Mathematics. Guide GEO Extended answer Problem solving GEO.02 Extended answer Problem solving
|
|
- Joseph Clark
- 6 years ago
- Views:
Transcription
1 1- Contents Mathematics Guide Question Item Objective Type Skill GEO Multiple-choice answer Applications GEO Extended answer Problem solving GEO.02 Extended answer Problem solving GEO Multiple-choice answer Applications GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving GEO.02 Extended answer Applications GEO Extended answer Problem solving GEO.02 Extended answer Applications GEO.02 Extended answer Problem solving GEO.02 Extended answer Concepts GEO.02 Extended answer Problem solving GEO.02 Extended answer Problem solving
2 GEO.02 Extended answer Problem solving 2- Correction key A
3 2 Example of an appropriate solution Find the measure of BON: m MOA = m BON = = 13 2 Find the measure of MAO: m MAO = 180 ( ) = 107 Find the measure of segment AO: sin ( MAO) sin ( AMO) m MO ( 107 ) sin ( 60 ) sin 100 cm = = m AO = m AO m AO sin m AO ( 60 ) sin ( 107 ) cm m AO cm Find the measure of OAB: m OAB = = 73 Find the measure of ABO: 100 cm m ABO = 180 ( ) = 43 Find the measure of segment AB:
4 Answer: Note: sin ( ABO) sin ( AOB) m AO = ( 43 ) sin ( 64 ) sin = cm m AB = m AB m AB sin m AB ( 64 ) sin ( 43 ) cm m AB cm cm From Point A to Point B, the marble travelled cm Accept answers in the range [119, 120]. A student can also approach this solution by finding the measure of segment BO instead of segment AO. A student can also approach this solution by finding 200 ( m MA + m BN). Students who have found the measure of either segment AO or segment BO have shown they have a partial understanding of the problem.
5 3 Example of an appropriate method Measure of CBD 180 ( ) = 60 Length of segment BD m BD sin 35 = 5.2 sin 60 m BD = metres Length of segment AB m AB = cos m AB = metres Length of segment BE Answer: Note: m BE = 2.5(3.326) = To the nearest tenth of a metre, pole BE measures 8.3 metres. The student who determined the length of BD, 3.44 metres, has demonstrated a partial understanding of the problem.
6 4 A
7 5 Example of an appropriate method SRL = 55 (corresponding angles, parallel lines) In small SLR 1030 m sin 55 = m SR m SR sin 55 = 1030 m 1030 m m SR = sin 55 m SR = m In the large SMB cos 55 = 980 m m SB m SB cos 55 = 980 m 980 m m SB = cos 55 m SB = m m RB = ( ) m m RB = 451
8 6 Answer: Because there are many ways to do this problem, and answers will vary as a result of rounding, accept 450 m to 453 m. Example of an appropriate method Order lengths of fencing and divide into quintiles: Using Hero's formula to find area of triangle: Answer: A = 34( 34 20)( 34 21)( 34 27) = = = Rupert will enclose m 2 of land. Note: Do not deduct any marks for incorrect rounding.
9 7 Example of an appropriate solution Matthew's route Distance from town A to cabin x cos 25 = 125 x Distance from cabin to town B x sin 25 = 125 x Total distance Difference in distances Answer: = km = km Cynthia's route Measure of angle A = sin A sin 120 sin A m A Measure of angle B 180 ( ) = Distance from town A to restaurant 125 b = sin 120 sin b Total distance = km To the nearest tenth, the difference between the two routes is 23.9 km.
10 Note: Accept answers in the range of 23.8 km to 24 km.
11 8 Example of an appropriate method Length of segment AD cos 20 = m AD 7.5 m AD = Measure of angle ABD m ABD = 180 m BAD m BDA m ABD = m ABD = 130 Length of segment BD m BD = sin BAD m BD = sin 20 m AD sin ABD sin 130 m BD Answer: Rounded to the nearest tenth, the length of the beam represented by segment BD is 3.1 m. Note: Students who use an appropriate method in order to determine the length of segment AD have shown that they have a partial understanding of the problem.
12 Do not penalize students who did not round off their final answer or who made a mistake in rounding it off.
13 9 Example of an appropriate solution Measure of side CD cos 26 = m CD 18 m CD Area of triangle ADC A Measure of angle B b h = m B = 180 ( ) = 68 Measure of segment AB 18 = sin 68 m AB sin 34 m AB Measure of segment BC m BC = sin sin 68 m BC C D 18 m 7.89 m A 78 B
14 Area of triangle ABC Perimeter = perimeter = p 2 A = p (p a) (p b) (p c) A ( )( )( ) A Total area of plot Answer: m 2 Helen will need to buy 160 pieces of sods of grass.
