# Mathematics (Project Maths Phase 1)

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 2012. M128 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination, 2012 Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Monday 11 June Morning 9:30 12: marks Examination number Centre stamp For examiner Question Mark Running total Total Grade

3 Section A Concepts and Skills 125 marks Answer all five questions from this section. Question 1 (25 marks) Peter and Niamh go to a large school. One morning, they arrive early. While they are waiting, they decide to guess whether each of the next three students to come in the door will be a boy or a girl. (a) Write out the sample space showing all the possible outcomes. For example, BGG is one outcome, representing Boy, Girl, Girl. (b) Peter says these outcomes are equally likely. Niamh says they are not. What do you need to know about the students in the school to decide which of them is correct? (c) If all the outcomes are equally likely, what is the probability that the three students will be two girls followed by a boy? (d) Niamh guesses that there will be at least one girl among the next three students. Peter guesses that the next three students will be either three boys or two boys and a girl. Who is more likely to be correct, assuming all outcomes are equally likely? Justify your answer. page running Leaving Certificate 2012 Page 3 of 19 Project Maths, Phase 1

4 Question 2 (25 marks) (a) In the Venn diagram below, the universal set is a normal deck of 52 playing cards. The two sets shown represent clubs and picture cards (kings, queens and jacks). Show on the diagram the number of elements in each region. Clubs Picture cards [ ] [ ] [ ] [ ] (b) (i) A card is drawn from a pack of 52 cards. Find the probability that the card drawn is the king of clubs. (ii) A card is drawn from a pack of 52 cards. Find the probability that the card drawn is a club or a picture card. (iii) Two cards are drawn from a pack of 52 cards. Find the probability that neither of them is a club or a picture card. Give your answer correct to two decimal places. Leaving Certificate 2012 Page 4 of 19 Project Maths, Phase 1

5 Question 3 A( 6, 1), B(12, 3), C(8, 5) and D (2, 7) are four points. (a) Plot the four points on the diagram below. y (25 marks) x (b) Describe two different ways of showing, using co-ordinate geometry techniques, that the points form a parallelogram ABCD. First method: Second method: This question continues on the next page. page running Leaving Certificate 2012 Page 5 of 19 Project Maths, Phase 1

6 (c) Use one of the ways you have described to show that ABCD is a parallelogram. Question 4 The diagram shows two circles c 1 and c2 of equal radius. c 1 has centre (0, 0) and it cuts the x-axis at (5, 0). (a) Find the equation of c 1. c 2 (25 marks) P c 1 (b) Show that the point P ( 3, 4) is on c 1. Leaving Certificate 2012 Page 6 of 19 Project Maths, Phase 1

7 (c) The two circles touch at P ( 3, 4). P is on the line joining the two centres. Find the equation of c 2. (d) Find the equation of the common tangent at P. page running Leaving Certificate 2012 Page 7 of 19 Project Maths, Phase 1

8 Question 5 Answer either 5A or 5B. Question 5A (25 marks) (a) (i) Write down a geometrical result that can be used to construct a tangent to a circle at a point. (ii) On the diagram shown, construct the tangent to the circle at A. A C (b) Construct the circumcentre and circumcircle of the triangle below, using only a straight edge and compass. Show all construction marks clearly. Leaving Certificate 2012 Page 8 of 19 Project Maths, Phase 1

9 OR Question 5B ABCD is a parallelogram. D C The points A, B and C lie on the circle which cuts [AD] at P. The line CP meets the line BA at Q. P Prove that CD = CP. Q A B page running Leaving Certificate 2012 Page 9 of 19 Project Maths, Phase 1

10 Section B Contexts and Applications 125 marks Answer Question 6 and Question 7. Question 6 (75 marks) The following table gives data on new private cars sold in Ireland in each quarter of each year from 2006 to New private cars sales Number of cars sold Engine type of cars sold Year January to April to July to October Annual March June Sept. to Dec. Total Petrol Diesel Other (Source: Central Statistics Office, (a) (i) Show the annual total sales of cars over the six years, using a suitable chart. (ii) Find the mean number of cars sold per year over the six years. Leaving Certificate 2012 Page 10 of 19 Project Maths, Phase 1

