2 1 yd 2 3 ft 3 ft = ))))) x ))))) x ))))) = 9 sq. ft yd yd. 60 yd 2 60 yd 2 3 ft 3 ft = ))))) x ))))) x ))))) = 540 ft 2 yd yd. MATH 310 TEST Measure April 5 2006 ANSWERS (6)1a. 1 yard (or 3 feet) Draw a sket ch w hich illust rat es the relat ionship betw een square yards and square feet. 1b. Show the dimensional analysis f or

More information

Section Volume, Mass, and Temperature

Section Volume, Mass, and Temperature Section 11.5 - Volume, Mass, and Temperature Surface Area is the number of square units covering a three dimensional figure; Volume describes how much space a three-dimensional figure contains. The unit

More information

( ) ) in 2 ( ) ) in 3

( ) ) in 2 ( ) ) in 3 Chapter 1 Test Review Question Answers 1. Find the total surface area and volume of a cube in which the diagonal measures yards. x + x ) = ) x = x x A T.S. = bh) = ) ) = 1 yd V = BH = bh)h = ) ) ) = yd.

More information

resources Symbols < is less than > is greater than is less than or equal to is greater than or equal to = is equal to is not equal to

resources Symbols < is less than > is greater than is less than or equal to is greater than or equal to = is equal to is not equal to Symbols < is less than > is greater than is less than or equal to is greater than or equal to resources = is equal to is not equal to is approximately equal to similar a absolute value: = ; - = (x, y)

More information

MENSURATION. Mensuration is the measurement of lines, areas, and volumes. Before, you start this pack, you need to know the following facts.

MENSURATION. Mensuration is the measurement of lines, areas, and volumes. Before, you start this pack, you need to know the following facts. MENSURATION Mensuration is the measurement of lines, areas, and volumes. Before, you start this pack, you need to know the following facts. When you see kilo, it indicates 000 in length, mass and capacity.

More information

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked

More information

English Measurement Relationships

English Measurement Relationships Math 30 Prealgebra Sec 10.1: Using Unit Fractions with U.S. and Metric Units Defn A unit fraction is a fraction that shows the relationship between units and is equal to 1. Ex English Measurement Relationships

More information

Dividing in Scientific Notation Name (page 778)

Dividing in Scientific Notation Name (page 778) LESSON 111 Dividing in Scientific Notation Name (page 778) To divide powers of 10, subtract the exponents. 10 7 10 4 = 10 7 4 = 10 3 To divide numbers in scientific notation: 1. Divide the decimal or whole

More information

The GED math test gives you a page of math formulas that

The GED math test gives you a page of math formulas that Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

More information

Answer Keys for Calvert Math

Answer Keys for Calvert Math Answer Keys for Calvert Math Lessons CMAKF- Contents Math Textbook... Math Workbook... Math Manual... Answer Keys Math Textbook Lessons Math Textbook Answer Key Lessons. Area and Circumference of Circles

More information

Grade 11 Mathematics Practice Test

Grade 11 Mathematics Practice Test Grade Mathematics Practice Test Nebraska Department of Education 204 Directions: On the following pages are multiple-choice questions for the Grade Practice Test, a practice opportunity for the Nebraska

More information

In problems #2 through #6, round your answers to the nearest tenth if necessary.

In problems #2 through #6, round your answers to the nearest tenth if necessary. Math 254CM Name Essential Mathematics Date Study Guide #5 Exam #5 is closed book. You will be given the Geometry handout and the Measurements handout. You may use a calculator on this exam. You must show

More information

New Rochelle High School Geometry Summer Assignment

New Rochelle High School Geometry Summer Assignment NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and

More information

Investigation Find the area of the triangle. (See student text.)