15 10 Example of an appropriate method Measure of segment AC tan 65 = 15 m AC 15 m AC = tan 65 m AC = Measure of segment BC m BC 7 4 = 3 Angle of elevation of point B 15 tan B = 3 tan B = 5 m B = Answer: The angle of elevation of the observer located at B is 79. A 65? 4 m B D C 15 m
16 11 Example of an appropriate method Height h 1 Height h 2 h1 tan 40 = 15 h 1 = 15 tan 40 h h2 tan 28 = 15 h 2 = 15 tan 28 h Height of the building h 1 + h Answer: The height of the building is m m 40 h 2 h 1
17 12 Example of an appropriate method Area of rectangle A = L l A = A = 5000 Area of triangle Total area Heron's formula: p(p a)(p b)(p c) A = Asking price A (117 50)(117 72)( ) A t = Area of rectangle + area of triangle A t = Price A t 1.35 = Answer: To purchase this property, Julio must pay $ Accept any answer in the interval [$ , $ ] also.
18
19 13 Example of an appropriate method of solution Measure of BC 64.3 m BC = sin 100 sin 30 m BC Perimeter of triangle ABC = s = semi-perimeter s Area of triangle ABC A 73.47( )( )( ) (Heron's formula) Answer Rounded to the nearest m 2, the area of the plot of land is 804 m 2. Accept an answer in the interval [803, 804].
20 Alternate solution: By drawing an altitude BD from B to AC, as shown in the diagram, and using the 1 fact that it is opposite a 30 angle, we find m BD to be (50) = 25 m. 2 Using the formula for the area of a triangle 2 1 Base Altitude we obtain 2 1 (25)(64.3) = Area of plot of land to the nearest m 2 is 804 m 2 A 50 m B 64.3 m D C
21 14 Example of an appropriate algebraic solution Krystal's distance from the base of the house tan 20 = m AB = 4 m AB 4 tan 20 Height of Krystal's house tan 40 = m BD m m BD = tan m Distance from window to the roof of the house m BD m BC = = m Answer The distance from window to the roof of the house is 5.2 m.
22 15 Example of an appropriate algebraic solution Volume of smaller box l w h = = 64 cm 3 Ratio of volumes 1728 = 64 Ratio of edges = Height of larger box Height = 8 3 = 24 cm Answer The height of the larger box is 24 cm.
23 16 Work : (example) Measure of BC cos 53 m BC Measure of BD Result sin 53 m BD m BD = = = = m BC cos 53 m BD m BC cos53 sin 53 The measure of segment BD is about 7.2 cm.
24 17 Example of an appropriate solution Measure of BD and of angle ADB m BD = m CD = 5 cm m ADB = 180 ( ) = 95 Measure of AD Measure of AB 5 m AD = sin 50 sin 35 5 sin 35 m AD = 3.74 sin 50 5 m AB = sin 50 sin 95 5 sin 95 m AB = 6.5 sin 50 Measure of half the perimeter (p) p 2 1 ( ) = 7.62 Area of triangle ABD S = p(p a) (p b) (p c) A 50 C D 5 cm B
25 18 S 7.62(7.62 5) ( ) ( ) S = Answer The area of triangle ABD is 9.31 cm 2. Accept answers that fall within the interval [9.21, 9.32]. Example of an appropriate solution I would find : The area of the triangle using Heron s formula Area = b h 2 Solve for h, h = 2 area b Any other plausible answer is acceptable.
26 19 Example of an appropriate solution Example 1 Measure of DC : Sin A = m DC m AC m DC = m AC sin A or m DC = 1 m sin m DC m Measure of ABC sin B = m DC m BC m B sin B = Final answer : Angle ABC measures or Example 3 The area of ABC using Heron s formula Example m 1m = sin sin ABC 1 sin sin πabc = 1.5 sin ABC m m ABC Final answer A D 46.57E C Angle ABC measures B
27 P = 2 1 ( ) = 2.25 Area = 2.25(2.25 1) (2.25 2) ( ) Area m 2 Measure of DC Area = Height = B h 2 2 area base Height = Measure of B sin B = m DC m BC m B sin B = Final answer Angle ABC measures
28 20 Example of an appropriate method Height of the tree tan 40 = m OP 10 m OP 8.39 Distance between Anthony and the tree tan m AP m AP Distance between Anthony and Steven Answer m AE m AE The distance between Anthony and Steven is metres. Accept all result in [13, 13.1] A S P 10 m O
29 21 Example of an appropriate method Length of side a sin 40 = 6 a Length of side b a = 6 sin 40 3,86 sin 50 = 6 b b = 6 sin 50 4,60 a b Area of triangle: = Quantity of paint Answer 1 L covers 2 m = (4 litres is not enough; she must buy 5 litres) Mara will have to buy 5 litres of paint. 50 a 6 m b 40
30 Mathematics Question Booklet Marie-Pierre is standing exactly half way between two office-building towers. These towers are on opposite sides of the street. Using a clinometer (a device used to measure angles) she calculates the angle formed by the top of each building. The two readings are 72 and 40. The distance between the two buildings is 66 metres. What is the difference between the heights of the two buildings? Round your answer to the nearest tenth of a metre m A) 73.9 m C) m B) m D) m
31 2 In a science experiment, a class wanted to calculate the distance a marble travelled from point A to point B on a slope with the measurements shown below: 100 cm M O A cm To help her students, the teacher gave out additional information: m AMO = 60 m AOB = 64 MOA BON How many centimetres did the marble travel from point A to point B? Show all your work. B N
32 3 A drawing of a banner is shown in the diagram on the right. Pole BE, supporting the banner, is 2.5 times the length of segment AB. What is the length of pole BE to the nearest tenth of a metre? Show all your work B A E D m C
33 4 Marie-Pierre is standing exactly half way between two office-building towers. These towers are on opposite sides of the street. Using a clinometer (a device used to measure angles) she calculates the angle formed by the top of each building. The two readings are 82.1 and The distance between the two buildings is 66 metres. What is the shortest distance between the two rooftops, represented by AB? Round your answer to the nearest tenth of a metre. A) m C) m B) m D) m
34 5 A street map of a part of a small town is shown below m (library) L (museum) M S (school) 980 m R (restaurant) 55 B (beach) What is the shortest distance from the beach to the restaurant? Round your answer to the nearest metre. - Two of the streets are parallel. - The distance from the museum to the beach is 980 m. - The distance from the school to the library is 1030 m.