11 (iii) Calculate the percentage increase in annual car sales between 2009 and (iv) Aoife says that this increase shows car sales are currently going well. Paul says that car sales are currently going badly. He says that sales have fallen by 52% since 2007 and that they are well below average. Complete the sentences below to give a criticism of each argument. Aoife s argument does not recognise that Paul s argument does not recognise that (v) Give a more balanced description of the pattern of car sales over the six years. (b) (i) Describe how the sales of the cars are distributed over the four quarters of each year. (ii) Suggest a reason for this pattern of sales. (iii) The sales for the first quarter of 2012 are Find, with justification, an estimate for the total annual sales for page running Leaving Certificate 2012 Page 11 of 19 Project Maths, Phase 1

12 (c) (i) Two pie charts are being used to show the change from 2006 to 2011 in the popularity of petrol and diesel cars. Complete the second pie chart. Diesel 25 4% Petrol 74 2% Other (ii) Which of the following statements best describes the change over time in the popularity of diesel cars as a percentage of the total? A. Diesel cars have suddenly become very popular in the last year or two. B. Diesel cars have increased very steadily in popularity over the last six years. C. Diesel cars have become very popular since car sales started to improve. D. Diesel cars got more popular each year, with an especially big increase in E. Diesel cars became popular as car sales fell but have been getting less popular as they rise again. Write the letter corresponding to the correct answer in the box. Leaving Certificate 2012 Page 12 of 19 Project Maths, Phase 1

13 (d) A survey of some of the most popular models of private cars sold in 2011 examined the CO 2 emissions in g/km from diesel engines and petrol engines. The data are as follows: Diesel engines 117, 125, 120, 125, 134, 110, 118, 114, 119, 119, 116, 107. Petrol engines 139, 133, 150, 157, 138, 159, 129, 138, 134, 129, 129, 136. (i) Construct a back-to-back stem-and-leaf plot of the above data. (ii) Does the information suggest that diesel engines produce lower CO 2 emissions than petrol engines? In your answer you should refer to the stem-and-leaf plot and to an appropriate measure of central tendency. (iii) Does the information suggest that there is a greater variation in the CO 2 emissions of diesel engines than petrol engines? In your answer you should refer to the stem-andleaf plot and an appropriate measure of variability. page running Leaving Certificate 2012 Page 13 of 19 Project Maths, Phase 1

14 Question 7 (50 marks) The planned supports for the roof of a building form scalene triangles of different sizes. (a) Explain what is meant by a scalene triangle. The triangle EFG is the image of the triangle CDE under an enlargement and the triangle CDE is the image of the triangle ABC under the same enlargement. G E A C B D F The proposed dimensions for the structure are AB = 7 2 m, BC = 8 m, CD = 9 m and DCB = 60. (b) Find the length of [FG]. (c) Find the length of [BD], correct to three decimal places. Leaving Certificate 2012 Page 14 of 19 Project Maths, Phase 1

15 (d) The centre of the enlargement is O. Find the distance from O to the point B. page running Leaving Certificate 2012 Page 15 of 19 Project Maths, Phase 1

16 (e) A condition of the planning is that the height of the point G above the horizontal line BF cannot exceed 11 6 m. Does the plan meet this condition? Justify your answer by calculation. Leaving Certificate 2012 Page 16 of 19 Project Maths, Phase 1

17 Section C Area and Volume (old syllabus) 50 marks Answer Question 8 from this section. Question 8 (50 marks) (a) The diagram shows a circle inscribed in a square. 2 The area of the square is 16 cm. (i) Find the radius length of the circle. (ii) Find the area of the shaded region, in cm 2, correct to one decimal place. page running Leaving Certificate 2012 Page 17 of 19 Project Maths, Phase 1

18 (b) In order to estimate the area of the irregular shape shown below, a horizontal line was drawn across the widest part of the shape and five offsets (perpendicular lines) were drawn at equal intervals along this line. (i) (ii) Find the lengths of the horizontal line and the offsets, taking each grid unit as 5 mm, and record the lengths on the diagram. Use Simpson s rule to estimate the area of the shape. Leaving Certificate 2012 Page 18 of 19 Project Maths, Phase 1