Investigation Find the area of the triangle. (See student text.) Selected ACE: Looking For Pythagoras Investigation 1: #20, #32. Investigation 2: #18, #38, #42. Investigation 3: #8, #14, #18. Investigation 4: #12, #15, #23. ACE Problem Investigation 1 20. Find the area

More information

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Red Accelerated Worked-Out Solutions 4 7 = = 4 49 = = 39 = = 3 81 = 243

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Red Accelerated Worked-Out Solutions 4 7 = = 4 49 = = 39 = = 3 81 = 243 Chapter 8 Opener Try It Yourself (p. 35). trapezoids. circles Large Perimeter Diameter Small Perimeter Diameter Average of Ratios 3. trapezoid, triangle. triangles 5. rectangle, triangle 6. rectangle,

More information

Topic 8: Measurement

Topic 8: Measurement 137 Topic 8: Measurement Topic 1 Integers Topic 2 Decimals Topic 3 Fractions Topic 4 Ratios Topic 5 Percentages Topic 6 Algebra Topic 7 Equations and Formulae Topic 8 Measurement Duration 2 weeks Content

More information

Georgia High School Graduation Test

Georgia High School Graduation Test Strand: Measurements & Geometry Georgia High School Graduation Test 1. Measurements & Geometry Definitions. inches A. Describe something that has a length of about 1 inch. B. Describe something that has

More information

California 5 th Grade Standards / Excel Math Correlation by Lesson Number

California 5 th Grade Standards / Excel Math Correlation by Lesson Number (Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with

More information

CCR Math - Grade 7 Practice Test

CCR Math - Grade 7 Practice Test R Math - Grade 7 Practice Test You may use a calculator for questions -7.. Use the picture below to answer the question. A B What is the probability of spinning a? A. B.. D. 5 3 5 3 5 A 3 Go on to the

More information

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior

More information

Geometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH!

Geometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! Geometry: Hutschenreuter Semester II Review B Name Period Date Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! 1. A parallelogram has a diagonal of 41 cm and side

More information

Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8

Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8 Kansas City Area Teachers of Mathematics 2013 KCATM Math Competition GEOMETRY GRADES 7-8 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators.

More information

5-7 The Pythagorean Theorem

5-7 The Pythagorean Theorem 5-7 The Pythagorean Theorem Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Classify each triangle by its angle measures. 1. 2. acute right 3. Simplify 12 4. If a = 6, b = 7, and c = 12, find

More information

LESSON 2: TRIANGULAR PRISMS, CYLINDERS, AND SPHERES. Unit 9: Figures and Solids

LESSON 2: TRIANGULAR PRISMS, CYLINDERS, AND SPHERES. Unit 9: Figures and Solids LESSON 2: TRIANGULAR PRISMS, CYLINDERS, AND SPHERES Unit 9: Figures and Solids base parallel two The sum of the area of the lateral faces (al sides except for the bases) The sum of all the area (lateral

More information

Summer Packet Pre-AP Algebra

Summer Packet Pre-AP Algebra Name: (5/11/17) Summer Packet Pre-AP Algebra 1-2018-19 To receive credit all work must be shown. There will be a test the first week back from summer on this packet. Any work done on additional paper must

More information

AREA. The Square Inch The Square Foot The Square Yard. 1 foot. 1 foot. The Square Mile The Square Meter The Square Centimeter. 1 meter.

AREA. The Square Inch The Square Foot The Square Yard. 1 foot. 1 foot. The Square Mile The Square Meter The Square Centimeter. 1 meter. Tallahassee Community College 48 AREA The area of a figure measures the surface of the figure. The unit of measure for area cannot be a linear unit. To measure area we use square units such as: The Square

More information

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD

1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD Chapter. Geometry Problems. LINE SEGMENTS Theorem : If ABC A B C, then the ratio of the areas is as follows: S ABC a b c ( ) ( ) ( ) S a b A BC c a a b c and b c Theorem : If DE//BC, then ABC ADE and AD

More information

Math-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms

Math-2A. Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms Math-A Lesson 10-3: Area of: -Triangles -rectangles -circles -trapezoids and Surface Area of: -Rectangular Prisms Describe the idea of area. Area attempts to answer the question how big is it? The area

More information

Grade 6 Mathematics Practice Test

Grade 6 Mathematics Practice Test Grade 6 Mathematics Practice Test Nebraska Department of Education 206 Directions: On the following pages are questions for the Grade 6 Practice Test, a practice opportunity for the Nebraska State Accountability

More information

PRACTICE TEST 1 Math Level IC

PRACTICE TEST 1 Math Level IC SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface

More information

Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning

Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia

More information

Math 005A Prerequisite Material Answer Key

Math 005A Prerequisite Material Answer Key Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)

More information

Kg hg dag g dg cg mg. Km hm dam m dm cm mm

Kg hg dag g dg cg mg. Km hm dam m dm cm mm Metric System Conversions Mass (g = gram) 0 0 0 0 0 0 Kg hg dag g dg cg mg 0 0 0 0 0 0 Distance or Length ( m = metre) 0 0 0 0 0 0 Km hm dam m dm cm mm 0 0 0 0 0 0 Area (m = square metre) 00 00 00 00 00

More information

Circle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral

Circle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral The angle in a semi-circle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must

More information

Measurement Year 9. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used.

Measurement Year 9. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Measurement Year 9 The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Precision and Estimation In general students should

More information

Customary Units of Measurement

Customary Units of Measurement Customary Units of Measurement What would it be like to have no system of measurement? If we are to measure something, we need a unit of measure. standard unit of measure: one that people have agreed to

More information

Number Sets 1,0,1,2,3,... } 3. Rational Numbers ( Q) 1. Natural Numbers ( N) A number is a rational number if. it can be written as where a and

Number Sets 1,0,1,2,3,... } 3. Rational Numbers ( Q) 1. Natural Numbers ( N) A number is a rational number if. it can be written as where a and Number Sets 1. Natural Numbers ( N) N { 0,1,,,... } This set is often referred to as the counting numbers that include zero.. Integers ( Z) Z {...,,, 1,0,1,,,... }. Rational Numbers ( Q) A number is a

More information

Alaska Mathematics Standards Vocabulary Word List Grade 4

Alaska Mathematics Standards Vocabulary Word List Grade 4 1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal

More information

Sect Formulas and Applications of Geometry:

Sect Formulas and Applications of Geometry: 72 Sect 2.6 - Formulas and Applications of Geometry: Concept # Solving Literal Equations for a particular variable. Now, we will examine solving formulas for a particular variable. Sometimes it is useful

More information

Applications Using Factoring Polynomials

Applications Using Factoring Polynomials Applications Using Factoring Polynomials This section will discuss applications involving the area of a rectangle, consecutive integers, and right triangles. Recall the steps that will help to translate

More information

Preliminary chapter: Review of previous coursework. Objectives

Preliminary chapter: Review of previous coursework. Objectives Preliminary chapter: Review of previous coursework Objectives By the end of this chapter the student should be able to recall, from Books 1 and 2 of New General Mathematics, the facts and methods that

More information

Grades 6 8 FCAT 2.0 Mathematics Reference Sheet

Grades 6 8 FCAT 2.0 Mathematics Reference Sheet Grades FCAT. Mathematics Reference Sheet Rectangle A bh Parallelogram A bh Triangle Trapezoid Area A A bh Circle A π r h (b b ) b h w d r base height width diameter radius slant height KEY A B C P S.A.

More information

COMMON UNITS OF PERIMITER ARE METRE

COMMON UNITS OF PERIMITER ARE METRE MENSURATION BASIC CONCEPTS: 1.1 PERIMETERS AND AREAS OF PLANE FIGURES: PERIMETER AND AREA The perimeter of a plane figure is the total length of its boundary. The area of a plane figure is the amount of

More information

The Metric System and Measurement

The Metric System and Measurement The Metric System and Measurement Introduction The metric system is the world standard for measurement. Not only is it used by scientists throughout the world, but most nations have adopted it as their

More information

Chapter 8 Solids. Pyramids. This is a square pyramid. Draw this figure and write names of edges. Height and Slant Height.