35 7 Cynthia and Matthew each rode from town A to town B on their bicycles. Their routes are represented in the diagram on the right. The diagram is not drawn to scale. The direct route between the two towns is 125 km. Restaurant Cynthia's route Town A Cynthia's route km To the nearest tenth, how much longer is Matthew's route than Cynthia's? Show all your work. 125 km Town B Matthew's route Matthew's route Cabin
36 8 9 The structure represented in the diagram below is used in a warehouse to lift objects off the ground and onto a shelf. A 7.5 m B E? C D Shelf Rounded to the nearest tenth, what is the length of the beam represented by segment BD? Show all your work. Helen's plot of land is represented by the diagram on the right. She wants to cover it with pieces of grass sod that each measure 1 square metre. How many pieces of grass sod will Helen need to buy? Show all your work. C D 18 m 7.89 m A 78 B
37 10 11 Two bird watchers, 4 metres apart, are located at positions A and B as shown on the figure. Both are looking at the top of a 15-metre tree. From point A, the angle of elevation is 65. What is the angle of elevation of the bird watcher at position B? Show all your work. Michel s room is on the second floor of his house. His neighbour lives in a flat-roofed building 15 metres away. From his window, Michel sees the top corner of his neighbour s building at an angle of elevation of 28, as shown in the diagram on the right. The angle of depression at which he sees the bottom corner of his neighbour s building is 40. What is the height of this building? Show all your work. A 65? 4 m B m 40 h 2 h 1 D C 15 m
38 22 13 Julio wants to purchase a waterfront property on Lake Malartic. The surveyor gave him a plan of the dimensions of the property. The asking price is $1.35 per square metre. How much would it cost Julio to buy this property? Show all your work. Triangle ABC shown on the right represents a plot of land in which: m AC = 64.3 m m AB = 50 m m B = 100 m BAC = 30 To the nearest m 2, what is the area of the plot of land? A 100 m 50 m m 50 m 64.3 m B m C
39 14 Krystal, standing at point A, uses a clinometer to determine the angles of elevation of her window and the roof of her house. These are 20 and 40 respectively. She knows that the top of her window is 4 m above the ground. This situation is represented in the diagram below. To the nearest tenth of a metre, how far is it from the top of her window to the roof of her house? A m? Roof Window
40 16 Given triangle ABC with right angle B. What is the measure of segment BD? Show your work. A 15 cm B D 53 C
41 17 18 Determine the area of triangle ABD illustrated in the diagram below. Show all your work. A 50 5 cm C D 40 Without doing any calculations, explain how you would determine that the height of BD relative to AC is cm. A 26 cm 35 cm B D cm B C
42 19 The diagram below represents the roof of a barn. The measure of angle BAC is What is the measure of angle ABC given that BC measures 1.5 m, AB measures 2 m and AC measures 1 m? Show all the work needed to solve the problem. A D C B
43 20 From point A, Anthony observes a bird at the top of the tree at an angle of 20. From point S, Steven observes the same bird at an angle of 40. Steven is 10 metres from the foot of the tree. What is the distance between Anthony and Steven? Show all your work A S P 10 m O
44 21 Mara has been given the job of decorating her company s staff room. She wants to draw a triangle on one of the walls and paint it blue. A sketch of the wall with the measures of the triangle is shown below. Mara must find the area of the blue triangle before buying the paint. Each litre of paint covers 2 square metres. The paint she wants is sold only in 1-litre containers. How many litres of paint will Mara have to buy? Show all your work m 40
Pre-Test. Use trigonometric ratios to find the value of x. Show all your work and round your answer to the nearest tenth.
Pre-Test Name Date 1. Write the trigonometric ratios for A. Write your answers as simplified fractions. A 6 cm 10 cm sin A cos A 8 10 5 6 10 3 5 C 8 cm B tan A 8 6 3 2. Write the trigonometric ratios for
More informationCBSE X Mathematics 2012 Solution (SET 1) Section D
Section D Q 9. A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. Let the number of books
More informationTo construct the roof of a house, an architect must determine the measures of the support beams of the roof.