19 (c) A solid wax candle is in the shape of a cylinder with a cone on top, as shown in the diagram. The diameter of the base of the cylinder is 3 cm and the height of the cylinder is 8 cm. The volume of the wax in the candle is (i) Find the height of the candle. 3 21π cm. 8 cm 3 cm (ii) Nine of these candles fit into a rectangular box. The base of the box is a square. Find the volume of the smallest rectangular box that the candles will fit into. page running Leaving Certificate 2012 Page 19 of 19 Project Maths, Phase 1

20 Leaving Certificate 2012 Ordinary Level Mathematics (Project Maths Phase 1) Paper 2 Monday 11 June Morning 9:30 12:00

### Mathematics (Project Maths Phase 3)

2014. M325 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 2014 Mathematics (Project Maths Phase 3) Paper 1 Foundation Level Friday 6 June Afternoon 2:00 4:30

### Mathematics A *P49303RA0128* Pearson Edexcel GCSE P49303RA. Paper 2 (Calculator) Foundation Tier. Thursday 9 June 2016 Morning Time: 1 hour 45 minutes

Write your name here Surname Pearson Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Thursday 9 June 2016 Morning Time: 1 hour 45 minutes Other names Candidate Number Foundation Tier Paper

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications

### Workout 5 Solutions. Peter S. Simon. Quiz, December 8, 2004

Workout 5 Solutions Peter S. Simon Quiz, December 8, 2004 Problem 1 Marika shoots a basketball until she makes 20 shots or until she has made 60% of her shots, whichever happens first. After she has made

### ALTERNATE Paper 1 (Non - calculator)

ALTERNATE Paper 1 (Non - calculator) November 2014 HIGHER Name: Total Marks: Q. Max Actual RAG Q. Max Actual RAG 1 3 14 4 2 2 15 4 3 3 16 4 4 3 17 4 5 4 18 5 6 4 19 4 7 4 20 5 8 4 21 2 9 4 22 6 10 2 23

### Mathematics Paper 2. Stage minutes. Name.. Additional materials: Ruler Calculator Tracing paper Geometrical instruments

1 55 minutes Mathematics Paper 2 Stage 8 Name.. Additional materials: Ruler Calculator Tracing paper Geometrical instruments READ THESE INSTRUCTIONS FIRST Answer all questions in the spaces provided on

### Math A Regents Exam 0800 Page a, P.I. A.A.12 The product of 2 3 x and 6 5 x is [A] 10x 8

Math A Regents Exam 0800 Page 1 1. 080001a, P.I. A.A.1 The product of x and 6 5 x is [A] x 8 [B] x 15 [C] 1x 8 [D] 1x 15 5. 080005a Which table does not show an example of direct variation? [A] [B]. 08000a,

### UNIT 10 PERIMETER AND AREA

UNIT 10 PERIMETER AND AREA INTRODUCTION In this Unit, we will define basic geometric shapes and use definitions to categorize geometric figures. Then we will use the ideas of measuring length and area

### Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)

Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change

### Name: Date: Time: Total marks available: Total marks achieved: Questions 1-11 Non Calculator Questions Calculator

Name: Date: Time: Total marks available: Total marks achieved: Questions 1-11 Non Calculator Questions 12-21 Calculator Questions Q1. Work out the area of this triangle....(total for Question is 3 marks)

### Grade 4 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 4 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology

### Methods in Mathematics Unit 1: Methods 1

Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 Practice Paper Time: 1 hour 45 minutes Foundation Tier Paper Reference 5MM1F/01

### Problem-solving pack. 1 The sum of two odd numbers is 80 and their difference is 6. Work out these numbers. (2 marks)

NAME 1 The sum of two odd numbers is 80 and their difference is 6. Work out these numbers. 2 Find three different prime numbers that add up to 21. 1 3 Sanjiv has 46 and Joshua has 38. Sanjiv gives Joshua

### DOWNSEND SCHOOL YEAR 5 EASTER REVISION BOOKLET

DOWNSEND SCHOOL YEAR 5 EASTER REVISION BOOKLET This booklet is an optional revision aid for the Summer Exam Name: Maths Teacher: Revision List for Summer Exam Topic Junior Maths Bk 3 Place Value Chapter