Chapter 8 Solids. Pyramids. This is a square pyramid. Draw this figure and write names of edges. Height and Slant Height. Chapter 8 Solids Pyramids This is a square pyramid. Draw this figure and write names of edges. Height and Slant Height Right angles of Square Pyramid. Write 1 problem of page 193 Answer: Area of square

More information

Odd numbers 4 2 = 4 X 4 = 16

Odd numbers 4 2 = 4 X 4 = 16 Even numbers Square numbers 2, 4, 6, 8, 10, 12, 1 2 = 1 x 1 = 1 2 divides exactly into every even number. 2 2 = 2 x 2 = 4 3 2 = 3 x 3 = 9 Odd numbers 4 2 = 4 X 4 = 16 5 2 = 5 X 5 = 25 1, 3, 5, 7, 11, 6

More information

6 th Grade Math Connects

6 th Grade Math Connects 6 th Grade Math Connects Chapter 1: Multiply and Divide Decimals Multi-Part Lesson 1: Multiply Decimals A: Estimate Products B: Explore Multiply Decimals by Whole Numbers C: Multiply Decimals by Whole

More information

Math Round. Any figure shown may not be drawn to scale.

Math Round. Any figure shown may not be drawn to scale. Indiana Academic Super Bowl Math Round 2019 Coaches Practice A Program of the Indiana Association of School Principals Students: Throughout this round we will be pronouncing mathematic symbols and concepts

More information

Ratio Problems Involving Name Totals (page 528)

Ratio Problems Involving Name Totals (page 528) LESSON 101 Ratio Problems Involving Name Totals (page 528) In some ratio problems a total is needed in order to solve the problem. 1. Fill in the ratio box with things you know. 2. Write a proportion.

More information

Chapter 2 Polynomial and Rational Functions

Chapter 2 Polynomial and Rational Functions SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear

More information

Thanks for downloading this product from Time Flies!

Thanks for downloading this product from Time Flies! Thanks for downloading this product from Time Flies! I hope you enjoy using this product. Follow me at my TpT store! My Store: https://www.teacherspayteachers.com/store/time-flies 2018 Time Flies. All

More information

Kansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7

Kansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7 Kansas City Area Teachers of Mathematics 2015 KCATM Math Competition GEOMETRY GRADE 7 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use calculators. Mark

More information

8 Mathematics STAAR. Test Practice. Texas. e S

8 Mathematics STAAR. Test Practice. Texas. e S Texas 8 Mathematics STAAR TM Test Practice ple Page m s Sa STAAR Ready will prepare students for the new, more rigorous STAAR test with STAAR Ready Test Practice, STAAR Ready Instruction, and STAAR i-ready.

More information

Measurement Year 11. Rounding

Measurement Year 11. Rounding Measurement Year 11 Rounding Do not round early. Students should carry all decimal places in working until the end of their calculations. They should then give their answers sensibly rounded. An answer

More information

Mathematics Conversions/Formula. S.A. 2 r. cylinder. V cone S.A. 4. sphere

Mathematics Conversions/Formula. S.A. 2 r. cylinder. V cone S.A. 4. sphere Mathematics 1201 Midterm Review 2015 Unit I: Measurement Conversions/Formula 1 ft. = 12 in. 1 in. = 2.5 cm 2 S.A. 2r 2rh cylinder V pyramid 1 (area of base)(height) 1 yd. = ft. 1 mi. = 1.6 km 2 S.A. cone

More information

Unit 1 - INTRODUCTION MEDICAL MATH Listening guide

Unit 1 - INTRODUCTION MEDICAL MATH Listening guide Unit 1 - INTRODUCTION MEDICAL MATH Listening guide Name Period 1. List one important reason that healthcare workers must be proficient in math. 2. Number forms: 3. Basic math: Counting numbers and zero

More information

Chapter 5: Measurement of Circles

Chapter 5: Measurement of Circles Chapter 5: Measurement of Circles Getting Started, p. 151 1. a) Perimeter, since the word around is used. b) Area, since since the word wrap is used. c) Perimeter, since the word wrap is used. 2. a) 5

More information

University of Houston High School Mathematics Contest Geometry Exam Spring 2015

University of Houston High School Mathematics Contest Geometry Exam Spring 2015 University of Houston High School Mathematics Contest Geometry Exam Spring 2015 Note that diagrams may not be drawn to scale. 1. A pool has a 4 foot wide sidewalk around it. If the pool is 28 feet long

More information

I.G.C.S.E. Volume & Surface Area. You can access the solutions from the end of each question

I.G.C.S.E. Volume & Surface Area. You can access the solutions from the end of each question I.G.C.S.E. Volume & Surface Area Index: Please click on the question number you want Question 1 Question Question Question 4 Question 5 Question 6 Question 7 Question 8 You can access the solutions from

More information

Be prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square.