Metric Relations Practice Name : 1 To construct the roof of a house, an architect must determine the measures of the support beams of the roof. m = 6 m m = 8 m m = 10 m What is the length of segment F?
More informationNAME DATE PERIOD. Find the geometric mean between each pair of numbers to the nearest tenth and and and 2
8-1 Practice Geometric Mean Find the geometric mean between each pair of numbers to the nearest tenth. 1. 8 and 12 2. 3 7 and 6 7 3. 4 and 2 5 Find the measure of the altitude drawn to the hpotenuse. State
More informationChapter 2: Trigonometry
Chapter 2: Trigonometry Section 2.1 Chapter 2: Trigonometry Section 2.1: The Tangent Ratio Sides of a Right Triangle with Respect to a Reference Angle Given a right triangle, we generally label its sides
More informationThe Primary Trigonometric Ratios Word Problems
The Primary Trigonometric Ratios Word Problems A. Determining the measures of the sides and angles of right triangles using the primary ratios When we want to measure the height of an inaccessible object
More informationGeometry Review- Chapter Find e, and express your answer in simplest radical form.
Name: Date: Period: Geometry Review- Chapter 10 1. The diagonal of a rectangle measures 15 cm long, and the width is 10. Find the height of the rectangle and epress your answer in simplest radical form.
More informationSample. Test Booklet. Subject: MA, Grade: HS Louisiana EoC 2013 Algebra I /Geometry. - signup at to remove - Student name:
Test Booklet Subject: MA, Grade: HS Louisiana EoC 2013 Algebra I /Geometry Student name: Author: Common Core District: Common Core Released Tests Printed: Friday November 08, 2013 1 Teresa is simplifying
More informationMath 11 Review Trigonometry
Math 11 Review Trigonometry Short Answer 1. Determine the measure of D to the nearest tenth of a degree. 2. Determine the measure of D to the nearest tenth of a degree. 3. Determine the length of side
More informationShow all work for full credit. Do NOT use trig to solve special right triangle problems (half credit).
Chapter 8 Retake Review 1 The length of the hypotenuse of a 30 60 90 triangle is 4. Find the perimeter. 2 What similarity statement can you write relating the three triangles in the diagram? 5 Find the
More informationCHAPTER 12 HERON S FORMULA Introduction
CHAPTER 1 HERON S FORMULA 1.1 Introduction You have studied in earlier classes about figures of different shapes such as squares, rectangles, triangles and quadrilaterals. You have also calculated perimeters
More informationPRACTICE PROBLEMS CH 8 and Proofs
GEOM PRACTICE PROBLEMS CH 8 and Proofs Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to
More informationGeometer: CPM Chapters 1-6 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer.
Semester 1 Closure Geometer: CPM Chapters 1-6 Period: DEAL Take time to review the notes we have taken in class so far and previous closure packets. Look for concepts you feel very comfortable with and
More informationTRIGONOMETRY USING THE RATIOS
TRIGONOMETRY USING THE RATIOS 2017 JCHL Paper 2 Question 8 (a) The diagram below shows two right-angled triangles, ABC and ACD. They have right angles at B and D, respectively. AB = 10, AC = 12, and AD
More information1. Which of the following segment lengths could be used to form a right triangle? A. 15, 36, 39 B. 3, 4, 7 C. 21, 45, 51 D.
This review is due on the day of your test: p 1 Multiple Choice. Choose the answer that best fits the solution. 1. Which of the following segment lengths could be used to form a right triangle? A. 15,
More informationYEAR 9 MATHS SEMESTER 1 EXAM REVISION BOOKLET 2018
YEAR 9 MATHS SEMESTER 1 EXAM REVISION BOOKLET 2018 Topics Examined Chapter 12 Measurement (Exercises 12.2 12.7; 6.2-6.3) o Unit Conversions o Perimeter, Area, Total Surface Area, Volume and Capacity of
More informationHigher Order Thinking Skill questions
Higher Order Thinking Skill questions TOPIC- Constructions (Class- X) 1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60. Then construct a triangle whose sides are times the corresponding
More informationInt Math 2B EOC FIG Assessment ID: ib C. DE = DF. A. ABE ACD B. A + C = 90 C. C + D = B + E D. A = 38 and C = 38
1 If ΔDEF and ΔJKL are two triangles such that D J, which of the following would be sufficient to prove the triangles are similar? A. DE = EF JK KL B. DE = EF JK JL C. DE = DF JK KL D. DE = DF JK JL 2
More informationThe Primary Trigonometric Ratios Word Problems
. etermining the measures of the sides and angles of right triangles using the primary ratios When we want to measure the height of an inaccessible object like a tree, pole, building, or cliff, we can
More informationMath 1201 Review Chapter 2
Math 01 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P Q 16 R a. tan Q = 0.428571; tan R = 0.75 c. tan Q =
More informationANSWER KEY. LEARNING ACTIVITY 1 Challenge a. A + B = (The sum of its adjacent interior angles between two parallel sides is + B = B = B =
LEARNING ACTIVITY 1 Challenge 1.1 ANSWER KEY 1. a. A + B (The sum of its adjacent interior angles between two parallel sides is + B B B C + D (The sum of its adjacent interior angles between two parallel
More informationCh. 2 Trigonometry Notes
First Name: Last Name: Block: Ch. 2 Trigonometry Notes 2.1 THE TANGENT RATIO 2 Ch. 2.1 HW: p. 75 #3 16, 19 4 2.2 USING THE TANGENT RATIO TO CALCULATE LENGTHS 5 Ch. 2.2 HW: p. 82 # 3 5 (a, c), #6 14 6 2.4
More informationUnit 5: Applying Similarity of Triangles
Unit 5: Applying Similarity of Triangles Lesson 2: Applying the Triangle Side Splitter Theorem and Angle Bisector Theorem Students understand that parallel lines cut transversals into proportional segments.