### 7 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers

Pellissippi State Middle School Mathematics Competition 7 th Grade Exam Scoring Format: points per correct response - each wrong response 0 for blank answers Directions: For each multiple-choice problem

### Paper 2. Calculator allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7

Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 2 Calculator allowed First name Last name School 2007 Remember The test is 1 hour long. You may use a calculator for any question in this test. You will need:

### Algebra - Equations and Inequalities (Questions)

GCSE Maths Question and Answers 2015 Table of Contents Algebra - Equations and Inequalities (Questions)... 3 Algebra - Equations and Inequalities (Answers)... 5 Angles (Questions)... 7 Angles (Answers)...

### GCSE Mathematics Practice Tests: Set 6

GCSE Mathematics Practice Tests: Set 6 Paper 1H (Non-calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil,

### 6 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers

Pellissippi State Middle School Mathematics Competition 6 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers Directions: For each multiple-choice problem

### 18.2 Geometric Probability

Name Class Date 18.2 Geometric Probability Essential Question: What is geometric probability? Explore G.13.B Determine probabilities based on area to solve contextual problems. Using Geometric Probability

### Date: Period: Quadrilateral Word Problems: Review Sheet

Name: Quadrilateral Word Problems: Review Sheet Date: Period: Geometry Honors Directions: Please answer the following on a separate sheet of paper. Completing this review sheet will help you to do well

### The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in

The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Retiring and Hiring A

### Foundation/Higher Crossover Questions

Foundation/Higher Crossover Questions Topics: Worded HCF and LCM Questions Equations with unknowns on both sides Unit Conversions Venn diagrams Worded two-way tables Basic Trigonometry Loci & Constructions

### Unit 2: Number, Algebra, Geometry 1 (Non-Calculator) Foundation Tier

Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Mathematics B Unit 2: Number, Algebra, Geometry 1 (Non-Calculator) Foundation Tier Thursday 4 June 2015 Morning

### Problem of the Month: Between the Lines

Problem of the Month: Between the Lines Overview: In the Problem of the Month Between the Lines, students use polygons to solve problems involving area. The mathematical topics that underlie this POM are

### Saxon Math Manipulatives in Motion Primary. Correlations

Saxon Math Manipulatives in Motion Primary Correlations Saxon Math Program Page Math K 2 Math 1 8 Math 2 14 California Math K 21 California Math 1 27 California Math 2 33 1 Saxon Math Manipulatives in

### Geometry Topic 4 Quadrilaterals and Coordinate Proof

Geometry Topic 4 Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 In the diagram below, parallelogram has diagonals and that intersect at point. Which expression is NOT always true? A. B. C. D. C

### HANOI STAR - APMOPS 2016 Training - PreTest1 First Round

Asia Pacific Mathematical Olympiad for Primary Schools 2016 HANOI STAR - APMOPS 2016 Training - PreTest1 First Round 2 hours (150 marks) 24 Jan. 2016 Instructions to Participants Attempt as many questions

### (Higher) Q1. Diagram NOT accurately drawn. LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm.

(Higher) Q1. Diagram NOT accurately drawn LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm. Calculate the size of the angle marked x. Give your answer correct to 1 decimal place.......................

### MATHEMATICS MARKS PAGE TOTAL KEY STAGE LEVELS 3 5 TEST A CALCULATOR NOT ALLOWED. First Name. Last Name.

MATHEMATICS KEY STAGE 2 2001 TEST A LEVELS 3 5 CALCULATOR NOT ALLOWED PAGE 3 5 7 9 11 13 15 17 TOTAL MARKS First Name Last Name School Instructions You may not use a calculator to answer any questions

### Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9 1)

Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9 1) *0123456789* MATHEMATICS 0626/05 Paper 5 (Core) For Examination from 2017 SPECIMEN PAPER Candidates

### 9-1: Circle Basics GEOMETRY UNIT 9. And. 9-2: Tangent Properties

9-1: Circle Basics GEOMETRY UNIT 9 And 9-2: Tangent Properties CIRCLES Content Objective: Students will be able to solve for missing lengths in circles. Language Objective: Students will be able to identify

