# Mathematics (Project Maths)

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 2010. M128 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination Mathematics (Project Maths) Paper 2 Ordinary Level Monday 14 June Morning 9:30 12: marks Examination number Centre stamp For examiner Question Mark Running total Total Grade

2 Instructions There are three sections in this examination paper: Section 0 Area and Volume (old syllabus) 50 marks 1 question Section A Concepts and Skills 125 marks 5 questions Section B Contexts and Applications 125 marks 3 questions Answer all nine questions, as follows: In Section 0, answer Question 1. In Section A, answer Questions 2, 3, 4, 5 and 6. In Section B, answer: Question 7 Question 8 either Question 9A or Question 9B. Write your answers in the spaces provided in this booklet. There is space for extra work at the back of the booklet. You may also ask the superintendent for more paper. Label any extra work clearly with the question number and part. The superintendent will give you a copy of the booklet of Formulae and Tables. You must return it at the end of the examination. You are not allowed to bring your own copy into the examination. Marks will be lost if all necessary work is not clearly shown. Answers should include the appropriate units of measurement, where relevant. Answers should be given in simplest form, where relevant. Leaving Certificate 2010 Page 2 of 19 Project Maths, Paper 2 Ordinary Level

3 Section 0 Area and Volume (old syllabus) 50 marks Answer Question 1 from this section. Question 1 (a) A circle is inscribed in a square as shown. The radius of the circle is 9 cm. (50 marks) (i) Find the perimeter of the square. 9 cm (ii) Calculate the area of the square. (b) The diagram shows a sketch of a field ABCD that has one uneven edge. At equal intervals of 5 m along [BC], perpendicular measurements are made to the uneven edge, as shown on the sketch. D A 7 5 m 6 m 5 m 8 5 m 7 m 4 5 m 9 5 m B 5 m C (i) Use Simpson s rule to estimate the area of the field. page running Leaving Certificate 2010 Page 3 of 19 Project Maths, Paper 2 Ordinary Level

4 (ii) The actual area of the field is 200 m 2. Find the percentage error in the estimate. (c) (i) The diameter of a solid metal sphere is 9 cm. Find the volume of the sphere in terms of π. (ii) The sphere is melted down. All of the metal is used to make a solid shape which consists of a cone on top of a cylinder, as shown in the diagram. The cone and the cylinder both have height 8 cm. The cylinder and the base of the cone both have radius r cm. r cm 8 cm Calculate r, correct to one decimal place. 8 cm Leaving Certificate 2010 Page 4 of 19 Project Maths, Paper 2 Ordinary Level

5 Section A Concepts and Skills 125 marks Answer all five questions from this section. Question 2 (a) A line crosses the x-axis at x = 3 and the y-axis at y = 2. Find the equation of the line (25 marks) (b) The equations of two lines l 1 and l 2 are: l : x+ 3y = 8 1 l2 : 6x 2y = 15. Determine whether these lines are perpendicular. Justify your answer clearly. page running Leaving Certificate 2010 Page 5 of 19 Project Maths, Paper 2 Ordinary Level

6 Question 3 (a) A circle has centre (0, 0) and passes through the point (3, 4). (25 marks) (i) Find the equation of the circle. (ii) Find the co-ordinates of the two points at which the circle crosses the y-axis. (b) A circle has centre (2, 4) and touches the y-axis. Find the equation of the circle Leaving Certificate 2010 Page 6 of 19 Project Maths, Paper 2 Ordinary Level

7 Question 4 (25 marks) (a) Using a calculator, or otherwise, find the mean and standard deviation of the data in the following frequency table. x f Mean = Standard deviation = (b) Below is a stem-and-leaf plot of the heights of a group of students, in centimetres Key: 13 3 means 133 cm. (i) How many students are in the group? Answer: (ii) What is the range of heights in the group? (iii) What percentage of the students are between 145 cm and 154 cm in height? page running Leaving Certificate 2010 Page 7 of 19 Project Maths, Paper 2 Ordinary Level