More informationCOMMON 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 informationMathematics Guide Page 9
Mathematics 568-536 Guide Page 9 Part C Questions 15 to 5 4 marks each No marks are to be given if work is not shown. Eamples of correct solutions are given. However, other acceptable solutions are possible.
More informationPrerequisite Skills. y x =
Prerequisite Skills BLM 1 1... Solve Equations 1. Solve. 2x + 5 = 11 x 5 + 6 = 7 x 2 = 225 d) x 2 = 24 2 + 32 2 e) 60 2 + x 2 = 61 2 f) 13 2 12 2 = x 2 The Pythagorean Theorem 2. Find the measure of the
More informationGeometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.
1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of
More informationMath 1201 Review Chapter 2
Math 1201 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P 12 Q 16 R a. tan Q = 0.428571; tan R = 0.75 c. tan
More informationSection 3.4 Solving Problems Using Acute Triangles
Section 3.4 Solving Problems Using Acute Triangles May 9 10:17 AM Example 1: Textbook page 154 Two security cameras in an museum must be adjusted to monitor a new display of fossils. The cameras are mounted
More informationAngles of Elevation and Depression
Angles of Elevation and Depression Study the following figure carefully. angle of elevation angle of depression When we see an object above us, the angle between our line of sight and the horizontal is
More informationGEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity
GEOMETRY Teacher: Mrs. Flynn Topic: Similarity Name: Date: Teacher: Mrs. Flynn Topic: Similarity 1. A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find
More informationLesson 11-5: Trigonometric Ratios
Math Regents Exam Questions - Pearson Integrated Algebra Lesson 11-5 Page 1 Lesson 11-5: Trigonometric Ratios Part 1: Finding Trigonometric Ratios 1. 080414a, P.I. A.A.42 Which ratio represents cos A in
More informationFinal Exam Review Packet
Final Exam Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 6 8 a.
More informationPre RMO Exam Paper Solution:
Paper Solution:. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3? Sum of Digits Drivable
More informationTRIGONOMETRY RATIOS. LCOL and JCHL Revision
TRIGONOMETRY RATIOS LCOL and JCHL Revision 2017 JCHL Paper 2 Question 8 (a) (i) The diagram below shows two right-angled triangles, ABC and ACD. They have right angles at B and D, respectively. AB = 10,
More information9.2. Length of Line Segments. Lesson Objectives. Find the lengths of line segments on the x-axis and y-axis.
9.2 Length of Line Segments Lesson Objectives Find lengths of horizontal and vertical line segments on the coordinate plane. Solve real-world problems involving coordinates and a coordinate plane. Learn
More informationGeneral Certificate of Secondary Education Higher Tier
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Pages 3 Mark General Certificate of Secondary Education Higher Tier 4 5 6 7 Mathematics (Linear) B Paper 2 Calculator
More informationHigher. Ch 19 Pythagoras, Trigonometry and Vectors. Bilton
Higher Ch 19 Pythagoras, Trigonometry and Vectors Bilton Questions Q1. Triangle ABC has perimeter 20 cm. AB = 7 cm. BC = 4 cm. By calculation, deduce whether triangle ABC is a right angled triangle. (Total
More informationMaths GCSE Langdon Park Foundation Calculator pack A
Maths GCSE Langdon Park Foundation Calculator pack A Name: Class: Date: Time: 96 minutes Marks: 89 marks Comments: Q1. The table shows how 25 students travel to school. Walk Bus Car Taxi 9 8 7 1 Draw a
More informationMATHEMATICS GRADE 12 SESSION 18 (LEARNER NOTES)
MATHEMATICS GRADE 1 SESSION 18 (LEARNER NOTES) TOPIC 1: TWO-DIMENSIONAL TRIGONOMETRY Learner Note: Before attempting to do any complex two or three dimensional problems involving trigonometry, it is essential
More informationPre-Junior Certificate Examination, Mathematics. Paper 2 Higher Level Time: 2 hours, 30 minutes. 300 marks
J.20 NAME SCHOOL Name/ver Printed: Checked: To: Updated: TEACHER Name/ver Complete Pre-Junior Certificate Examination, 2015 Paper 2 Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question
More informationYear 11 Math Homework
Yimin Math Centre Year 11 Math Homework Student Name: Grade: Date: Score: Table of contents 8 Year 11 Topic 8 Trigonometry Part 5 1 8.1 The Sine Rule and the Area Formula........................... 1 8.1.1
More informationVisit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths
Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here
More information12-1 Trigonometric Functions in Right Triangles. Find the values of the six trigonometric functions for angle θ.