### Square Roots and the Pythagorean Theorem

UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest

### GCSE 9-1 Higher Edexcel Set B Paper 1 - Non Calculator

Name: GCSE 9-1 Higher Edexcel Set B Paper 1 - Non Calculator Equipment 1. A black ink ball-point pen. 2. A pencil. 3. An eraser. 4. A ruler. 5. A pair of compasses. 6. A protractor. Guidance 1. Read each

### PROBABILITY. 1. Introduction. Candidates should able to:

PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation

### Reigate Grammar School. 11+ Entrance Examination January 2014 MATHEMATICS

Reigate Grammar School + Entrance Examination January 204 MATHEMATICS Time allowed: 45 minutes NAME Work through the paper carefully You do not have to finish everything Do not spend too much time on any

### Mathematics Success Grade 6

T428 Mathematics Success Grade 6 [OBJECTIVE] The students will plot ordered pairs containing rational values to identify vertical and horizontal lengths between two points in order to solve real-world

### Excel / Education. GCSE Mathematics. Paper 3B (Calculator) Higher Tier. Time: 2 hours. Turn over

Excel / Education GCSE Mathematics Paper 3B (Calculator) Higher Tier Time: 2 hours 3B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil,

### 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) Tuesday 6 November 2012 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference

### Print n Play Collection. Of the 12 Geometrical Puzzles

Print n Play Collection Of the 12 Geometrical Puzzles Puzzles Hexagon-Circle-Hexagon by Charles W. Trigg Regular hexagons are inscribed in and circumscribed outside a circle - as shown in the illustration.

### Sample Questions Set 1 Class IX CBSE MATHS. CBSE :: ICSE :: Matriculation :: Engineering Tuitions and Coaching

Sample Questions Set 1 Class IX CBSE MATHS Section A 1. Write the mean of perimeters of two squares having sides x and y units. 2. A cuboidal block of wood is of dimensions 5m x 2m x 1m. Find the number

### Find the area and perimeter of any enlargement of the original rug above. Your work must include the following:

7-1.Your friend Alonzo owns a rug manufacturing company, which is famous for its unique designs. Each rug design has an original size as well as enlargements that are exactly the same shape. Find the area

### International Contest-Game MATH KANGAROO

International Contest-Game MATH KANGAROO Part A: Each correct answer is worth 3 points. 1. The number 200013-2013 is not divisible by (A) 2 (B) 3 (C) 5 (D) 7 (E) 11 2. The eight semicircles built inside

### Secondary Cycle Two Year One June 2008 Competency 2 and Competency 3 Situations

Mathematics Examination 563-306 Secondary Cycle Two Year One June 2008 Competency 2 and Competency 3 Situations Time: 3 hours Student Booklet Name : Group : June 2008 The following criteria will be used

### 9.1 and 9.2 Introduction to Circles

Date: Secondary Math 2 Vocabulary 9.1 and 9.2 Introduction to Circles Define the following terms and identify them on the circle: Circle: The set of all points in a plane that are equidistant from a given

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications

### Chapter 5. Drawing a cube. 5.1 One and two-point perspective. Math 4520, Spring 2015

Chapter 5 Drawing a cube Math 4520, Spring 2015 5.1 One and two-point perspective In Chapter 5 we saw how to calculate the center of vision and the viewing distance for a square in one or two-point perspective.

### GCSE Mathematics Practice Tests: Set 1

GCSE Mathematics Practice Tests: Set 1 Paper 3F (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser,

### B262A. MATHEMATICS B (MEI) Paper 2 Section A (Foundation Tier) GENERAL CERTIFICATE OF SECONDARY EDUCATION. Wednesday 14 January 2009 Afternoon WARNING

F GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS B (MEI) Paper 2 Section A (Foundation Tier) B262A *CUP/T61563* Candidates answer on the question paper OCR Supplied Materials: None Other Materials

### THE NORTH LONDON INDEPENDENT GIRLS SCHOOLS CONSORTIUM MATHEMATICS

THE NORTH LONDON INDEPENDENT GIRLS SCHOOLS CONSORTIUM Group 2 YEAR 7 ENTRANCE EXAMINATION MATHEMATICS Friday 6 January 2017 Time allowed: 1 hour 15 minutes First Name:... Surname:... Instructions: Please