8 Question 5 (a) (25 marks) Helen has enough credit to download three songs from the internet. There are seven songs that she wants. (i) How many different possible selections of three songs can she make? (ii) If there is one particular song that she definitely wants, how many different selections can she now make? (b) (i) Two fair coins are tossed. What is the probability of getting two heads? (ii) Two fair coins are tossed 1000 times. How often would you expect to get two heads? (c) Síle hands Pádraig a fair coin and tells him to toss it ten times. She says that if he gets ten heads then she will give him a prize. The first nine tosses are all heads. How likely is it that the last toss will also be a head? Tick the correct answer, and give a reason. Extremely unlikely Fairly unlikely chance Fairly likely Almost certain Reason: Leaving Certificate 2010 Page 8 of 19 Project Maths, Paper 2 Ordinary Level

9 Question 6 (25 marks) The diagram shows a triangle ABC in which AB = 6 cm, CB = 10 cm, and ABC = 50. A B C (a) Calculate the area of triangle ABC, correct to the nearest cm 2. (b) Calculate the length of [AC], correct to one decimal place. (c) The triangle A BC is the image of triangle ABC under the enlargement with centre B and scale factor 3. Find the area of A BC, correct to the nearest cm 2. page running Leaving Certificate 2010 Page 9 of 19 Project Maths, Paper 2 Ordinary Level

10 Section B Contexts and Applications 125 marks Answer Question 7, Question 8, and either Question 9A or Question 9B. Question 7 Probability and Statistics (40 marks) The table below gives motor insurance information for fully licensed, 17 to 20-year-old drivers in Ireland in All drivers who had their own insurance policy are included. Number of drivers Number of claims Average cost per claim Male Female Questions (a) to (e) below refer to drivers in the table above only. (Source: adapted from: Financial Regulator. Private Motor Insurance Statistics 2007.) (a) What is the probability that a randomly selected male driver made a claim during the year? Give your answer correct to three decimal places. (b) What is the probability that a randomly selected female driver made a claim during the year? Give your answer correct to three decimal places. (c) What is the expected value of the cost of claims on a male driver s policy? (d) What is the expected value of the cost of claims on a female driver s policy? Leaving Certificate 2010 Page 10 of 19 Project Maths, Paper 2 Ordinary Level

11 (e) The male drivers were paying an average of 1688 for insurance in 2007 and the female drivers were paying an average of Calculate the average surplus for each group, and comment on your answer. (Note: the surplus is the amount paid for the policy minus the expected cost of claims.) Male Female Comment: (f) A 40-year-old female driver with a full license has a probability of 0 07 of making a claim during the year. The average cost of such claims is How much should a company charge such drivers for insurance in order to show a surplus of 175 per policy? page running Leaving Certificate 2010 Page 11 of 19 Project Maths, Paper 2 Ordinary Level

12 Question 8 Geometry and Trigonometry (40 marks) Windows are sometimes in the shape of a pointed arch, like the one shown in the picture. A person is designing such an arched window. The outline is shown in the diagram below the picture. The centre for the arc AB is C and the centre for the arc AC is B. BD = 2 4 metres and DE = 1 8 metres. (a) Show that ABC = 60. A B C (b) Find the length of the arc AB. Give your answer in metres, correct to three decimal places. D E (c) Find the length of the perimeter of the window. Give your answer in metres, correct to two decimal places. Leaving Certificate 2010 Page 12 of 19 Project Maths, Paper 2 Ordinary Level

13 (d) Find the height of the window. Give your answer in metres, correct to two decimal places. (e) Make an accurate scaled drawing below of the outline of the window, using the scale 1:30. That is, 1 cm on your diagram should represent 30 cm in reality. page running Leaving Certificate 2010 Page 13 of 19 Project Maths, Paper 2 Ordinary Level

14 Question 9A Probability and Statistics (45 marks) Students in two schools one in County Kerry and the other in County Offaly were arguing about which county had the nicest weather in the summer. They agreed to record the highest temperature at each school on ten randomly selected days during the summer of The results were as follows: Temperature at Kerry school (/ C) Temperature at Offaly school (/ C) (a) Construct a back-to-back stem-and-leaf plot of the above data. (b) State two differences between the two distributions. Difference 1: Difference 2: (c) Perform a Tukey Quick Test on the data, stating clearly what can be concluded. Leaving Certificate 2010 Page 14 of 19 Project Maths, Paper 2 Ordinary Level