Find the values of the six trigonometric functions for angle θ. 1. Opposite side = 8 Adjacent Side = 6 Let x be the hypotenuse. By the Pythagorean theorem, Therefore, hypotenuse = 10. The trigonometric
More informationE Math (4016/01) Total marks : 80. x 1. Solve Answer x = [1]
Requirement : Answer all questions Total marks : 80 Duration : hours x 1. Solve 14 8. 5 8 14 30 x 5 Answer x = [1]. Frank bought an antique vase for $345. One year later he sold it for a profit of 180%
More informationPLC Papers Created For:
PLC Papers Created For: Year 10 Topic Practice Papers: Pythagoras and Trigonometry Pythagoras 1 Grade 5 Objective: Know and use Pythagoras's theorem for right-angled triangles Question 1 ABC is a right
More informationPre-AP Geometry 8-4 Study Guide: Angles of Elevation and Depression (pp ) Page! 1 of! 8
Page! 1 of! 8 Attendance Problems. 1. Identify the the pair of alternate interior angles. 2. Use a calculator to find! tan 30 to the nearest ten-thousandth. 3. Solve! tan 54 = 2500 Round your answer to
More informationTrigonometry Unit 5. Reflect previous TEST mark, Overall mark now. Looking back, what can you improve upon?
1 U n i t 5 11C Date: Name: Tentative TEST date Trigonometry Unit 5 Reflect previous TEST mark, Overall mark now. Looking back, what can you improve upon? Learning Goals/Success Criteria Use the following
More information1. 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 informationAssignment Assignment for Lesson 5.1
Assignment Assignment for Lesson.1 Name Date Ace Reporter Review of Ratio and Proportion Write a ratio that is equivalent to each ratio. 1. 6 12 2. 7 12 3. 4 4. 14 : 7 1. 3 : 2 6. 1.2 : 7 Solve each proportion.
More informationExponent Laws. a m a n = a m + n a m a n = a m n, a 0. ( ab) m = a m b m. ˆ m. = a m. a n = 1 a n, a 0. n n = a. Radicals. m a. n b Ë. m a. = mn.
Name:. Math 0- Formula Sheet Sequences and Series t n = t + ( n )d S n = n È t ÎÍ + ( n )d S n = n Ê Á t + t n ˆ t n = t r n Ê t r n ˆ Á S n =, r r S n = rt n t r, r S = t r, r Trigonometry Exponent Laws
More informationApplications of Mathematics
Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 2: Applications 2 For Approved Pilot Centres ONLY Higher Tier Friday 14 June 2013 Morning
More informationFINAL EXAM PAPER 4 MAY 2014
Q1. Fatima and Mohammed each buys a bike. FINAL EXAM PAPER 4 MAY 2014 (a) Fatima buys a city-bike which has a price of $120. She pays 50 % of this price and then pays $20 per month for 6 months. (i) How
More informationReview Document MTH
Review Document MTH-2101-3 Created by Martine Blais Commission scolaire des Premières-Seigneuries Mai 2010 Translated by Marie-Hélène Lebeault November 2017 Producing an algebraic model 1. How do you go
More informationPLC Papers. Created For:
PLC Papers Created For: Bearings 1 Grade 4 Objective: Measure and use bearings (including the 8 compass point bearings). Question 1. On what bearing are the following directions? (a) North (b) South East
More information1201 Common Mathematics Assessment - June 2013 Answer Sheet. Name
1201 Common Mathematics Assessment - June 2013 Answer Sheet Name Mathematics Teacher: 1. A B C D 2. A B C D 3. A B C D 4. A B C D 5. A B C D 6. A B C D 7. A B C D 8. A B C D 9. A B C D 10. A B C D 11.
More informationName: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX
Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement
More information4 ft. 12 ft. 4) A student s final grade is computed based on the following distribution:
) 00 patients are given a new drug. 90 patients show improvement. 5 patients have side effects. 95 have no effect from the drug at all. How many show improvement and have side effects? a. 0 b. c. 05 d.