Be prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square. Math 254SI Practice Problem Set 5 (Chapter 8&9) Do these problems on a separate piece of paper(s). Remember that the quiz is closed book and closed notes except for the Geometry handout that I will provide.

More information

Math Self-Test Version Form A Measurement and Geometry

Math Self-Test Version Form A Measurement and Geometry Math Self-Test Version 0.1.1 Form A Measurement and Geometry Draw each object and describe the key characteristics that define the object. [3 pts. each] 1) Acute Triangle 2) Arc 3) Chord 4) Cube 5) Cylinder

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

Mesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc. Page 1 of 44

Mesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc.   Page 1 of 44 Mesa Public Schools Assessment Summary: Q3 practice test Powered by SchoolCity Inc. www.schoolcity.com Page 1 of 44 Assessment Summary: Q3 practice test Year: 2016-2017 Subject: Math Total Items: 43 Total

More information

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 5 NUMBER AND NUMBER SENSE 5.1 The student will a. read, write, and identify the place values

More information

Technique 1: Volumes by Slicing

Technique 1: Volumes by Slicing Finding Volumes of Solids We have used integrals to find the areas of regions under curves; it may not seem obvious at first, but we can actually use similar methods to find volumes of certain types of

More information

11.3 areas of circles and sectors 2016 ink.notebook. April 12, Page 134 Page Areas of Circles and Sectors. Standards.

11.3 areas of circles and sectors 2016 ink.notebook. April 12, Page 134 Page Areas of Circles and Sectors. Standards. 11.3 areas of circles and sectors 2016 ink.notebook Page 134 Page 133 11.3 Areas of Circles and Sectors Round to the nearest Lesson Objectives Standards Lesson Notes 11.3 Areas of Circles and Sectors Lesson

More information

Circles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume

Circles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume Analytical Geometry Circles and Volume Circles and Volume There is something so special about a circle. It is a very efficient shape. There is no beginning, no end. Every point on the edge is the same

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MGF 1106 Exam #3 Review Sheet Chapters 8-9 Fill in the missing value. 1) 816 mm = cm 2) 54.96 m = km 3) 492 L = ml 4) 800 mg = kg 5) 25 kg = mg Arrange the quantities in order from smallest to largest.

More information

NUMERACY TOOLKIT TOOLKIT NUMERACY

NUMERACY TOOLKIT TOOLKIT NUMERACY NUMERACY TOOLKIT TOOLKIT NUMERACY Addition Calculating methods Example 534 + 2678 Place the digits in the correct place value columns with the numbers under each other. Th H T U Begin adding in the units

More information

Modeling with Volume

Modeling with Volume 1.2 Modeling with Essential Question How can you use the mass and volume of an object to describe the density of the object? Finding Densities Work with a partner. Approximate the volume of each object

More information

Grade 7/8 Math Circles Fall Nov. 4/5 Solution Set - The Pythagorean Theorem

Grade 7/8 Math Circles Fall Nov. 4/5 Solution Set - The Pythagorean Theorem 1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 014 - Nov. 4/5 Solution Set - The Pythagorean Theorem 1. Let a and b be the lengths

More information

Grade 11 Mathematics Practice Test

Grade 11 Mathematics Practice Test Grade Mathematics Practice Test Nebraska Department of Education 00 Directions: On the following pages are multiple-choice questions for the Grade Practice Test, a practice opportunit for the Nebraska

More information

Domain: Cluster: Level: Mathematical Content Standard: Featured Mathematical Correlated WA Standard: Practice:

Domain: Cluster: Level: Mathematical Content Standard: Featured Mathematical Correlated WA Standard: Practice: Domain: 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

More information

May 05, surface area and volume of spheres ink.notebook. Page 171. Page Surface Area and Volume of Spheres.