15 (d) The students in Offaly looked also at the amount of sunshine. They recorded the number of hours of sunshine each day in July The data are summarised in the table below. Hours of sunshine Number of days Draw a cumulative frequency curve to represent this data, using the scale indicated. Number of days (cumulative) 2 2 Hours of sunshine (e) Use your cumulative frequency curve to estimate: (i) (ii) the median number of hours of sunshine the number of days with more than 7 hours of sunshine. (f) The mean amount of sunshine per day in Offaly in July generally is 4 24 hours. A day is chosen at random from the days in July 2009, as described in part (d) above. What is the probability that the amount of sunshine on that day was less than the mean? (Data in this question adapted from Monthly Weather Bulletin, July 2009, at page running Leaving Certificate 2010 Page 15 of 19 Project Maths, Paper 2 Ordinary Level

16 Question 9B Geometry and Trigonometry (45 marks) (a) The photograph shows the Dockland building in Hamburg, Germany. The diagram below is a side view of the building. It is a parallelogram. The parallelogram is 29 metres high. The top and bottom edges are 88 metres long. Photo by NatiSythen. Wikipedia Commons. License: CC-SA A B D C. (i) Find the area of this side of the building. (ii) If BD = AD, find BC. Leaving Certificate 2010 Page 16 of 19 Project Maths, Paper 2 Ordinary Level

17 (iii) The lines BC and AD are parallel. Find the distance between these parallel lines. (b) There is a theorem on your geometry course that can be used to construct the tangent to a circle at a given point on the circle. State this theorem and use it to construct the tangent to the circle shown at the point P. Theorem: P (c) In the diagram, the line l is a tangent to the circle. Find the values of x, y and z. l y z x = x y = 42 z = page running Leaving Certificate 2010 Page 17 of 19 Project Maths, Paper 2 Ordinary Level

18 You may use this page for extra work Leaving Certificate 2010 Page 18 of 19 Project Maths, Paper 2 Ordinary Level

19 You may use this page for extra work page running Leaving Certificate 2010 Page 19 of 19 Project Maths, Paper 2 Ordinary Level

20 page running Leaving Certificate Ordinary Level Mathematics (Project Maths) Paper 2 Monday 14 June Morning 9:30 12:00

### Mathematics (Project Maths)

2010. M128 S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination Sample Paper Mathematics (Project Maths) Paper 2 Ordinary Level Time: 2 hours, 30 minutes 300 marks

### Mathematics (Project Maths Phase 1)

2012. M128 S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination, 2012 Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours, 30

### Mathematics (Project Maths Phase 3)

2013. M328 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2013 Mathematics (Project Maths Phase 3) Paper 2 Ordinary Level Monday 10 June Morning 9:30 12:00

### Mathematics (Project Maths Phase 3)

2014. M328 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 2 Ordinary Level Monday 9 June Morning 9:30 12:00 300

### Mathematics (Project Maths)

2010. M130 S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination Sample Paper Mathematics (Project Maths) Paper 2 Higher Level Time: 2 hours, 30 minutes 300 marks

### Mathematics (Project Maths)

Pre-Leaving Certificate Examination Mathematics (Project Maths) Paper 2 Higher Level February 2010 2½ hours 300 marks Running total Examination number Centre stamp For examiner Question Mark 1 2 3 4 5

### Mathematics (Project Maths Phase 3)

01. M37 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination, 01 Mathematics (Project Maths Phase 3) Paper 1 Ordinary Level Friday 8 June Afternoon :00 4:30 300 marks

### Mathematics (Project Maths Phase 1)

2011. S133S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours 300 marks Running

### Mathematics (Project Maths Phase 3)

2014. M329 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 1 Higher Level Friday 6 June Afternoon 2:00 4:30 300

### Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination Mathematics

2016. M30 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2016 Mathematics Paper 2 Higher Level Monday 13 June Morning 9:30 12:00 300 marks Examination number

### Mathematics (Project Maths Phase 1)

2013. S135 S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination, 2013 Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Higher Level Time: 2 hours, 30 minutes

### Mathematics (Project Maths Phase 1)

2011. S135S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination 2011 Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Higher Level Time: 2 hours, 30 minutes