More informationClass 10 Application of Trigonometry [Height and Distance] Solved Problems
Class 10 Application of Trigonometry [Height and Distance] Solved Problems Question 01: The angle of elevation of an areoplane from a point on the ground is 45 o. After a flight of 15 seconds, the elevation
More informationSupervising Examiner s/ Invigilator s initial: Total Marks : 100
Index No: 0 1 0 1 4 Alternative No. Supervising Examiner s/ Invigilator s initial: Mathematics READ THE FOLLOWING DIRECTIONS CAREFULLY: Writing Time: 3 hours Total Marks : 100 1. Do not write for the first
More information#12 Algebra 2 Notes Using Trig in Real Life
#12 Algebra 2 Notes 13.1 Using Trig in Real Life #12 Algebra 2 Notes: 13.1 using Trig in Real Life Angle of Elevation Angle of Elevation means you are looking upward and is usually measured from the ground
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, August 16, :30 to 11:30 a.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, August 16, 000 8:30 to 11:30 a.m., only Notice... Scientific
More informationComprehensive Exam Number 55
568-56 Mathematics Comprehensive Eam Number 55 GUIDE Secondary 5 September, 005 Guide Page 1 1. GENERAL INFORMATION 1.1 Program Mathematics, Secondary 5 (568-56) 1. Origin Mathematics and Science & Technology
More informationGeometry Right Triangles and Trigonometry
Geometry Right Triangles and Trigonometry Day Date lass Homework Th 2/16 F 2/17 N: Special Right Triangles & Pythagorean Theorem Right Triangle & Pythagorean Theorem Practice Mid-Winter reak WKS: Special
More informationFriday 7 November 2014 Morning
H Friday 7 November 2014 Morning GCSE MATHEMATICS A A503/02 Unit C (Higher Tier) * 3 0 5 6 4 8 7 7 6 8 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required:
More informationMultiplication and Division
UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac
More informationUnit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4
Name: Geometry Period Unit 5: Congruency Part 1 of 3: Intro to Congruency & Proof Pieces Lessons 5-1 through 5-4 In this unit you must bring the following materials with you to class every day: Please
More informationb, P.I. A2.N.5
Math B Regents Exam 0609 Page. 06090b, P.I. A.M. The number of degrees equal to 5 9 radians is [A] 90 [B] 45 [C] 900 [D] 00. 06090b, P.I. A.G. The accompanying graph shows the curves of best fit for data
More informationDay 1: Indices. Question 1 a Write down the value of. Question 2 Evaluate: Question 3 Work out. Give your answer in its simplest form.
Day 1: Indices a Write down the value of i 5 0 ii 4-2 b Simplify 16 3 1 4 8 3 Evaluate: i 27 2 3 ii 2 3 2 Question 3 Work out Give your answer in its simplest form Day 2: Angles Two tangents are drawn
More informationSUGGESTED ANSWER KEY DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN. Mathematics COMMON FINAL EXAM June 2014
Name: Teacher: SUGGESTED ANSWER KEY HP DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN Mathematics 01 COMMON FINAL EXAM June 014 Value: 70 Marks Duration: Hours General
More information3 Answer all the questions.
1 Evaluate Answer all the questions. (a) 8.679.547, 9.5 48.8 0.15 [B1] (b) (5.4 10 4 ) (1.46 10 - ). Give your answer in standard form..66 10 7 [B1] Answer (a). [1] (b). [1]. An express train travelled
More informationC accurately drawn. Calculate the upper bound for the area of triangle ABC. .. mm 2 (2)
1. C Diagram NOT accurately drawn A B The diagram shows a triangle ABC. Angle ABC is exactly 90. AB = 83 mm correct to 2 significant figures. BC = 90 mm correct to 1 significant figures. (a) Calculate
More informationReal-World Problems: Circles
11.3 Real-World Problems: Circles Lesson Objectives Solve real-world problems involving area and circumference of circles. Solve real-world problems involving semicircles, quadrants, and composite figures.
More informationMathematics 10C. UNIT ONE Measurement. Unit. Student Workbook. Lesson 1: Metric and Imperial Approximate Completion Time: 3 Days
Mathematics 10C Student Workbook Unit 1 0 1 2 Lesson 1: Metric and Imperial Approximate Completion Time: 3 Days Lesson 2: Surface Area and Volume Approximate Completion Time: 2 Days hypotenuse adjacent
More informationUnit 3 Practice Test Questions Trigonometry
Unit 3 Practice Test Questions Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How you would determine the indicated angle measure, if it
More informationName Date Class. 5 y x + 7
Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6?
More informationHigher Tier Friday 4 November 2005 Morning Time: 2 hours
Centre No. Candidate No. Surname Signature Initial(s) Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Friday 4 November 2005 Morning Time: 2 hours Examiner s use only
More informationMATHEMATICS. Unit 2. Relationships
MATHEMATICS Unit 2 Relationships The Straight Line Eercise 1 1) Given 3 find when: a) 2 b) 4 2) Given 4 find when: a) 3 b) 1 3) Given 2 find when: a) 1 b) 2 4) Given 3 find when: a) 5 b) 5) Given 2 7 find
More informationE Math (4048/01) Total marks : (a) Simplify 3 2x 1. Answer. [2] (b) Factorise 6x. 2. Factorise completely 4ax 12by 16ay 3bx
Requirement : Answer all questions Total marks : 80 Duration : 2 hour 1. (a) Simplify 3 2x 1 1. Answer. [1] (b) Factorise 6x 18xy. Answer. [1] 2. Factorise completely 4ax 12by 16ay 3bx. Prepared by Mr
More informationMath 10C: Measurement PRACTICE EXAM
Math 10C: Measurement PRACTICE EXAM 1. The distance from your house to a friend s house is best measured using: A. a tape measure. B. a 30 cm ruler. C. Vernier calipers. D. a trundle wheel. 0 10 20 30
More informationGCSE 4370/06 MATHEMATICS LINEAR PAPER 2 HIGHER TIER
Surname Centre Number Candidate Number Other Names 0 GCSE 4370/06 MATHEMATICS LINEAR PAPER 2 HIGHER TIER A14-4370-06 A.M. MONDAY, 10 November 2014 2 hours For s use Question Maximum Mark Mark Awarded 1.