May 05, surface area and volume of spheres ink.notebook. Page 171. Page Surface Area and Volume of Spheres. 12.6 surface area and volume of spheres ink.notebook Page 171 Page 172 12.6 Surface Area and Volume of Spheres Page 173 Page 174 Page 175 1 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards

More information

Measurement Year 10. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used.

Measurement Year 10. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Measurement Year 10 The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Precision and Estimation In general students should

More information

Surface Areas of Prisms and Cylinders. Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary.

Surface Areas of Prisms and Cylinders. Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary. 12-2 Skills Practice Surface Areas of Prisms and Cylinders Find the lateral area and surface area of each prism. Round to the nearest tenth if necessary. 12 yd 6 m 12 yd 10 yd 8 m 12 m 3. 4. 6 in. 8 in.

More information

Algebra 2 End of Course Review

Algebra 2 End of Course Review 1 Natural numbers are not just whole numbers. Integers are all whole numbers both positive and negative. Rational or fractional numbers are all fractional types and are considered ratios because they divide

More information

Calculating methods. Addition. Multiplication. Th H T U Th H T U = Example

Calculating methods. Addition. Multiplication. Th H T U Th H T U = Example 1 Addition Calculating methods Example 534 + 2678 Place the digits in the correct place value columns with the numbers under each other. Th H T U Begin adding in the units column. 5 3 4 + 12 16 17 8 4+8

More information

Grade 7 Mathematics Practice Test

Grade 7 Mathematics Practice Test Grade 7 Mathematics Practice Test Nebraska Department of Education 2014 Directions: On the following pages are multiple-choice questions for the Grade 7 Practice Test, a practice opportunity for the Nebraska

More information

T H E A L G E B R A G L O S S A R Y

T H E A L G E B R A G L O S S A R Y T H E A L G E B R A G L O S S A R Y Absolute Value A The distance from a number to 0 on the number line, and denoted with vertical bars. Examples: 7 = 7 6 = 6 0 = 0 Notice that, since distance is never

More information

MCA/GRAD Formula Review Packet

MCA/GRAD Formula Review Packet MCA/GRAD Formula Review Packet 1 2 3 4 5 6 The MCA-II / BHS 2 Math Plan GRAD Page 1 of 16 Portions Copyright 2005 by Claude Paradis 8 9 10 12 11 13 14 15 16 1 18 19 20 21 The MCA-II / BHS 2 Math Plan GRAD

More information

Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles

Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean

More information

Chapter Start Thinking. 10π 31.4 cm. 1. 5π 15.7 cm 2. 5 π 7.9 cm π 13.1 cm Warm Up , 8π 2. 90,15π 3.

Chapter Start Thinking. 10π 31.4 cm. 1. 5π 15.7 cm 2. 5 π 7.9 cm π 13.1 cm Warm Up , 8π 2. 90,15π 3. x = 8andx = 7 8. x = andx = 7. x = 0. x = 10 x = 11. x = 18. x =. x = 8 x = 1. x = x = 1 8. x = 175. 0. 5 8.. 8. 1. 18 8. a. x + 11 b. c. 11 d. 17. (, ) 50. 5 15 7, 5, 11, 1 7, 5 1, 5 1 1, 11, 5 75 58.

More information

1. Use. What are the vertices of A.,, B.,, C.,, D.,,

1. Use. What are the vertices of A.,, B.,, C.,, D.,, 1. Use. What are the vertices of A.,, B.,, C.,, D.,, 2. Given, how are the distances to the origin from each image point related to the distance to the origin from each corresponding preimage point? A.

More information

Expressions and the Number System

Expressions and the Number System Name: 8 th Grade Math 1 st Semester Review Pd: Expressions and the Number System 1. A square rug has an area of 225 square feet. How long is each side of the rug? A 15 feet B 22.5 feet C 23 feet D 25 feet

More information

Name: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?

Name: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane? GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and

More information

1~ 5~ 10~ 25~ $0.01 $0.05 $0.10 $0.25 ~ Write at least 5 'names in. the D.box~. - D. Work Box. Ten how you solved this problem.