### Mathematics (Project Maths Phase 2)

2013. M230S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certiﬁcate Examination 2013 Sample Paper Mathematics (Project Maths Phase 2) Paper 2 Higher Level Time: 2 hours, 30 minutes

### MATHEMATICS: PAPER II

NATIONAL SENIOR CERTIFICATE EXAMINATION SUPPLEMENTARY 2014 MATHEMATICS: PAPER II Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 10 pages, a

### Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination 2015. Mathematics

015. M7 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 015 Mathematics Paper 1 Ordinary Level Friday 5 June Afternoon :00 4:30 300 marks Running total Examination

### Mathematics (Project Maths Phase 3)

013. M37 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 013 Mathematics (Project Maths Phase 3) Paper 1 Ordinary Level Friday 7 June Afternoon :00 4:30 300

### Junior Math Circles November 18, D Geometry II

1 University of Waterloo Faculty of Mathematics Junior Math Circles November 18, 009 D Geometry II Centre for Education in Mathematics and Computing Two-dimensional shapes have a perimeter and an area.

### Cork Institute of Technology. CIT Mathematics Examination, Paper 1 Sample Paper A

Cork Institute of Technology CIT Mathematics Examination, 2015 Paper 1 Sample Paper A Answer ALL FIVE questions. Each question is worth 20 marks. Total marks available: 100 marks. The standard Formulae

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

### Mathematics (Project Maths Phase 2)

2012. S234 Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination, 2012 Mathematics (Project Maths Phase 2) Paper 1 Higher Level Friday 8 June Afternoon 2:00 to 4:30

### Topics Covered on Geometry Placement Exam

Topics Covered on Geometry Placement Exam - Use segments and congruence - Use midpoint and distance formulas - Measure and classify angles - Describe angle pair relationships - Use parallel lines and transversals

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### Thursday 28 February 2013 Afternoon

H Thursday 28 February 2013 Afternoon GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J533610313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

### HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 1999 MATHEMATICS PAPER 2

99-CE MATHS Paper HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 999 MATHEMATICS PAPER 5 am 45 pm (½ hours) Subject Code 80 Read carefully the instructions on the Answer

### Shape, Space and Measure

Name: Shape, Space and Measure Prep for Paper 2 Including Pythagoras Trigonometry: SOHCAHTOA Sine Rule Cosine Rule Area using 1-2 ab sin C Transforming Trig Graphs 3D Pythag-Trig Plans and Elevations Area

### CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

### = = 4 + = 4 + = 25 = 5

1 4 1 4 1 4 = 4 6+ 1 = 4 + = 4 + = 25 = 5 5. Find the side length of each square as a square root. Then estimate the square root. A B C D A side length B side length C side length D side length = 4 2+

### Geometry Final Exam Review Worksheet

Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.

### MATHEMATICS: PAPER II

NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2015 MATHEMATICS: PAPER II EXAMINATION NUMBER Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of

### Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Thursday 5 November 2009 Morning Time: 1 hour 45 minutes

Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Surname Signature Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Thursday 5 November 2009 Morning

### Section 2.1 Rectangular Coordinate Systems

P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

### You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser. Tracing paper may be used.

Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 1 (Non-Calculator) Monday 11 June 2012 Afternoon Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference

### WEDNESDAY, 2 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working.

C 500/1/01 NATIONAL QUALIFICATIONS 01 WEDNESDAY, MAY 1.0 PM.5 PM MATHEMATICS STANDARD GRADE Credit Level Paper 1 (Non-calculator) 1 You may NOT use a calculator. Answer as many questions as you can. Full

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

### Wednesday 6 November 2013 Morning

H Wednesday 6 November 2013 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J540550313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical

### REVISED GCSE Scheme of Work Mathematics Higher Unit T3. For First Teaching September 2010 For First Examination Summer 2011

REVISED GCSE Scheme of Work Mathematics Higher Unit T3 For First Teaching September 2010 For First Examination Summer 2011 Version 1: 28 April 10 Version 1: 28 April 10 Unit T3 Unit T3 This is a working

### Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Monday 18 May 2009 Afternoon Time: 1 hour 45