### ANSWER KEY Grade 8 Mathematics Western School District 2010

ANSWER KEY Grade 8 Mathematics Western School District 2010 Section A: Non-Calculator 1. A 6. A 2. D 7. B 3. D 8. B 4. A 9. C 5. C 10. A Grade 8 Math Sample Exam June 2010 Page 1 Section A: Constructed

### Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0

Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume

### Mathematics Achievement

Section Mathematics Achievement 7 Questions Time: 0 minutes Each question is followed by four suggested answers. Read each question and then decide which one of the four suggested answers is best. Find

### Name Date Period STUDY GUIDE Summative Assessment #5 6 th Grade Math Covering and Surrounding

Name Date Period STUDY GUIDE Summative Assessment #5 6 th Grade Math Covering and Surrounding 1) Mr. and Mrs. Hunter tiled their rectangular porch using 1ft. by 1ft. square tiles. The rectangular porch

### Sample. Test Booklet. Subject: MA, Grade: 08 MEA 2008 Grade 8 Math. - signup at to remove - Student name:

Test Booklet Subject: MA, Grade: 08 MEA 2008 Grade 8 Math Student name: Author: Maine District: Maine Released Tests Printed: Wednesday January 02, 2013 1 Use the menu below to answer this question. A

### MATH KANGARO O INSTRUCTIONS GRADE

INTERNATIONAL CO NTES T -GAME MATH KANGARO O CANADA, 201 7 INSTRUCTIONS GRADE 11-1 2 1. You have 75 minutes to solve 30 multiple choice problems. For each problem, circle only one of the proposed five

### h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.

ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this

### Problem of the Month: Between the Lines

Problem of the Month: Between the Lines The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common

### Planes, Tetrahedra, and Cross Sections

Planes, Tetrahedra, and Cross Sections Los Angeles Math Circle February 26, 2017 Warm Up Problems 1. Is it possible to cut a square into 7 smaller squares, not necessarily of equal size? If so, show how

### SHAPE level 2 questions. 1. Match each shape to its name. One is done for you. 1 mark. International School of Madrid 1

SHAPE level 2 questions 1. Match each shape to its name. One is done for you. International School of Madrid 1 2. Write each word in the correct box. faces edges vertices 3. Here is half of a symmetrical

### bar graph, base (geometry), base (number)

The 3 5 MATH Concept Learning Bricks packet is organized alphabetically, with each concept explanation (concept, question, answer, gesture, and examples) listed first and the Concept Learning Brick visual

### Geometer s Skethchpad 8th Grade Guide to Learning Geometry

Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

### MAGDALEN COLLEGE SCHOOL OXFORD 11+/Pre Test ENTRANCE EXAMINATION Specimen MATHEMATICS

For Markers Use Only Mark First Name:... Surname: Current School: MAGDALEN COLLEGE SCHOOL OXFORD 11+/Pre Test ENTRANCE EXAMINATION Specimen MATHEMATICS Please read this information before the examination

### TEKSING TOWARD STAAR MATHEMATICS GRADE 7. Projection Masters

TEKSING TOWARD STAAR MATHEMATICS GRADE 7 Projection Masters Six Weeks 1 Lesson 1 STAAR Category 1 Grade 7 Mathematics TEKS 7.2A Understanding Rational Numbers A group of items or numbers is called a set.

### ISOMETRIC PROJECTION. Contents. Isometric Scale. Construction of Isometric Scale. Methods to draw isometric projections/isometric views

ISOMETRIC PROJECTION Contents Introduction Principle of Isometric Projection Isometric Scale Construction of Isometric Scale Isometric View (Isometric Drawings) Methods to draw isometric projections/isometric

### JUNIOR CERTIFICATE 2009 MARKING SCHEME TECHNICAL GRAPHICS HIGHER LEVEL

. JUNIOR CERTIFICATE 2009 MARKING SCHEME TECHNICAL GRAPHICS HIGHER LEVEL Sections A and B Section A any ten questions from this section Q1 12 Four diagrams, 3 marks for each correct label. Q2 12 2 marks

### EXCELLENCE IN MATHEMATICS EIGHTH GRADE TEST CHANDLER-GILBERT COMMUNITY COLLEGE S. THIRTEENTH ANNUAL MATHEMATICS CONTEST SATURDAY, JANUARY 19 th, 2013