1~ 5~ 10~ 25~ $0.01 $0.05 $0.10 $0.25 ~ Write at least 5 'names in. the D.box~. - D. Work Box. Ten how you solved this problem. Work Box MATHlOG Ten how you solved this problem Write at least 5 'names in the Dbox~ - D ~' : ' - ' :- @ @ @ @ 1~ 5~ 10~ 25~ $001 $005 $010 $025 ~! ~ ::i: ; '! ~ - ~ ' ~ ~ ~ -~ ~ ~ DO '"

More information

Newbattle Community High School National 5 Mathematics. Key Facts Q&A

Newbattle Community High School National 5 Mathematics. Key Facts Q&A Key Facts Q&A Ways of using this booklet: 1) Write the questions on cards with the answers on the back and test yourself. ) Work with a friend who is also doing National 5 Maths to take turns reading a

More information

Geometric Formulas (page 474) Name

Geometric Formulas (page 474) Name LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:

More information

Academic Challenge 2012 Regional Math Solutions. (x 2)(x 3) 2. Ans C: As the rational expression for f(x) everywhere x is not 3 factors into

Academic Challenge 2012 Regional Math Solutions. (x 2)(x 3) 2. Ans C: As the rational expression for f(x) everywhere x is not 3 factors into Academic Challenge 0 Regional Math Solutions Ans C: 8 4 ( 70)( 55) = = 4 9 7 6 ( )( ) Ans C: As the rational epression for f() everywhere is not factors into, it is evident that f() = ecept at = Thus,

More information

AP CALCULUS Summer Assignment 2014

AP CALCULUS Summer Assignment 2014 Name AP CALCULUS Summer Assignment 014 Welcome to AP Calculus. In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work this summer. The following assignment

More information

= = =

= = = . D - To evaluate the expression, we can regroup the numbers and the powers of ten, multiply, and adjust the decimal and exponent to put the answer in correct scientific notation format: 5 0 0 7 = 5 0

More information

MCAS Review - Measurement Session 4A

MCAS Review - Measurement Session 4A lass: ate: I: MS Review - Measurement Session 4 Multiple hoice Identify the choice that best completes the statement or answers the question. 1 circle has an area of 16π square centimeters. What is the

More information

Chapter 6. Ratio, Proportion and Measurement

Chapter 6. Ratio, Proportion and Measurement Chapter 6. Ratio, Proportion and Measurement 6.1 Ratios 6.2 Proportion 6.3 American Units of Measurement 6.4 Metric Units of Measurement 6.5 Converting between American and Metric Units 1 6.1 Ratios 1.

More information

Analysis of California Mathematics standards to Common Core standards-grade 3

Analysis of California Mathematics standards to Common Core standards-grade 3 Analysis of California Mathematics standards to Common Core standards-grade 3 Strand CA Math Standard Domain Common Core Standard (CCS) Alignment Comments in reference to CCS 1.0 Number Sense 1.0 Students

More information

Algebra I. Exponents and Polynomials. Name

Algebra I. Exponents and Polynomials. Name Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT

More information

Taking away works in exactly the same way as adding. The only difference is that the final answer has a take away sign in place of the add sign.

Taking away works in exactly the same way as adding. The only difference is that the final answer has a take away sign in place of the add sign. Taking away works in exactly the same way as adding. The only difference is that the final answer has a take away sign in place of the add sign. Example Take away, giving your answer as a single fraction

More information

6 th Grade Math. Full Curriculum Book. Sample file. A+ Interactive Math (by A+ TutorSoft, Inc.)

6 th Grade Math. Full Curriculum Book. Sample file. A+ Interactive Math (by A+ TutorSoft, Inc.) 6 th Grade Math Full Curriculum Book Release 7 A+ Interactive Math (by A+ TutorSoft, Inc.) Email: info@aplustutorsoft.com www.aplustutorsoft.com Page 3 of 518 Copyright 2014 A+ TutorSoft Inc., All Rights

More information

8 th Grade Math Connects

8 th Grade Math Connects 8 th Grade Math Connects Chapter 1: Rational Numbers and Percent Multi-Part Lesson 1: Rational Numbers A: Rational Numbers B: Add and Subtract Rational Numbers C: Multiply Rational Numbers D: Divide Rational

More information