### In Problems #1 - #4, find the surface area and volume of each prism.

Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

### HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 2001 MATHEMATICS PAPER 2

00-CE MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 00 MATHEMATICS PAPER 5 am 45 pm (½ hours) Subject Code 80 Read carefull the instructions on the Answer Sheet

### MATHEMATICS PAPER 2. Samir Daniels Mathematics Paper 2 Page 1

MATHEMATICS PAPER 2 Geometry... 2 Transformations... 3 Rotation Anticlockwise around the origin... 3 Trigonometry... 4 Graph shifts... 4 Reduction Formula... 4 Proving Identities... 6 Express in terms

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

### General Certificate of Secondary Education January 2014. Mathematics Unit T3 (With calculator) Higher Tier [GMT31] FRIDAY 10 JANUARY, 9.15am 11.

Centre Number 71 Candidate Number General Certificate of Secondary Education January 2014 Mathematics Unit T3 (With calculator) Higher Tier [GMT31] MV18 FRIDAY 10 JANUARY, 9.15am 11.15 am TIME 2 hours,

### Wednesday 5 November 2014 Morning Time: 1 hour 45 minutes

Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Mathematics A Paper 1 (Non-Calculator) Wednesday 5 November 2014 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier

### Monday 11 June 2012 Afternoon

THIS IS A NEW SPECIFICATION H Monday 11 June 2012 Afternoon GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) *A517000612* Candidates answer on the Question Paper. OCR supplied materials: None Other materials

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Centre Number Tuesday 6 January 015 Afternoon Time: hours Candidate Number Higher Tier Paper Reference

### Geometry Regents Review

Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel International GCSE Centre Number Mathematics B Paper 2 Candidate Number Thursday 4 June 2015 Morning Time: 2 hours 30 minutes Paper Reference 4MB0/02

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS

Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided

### National Quali cations 2015

H National Quali cations 05 X77/76/ WEDNESDAY, 0 MAY 9:00 AM 0:0 AM Mathematics Paper (Non-Calculator) Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given only

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

### Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. SAMPLE RESPONSE SET

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. SAMPLE RESPONSE SET Table of Contents Question 29................... 2 Question 30...................

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Catholic Schools Trial Examination 2004 Mathematics

0 Catholic Trial HSC Examination Mathematics Page Catholic Schools Trial Examination 0 Mathematics a If x 5 = 5000, find x correct to significant figures. b Express 0. + 0.. in the form b a, where a and

### CHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY

CHAPTER 8: ACUTE TRIANGLE TRIGONOMETRY Specific Expectations Addressed in the Chapter Explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Monday 1 January 015 Afternoon Time: hours Candidate Number

### TUESDAY, 6 MAY 9.00 AM 9.45 AM. 2 Full credit will be given only where the solution contains appropriate working.

X00//0 NATIONAL QUALIFICATIONS 04 TUESDAY, 6 MAY 9.00 AM 9.45 AM MATHEMATICS INTERMEDIATE Units, and Paper (Non-calculator) Read carefully You may NOT use a calculator. Full credit will be given only where

### Specimen paper MATHEMATICS HIGHER TIER. Time allowed: 2 hours. GCSE BITESIZE examinations. General Certificate of Secondary Education

GCSE BITESIZE examinations General Certificate of Secondary Education Specimen paper MATHEMATICS HIGHER TIER 2005 Paper 1 Non-calculator Time allowed: 2 hours You must not use a calculator. Answer all

### G C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.

### National 4: Expressions and Formulae

Biggar High School Mathematics Department National 4 Pupil Booklet National 4: Expressions and Formulae Learning Intention Success Criteria I can simplify algebraic expressions. I can simplify and carry

### SECONDARY FOUR NORMAL ACADEMIC PRELIMINARY EXAMINATION 2013 MATHEMATICS 4042/01 PAPER 1

Name Class Registration Number SECONDARY FOUR NORMAL ACADEMIC PRELIMINARY EXAMINATION 013 MATHEMATICS 404/01 PAPER 1 Duration: hours Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST

### Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Edexcel IGCSE Centre Number Mathematics A Paper 3H Monday 6 June 2011 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA0/3H You must have:

### EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number

KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number 1.1 Calculations 1.2 Decimal Numbers 1.3 Place Value Use priority of operations with positive and negative numbers. Simplify

### CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

### Wednesday 15 January 2014 Morning Time: 2 hours

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number

### GRADE 12 SEPTEMBER 2014 MATHEMATICS P2

NATIONAL SENIOR CERTIFICATE GRADE 1 SEPTEMBER 014 MATHEMATICS P MARKS: 150 TIME: 3 hours *MATHE* This question paper consists of 15 pages, including diagram sheets and 1 information sheet. MATHEMATICS

### Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles

Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.

### Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Friday 11 June 2010 Morning Time: 1 hour 45 minutes

### MINISTRY OF EDUCATION

REPUBLIC OF NAMIBIA MINISTRY OF EDUCATION NAMIBIA SENIOR SECONDARY CERTIFICATE MATHEMATICS SPECIMEN PAPERS 1, MARK SCHEMES AND ANALYSIS HIGHER LEVEL GRADES 11 1 THESE PAPERS AND MARK SCHEMES SERVE TO EXEMPLIFY

### Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

### Section A Concepts and Skills 150 marks

Section A Concepts and Skills 150 marks Question 1 (25 marks) The random variable X has a discrete distribution. The probability that is takes a value other than 13, 14, 15 or 16 is negligible. (a) Complete

### Winter 2016 Math 213 Final Exam. Points Possible. Subtotal 100. Total 100

Winter 2016 Math 213 Final Exam Name Instructions: Show ALL work. Simplify wherever possible. Clearly indicate your final answer. Problem Number Points Possible Score 1 25 2 25 3 25 4 25 Subtotal 100 Extra

### INDUSTRIAL TECHNOLOGY TECHNICAL DRAWING LEVEL 9

INDUSTRIAL TECHNOLOGY TECHNICAL DRAWING LEVEL 9 Reduction and enlargement of plane figures to reduce plane figure by lengths of sides using the polar method. - Reading Suppose the ratio is skills. 1:3.

### Radius, diameter, circumference, π (Pi), central angles, Pythagorean relationship. about CIRCLES

Grade 9 Math Unit 8 : CIRCLE GEOMETRY NOTES 1 Chapter 8 in textbook (p. 384 420) 5/50 or 10% on 2011 CRT: 5 Multiple Choice WHAT YOU SHOULD ALREADY KNOW: Radius, diameter, circumference, π (Pi), central

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

### CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

### Working in 2 & 3 dimensions Revision Guide

Tips for Revising Working in 2 & 3 dimensions Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. List the topics and plan a revision timetable.

### Monday 11 June 2012 Afternoon

THIS IS A NEW SPECIFICATION H Monday 11 June 2012 Afternoon GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J517130612* Candidates answer on the Question Paper. OCR supplied materials: None Other materials

### 1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.

1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### SOLID SHAPES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier

Mathematics Revision Guides Solid Shapes Page 1 of 19 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SOLID SHAPES Version: 2.1 Date: 10-11-2015 Mathematics Revision Guides Solid

### 24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 12: Geometry - 2D Figures and 3D Solids

24HourAnsers.com Online Homeork Focused Exercises for Math SAT Skill Set 12: Geometry - 2D Figures and 3D Solids Many of the problems in this exercise set came from The College Board, riters of the SAT

### MATHEMATICS: PAPER I. 5. You may use an approved non-programmable and non-graphical calculator, unless otherwise stated.

NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 015 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 1 pages and an Information

### Geometry Credit Recovery

Geometry Credit Recovery COURSE DESCRIPTION: This is a comprehensive course featuring geometric terms and processes, logic, and problem solving. Topics include parallel line and planes, congruent triangles,

### EVERY DAY COUNTS CALENDAR MATH 2005 correlated to

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:

### Each pair of opposite sides of a parallelogram is congruent to each other.

Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Monday, January 26, 2004 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A Monday, January 26, 2004 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your name and the

### LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

### MATHEMATICS SUBJECT 4008/4028

MATHEMATICS PAPER 2 SUBJECT 4008/4028 GENERAL COMMENTS General performance of candidates was poor with the majority in the 0-10 marks group. This shows that candidates were not prepared thoroughly for