More informationMATHEMATICS National Qualifications - Intermediate 1 Maths Units 1 and 2 Paper 1 (non-calculator)
Prel Examination 005 / 06 MATHEMATICS National Qualifications - Intermediate Maths Units and Paper (non-calculator) Time allowed - 35 minutes Fill in these oxes and read carefully what is printed elow
More informationCourse End Review Grade 10: Academic Mathematics
Course End Review Grade 10: Academic Mathematics Linear Systems: 1. For each of the following linear equations place in y = mx + b format. (a) 3 x + 6y = 1 (b) 4 x 3y = 15. Given 1 x 4y = 36, state: (a)
More informationSenior Math Summer Packet. A. f (x) = x B. f (x) = 2 x. C. f (x) = x 2 D. f (x) = sin x
Name: Date: 1. The set of scores on a mathematics test is 72, 80, 80, 82, 87, 89, and 91. The mean score is A. 8 B. 83 C. 82 D. 80 5. Which function is one-to-one? A. f (x) = x B. f (x) = 2 x C. f (x)
More informationGrade 9 Circles. Answer the questions. For more such worksheets visit
ID : ae-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer the questions (1) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel
More informationAREA RELATED TO CIRCLES
CHAPTER 11 AREA RELATED TO CIRCLES (A) Main Concepts and Results Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle
More information4.4 Solving Problems Using
4.4 Solving Prolems Using Otuse Triangles YOU WILL NEED calculator ruler EXPLORE The cross-section of a canal has two slopes and is triangular in shape. The angles of inclination for the slopes measure
More informationAssignment 1 and 2: Complete practice worksheet: Simplifying Radicals and check your answers
Geometry 0-03 Summary Notes Right Triangles and Trigonometry These notes are intended to be a guide and a help as you work through Chapter 8. These are not the only thing you need to read, however. Rely
More informationMathematics Department
Mathematics Department Grade 9 Placement Test Name This assessment will help the maths department to make a provisional placement. The final placement will be determined after a suitable period of in-class
More informationINSTRUCTIONS. F.3 2 nd Maths Examination (1011) P1/14
INSTRUCTIONS 1. The total mark of this paper is 100. 2. This paper consists of THREE sections, A, B and C. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer
More information1201 Common Mathematics Assessment Answer Sheet Name: Mathematics Teacher:
1201 Answer Sheet Name: Mathematics Teacher: 1. A B C D 2. A B C D 3. A B C D 4. A B C D 5. A B C D 6. A B C D 7. A B C D 8. A B C D 9. A B C D 10. A B C D 11. A B C D 12. A B C D 13. A B C D 14. A B C
More information2017 CAT. Test Name 2017 CAT Total Questions 100 Total Time 180 Mins. Section Name No. of Questions Time limit Marks per Question Negative Marking
2017 CAT Directions of Test Test Name 2017 CAT Total Questions 100 Total Time 180 Mins Section Name No. of Questions Time limit Marks per Question Negative Marking Verbal Ability 34 1:0(h:m) 3 1/3 DI &
More information4.3. Although geometry is a mathematical study, it has a history that is very much tied. Keep It in Proportion. Theorems About Proportionality
Keep It in Proportion Theorems About Proportionality.3 Learning Goals In this lesson, you will: Prove the Angle Bisector/Proportional Side Theorem. Prove the Triangle Proportionality Theorem. Prove the
More information4. Find the areas contained in the shapes. 7. Find the areas contained in the shapes.
Geometry Name: Composite Area I Worksheet Period: Date: 4. Find the areas contained in the shapes. 7. Find the areas contained in the shapes. 4 mm 2 mm 2 mm 4 cm 3 cm 6 cm 4 cm 7 cm 9. Find the shaded
More informationOn a separate sheet of paper, answer the following questions by showing ALL of your work.
Final Exam Review Cummulative Math 20-1 Ch.1 Sequence and Series Final Exam Review On a separate sheet of paper, answer the following questions by showing ALL of your work. 1. The common difference in
More informationCDS-I 2019 Elementary Mathematics (Set-C)
1 CDS-I 019 Elementary Mathematics (Set-C) Direction: Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the
More informationMath 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the
More informationLet be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree.
Ch. 9 Test - Geo H. Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree. 1. 2. 3. a. about 58.0 c. about 1.0 b. about 49.4 d. about 32.0 a. about 52.2
More informationUnit 3 Right Triangle Trigonometry - Classwork
Unit 3 Right Triangle Trigonometry - Classwork We have spent time learning the definitions of trig functions and finding the trig functions of both quadrant and special angles. But what about other angles?
More informationMath 2201 Chapter 3 Review. 1. Solve for the unknown side length. Round your answer to one decimal place.
Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Solve for the unknown side length. Round your answer to one decimal place. a. 4.1 b. 5.1 c. 4.7 d. 5.6
More information