EXCELLENCE IN MATHEMATICS EIGHTH GRADE TEST CHANDLER-GILBERT COMMUNITY COLLEGE S THIRTEENTH ANNUAL MATHEMATICS CONTEST SATURDAY, JANUARY 19 th, 2013 1. DO NOT OPEN YOUR TEST BOOKLET OR BEGIN WORK UNTIL

### Locus Locus. Remarks

4 4. The locus of a point is the path traced out by the point moving under given geometrical condition (or conditions). lternatively, the locus is the set of all those points which satisfy the given geometrical

### American Mathematics Competitions. Practice 8 AMC 8

American Mathematics Competitions Practice 8 AMC 8 (American Mathematics Contest 8) INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU.. This is a twenty-five question multiple choice

### MAT.HS.PT.4.CANSB.A.051

MAT.HS.PT.4.CANSB.A.051 Sample Item ID: MAT.HS.PT.4.CANSB.A.051 Title: Packaging Cans Grade: HS Primary Claim: Claim 4: Modeling and Data Analysis Students can analyze complex, real-world scenarios and

### Year 5 Maths Assessment Guidance - NUMBER Working towards expectations. Meeting expectations 1 Entering Year 5

5.1.a.1 Count forwards and backwards with positive and negative whole numbers, including through zero (^) 5.1.a.2 Count forwards or backwards in steps of powers of 10 for any given number to 1 000 000

### 6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line.

6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. Toolkit: - Rate of change - Simplifying fractions Main Ideas: Definitions Rise: the vertical distance between two

### 11 1 Reteach Lines That Intersect Circles

11 1 Reteach Lines That Intersect Circles Free PDF ebook Download: 11 1 Reteach Lines That Intersect Circles Download or Read Online ebook 11 1 reteach lines that intersect circles in PDF Format From The

### Familiarisation. Mathematics 2. Read the following with your child:

Mathematics 2 Read the following with your child:. This is a multiple-choice paper, in which you have to mark your answer to each question on the separate answer sheet. You should mark only one answer

### Maths Higher Level Coordinate geometry

Maths Higher Level Coordinate geometry It is not necessary to carry out all the activities contained in this unit. Please see Teachers Notes for explanations, additional activities, and tips and suggestions.

### Decide how many topics you wish to revise at a time (let s say 10)

1 Minute Maths for the Higher Exam (grades B, C and D topics*) Too fast for a first-time use but... brilliant for topics you have already understood and want to quickly revise. for the Foundation Exam

### Coordinate Algebra 1 Common Core Diagnostic Test 1. about 1 hour and 30 minutes for Justin to arrive at work. His car travels about 30 miles per

1. When Justin goes to work, he drives at an average speed of 55 miles per hour. It takes about 1 hour and 30 minutes for Justin to arrive at work. His car travels about 30 miles per gallon of gas. If

### The Geometer s Sketchpad Unit 1. Meet Geometer s Sketchpad

Trainer/Instructor Notes: Geometer s Sketchpad Training Meet Geometer s Sketchpad The Geometer s Sketchpad Unit 1 Meet Geometer s Sketchpad Overview: Objective: In this unit, participants become familiar

### Big Ideas Math: A Common Core Curriculum Geometry 2015 Correlated to Common Core State Standards for High School Geometry

Common Core State s for High School Geometry Conceptual Category: Geometry Domain: The Number System G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,

### Investigation. Triangle, Triangle, Triangle. Work with a partner.

Investigation Triangle, Triangle, Triangle Work with a partner. Materials: centimetre ruler 1-cm grid paper scissors Part 1 On grid paper, draw a large right triangle. Make sure its base is along a grid

### Pascal Contest (Grade 9) Wednesday, February 23, 2005

Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario Pascal Contest (Grade 9) Wednesday, February 23, 2005 C.M.C.

2014 MATH Olympiad [Grade1] 1 25 11 19 21 140 31 24 41 2 21 12 21 22 607 32 8 42 6 3 7 13 8 23 802 33 18 43 3 4 7 14 9 24 35 34 16 44 23 28 5 8 15 16 25 667 35 9 45 6 5 16 3 26 268 36 83 46 3 7 17 17 9

### 8 th Grade Domain 3: Geometry (28%)

8 th Grade Domain 3: Geometry (28%) 1. XYZ was obtained from ABC by a rotation about the point P. (MGSE8.G.1) Which indicates the correspondence of the vertices? A. B. C. A X, B Y, C Z A Y, B Z, C X A

### - Chapter 1: "Symmetry and Surface Area" -

Mathematics 9 C H A P T E R Q U I Z Form P - Chapter 1: "Symmetry and Surface Area" - Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the figure, the

### Tangents and Chords Off On a Tangent

Tangents and Chords SUGGESTED LERNING STRTEGIES: Group Presentation, Think/Pair/Share, Quickwrite, Interactive Word Wall, Vocabulary Organizer, Create Representations, Quickwrite CTIVITY 4.1 circle is

### GCSE Mathematics (Non-calculator Paper)

Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature GCSE Mathematics (Non-calculator Paper) Practice Paper Style Questions Topic: Loci & Constructions

### 14th Bay Area Mathematical Olympiad. BAMO Exam. February 28, Problems with Solutions

14th Bay Area Mathematical Olympiad BAMO Exam February 28, 2012 Problems with Solutions 1 Hugo plays a game: he places a chess piece on the top left square of a 20 20 chessboard and makes 10 moves with

### 1. Algebra Grade 8 A-2

1. Algebra Grade 8 A-2 A friend of yours did not understand how to evaluate each of the following on a quiz. m + 3 3 when m = 2 1 4 2 5n - 12.3 when n = 8.6 (p - 6) when p = -15 1. Write a step by step

### Set 1: Set 2:

CCGPS Benchmark 3 (2014-2015) REVIEW Name 1. 21 students in a social studies class took a test, and their average score was 87%. William was absent that day. He came back, took the test, and got a 95%.

### GCSE (9 1) Mathematics J560/05 Paper 5 (Higher Tier) Sample Question Paper. Date Morning/Afternoon Time allowed: 1 hour 30 minutes

Oxford Cambridge and RSA GCSE (9 1) Mathematics J560/05 Paper 5 (Higher Tier) Sample Question Paper H Date Morning/Afternoon Time allowed: 1 hour 30 minutes You may use: Geometrical instruments Tracing

### Geometry For Technical Drawing Chapter 4

Geometry For Technical Drawing Chapter 4 Sacramento City College EDT 300/ENGR 306 EDT 300/ENGR 306 1 Objectives Identify and describe geometric shapes and constructions used by drafters. Construct various

### SET THEORY AND VENN DIAGRAMS

Mathematics Revision Guides Set Theory and Venn Diagrams Page 1 of 26 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier SET THEORY AND VENN DIAGRAMS Version: 2.1 Date: 15-10-2015 Mathematics

### Everyday Math Assessment Opportunities Grade 4 MMR = Mental Math Reflex, TLG = Teacher s Lesson Guide, SL = Study Link. Unit 1

= Mental Math Reflex, TLG = Teacher s Lesson Guide, SL = Study Link Unit 1 1a B Use a compass and straightedge to 1.8 1.8 p. 12 & 13 construct geometric figures. p. 22 & 23 p. 8 #2 & 3 1b Identify properties

### Poker: Probabilities of the Various Hands

Poker: Probabilities of the Various Hands 22 February 2012 Poker II 22 February 2012 1/27 Some Review from Monday There are 4 suits and 13 values. The suits are Spades Hearts Diamonds Clubs There are 13

### Book 10: Slope & Elevation

Math 21 Home Book 10: Slope & Elevation Name: Start Date: Completion Date: Year Overview: Earning and Spending Money Home Travel and Transportation Recreation and Wellness 1. Budget 2. Personal Banking

### Introduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states:

Worksheet 4.11 Counting Section 1 Introduction When looking at situations involving counting it is often not practical to count things individually. Instead techniques have been developed to help us count

### Activity 5.2 Making Sketches in CAD

Activity 5.2 Making Sketches in CAD Introduction It would be great if computer systems were advanced enough to take a mental image of an object, such as the thought of a sports car, and instantly generate