Mathematics (Project Maths Phase 3)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Mathematics (Project Maths Phase 3)"

Transcription

1 *B6* Pre-Leaving Certificate Examination, 2014 Triailscrúdú na hardteistiméireachta, 2014 Mathematics (Project Maths Phase 3) Paper 1 Ordinary Level 2½ hours 300 marks Name: School: Address: Class: Teacher: For examiner Question Mark Total Page 1 of 24

2 Instructions There are two sections in this examination paper: Section A Concepts and Skills 150 marks 6 questions Section B Contexts and Applications 150 marks 3 questions Answer all nine questions. 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 Formulae and Tables booklet. 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. Write down the make and model of your calculator(s) here: Page 2 of 24

3 Section A Concepts and Skills 150 marks Answer all six questions from this section. Question 1 (25 marks) (a) Solve the equations and verify your solutions. 3x+ 2y = 7 5x + 37= 3y Page 3 of 24

4 (b) Solve the inequality 3x+ 5 6x 10, where x. (c) Show the solution set to part (b) on the number line below. Page 4 of 24

5 Question 2 (25 marks) The width of a rectangular vegetable patch is x metres. Its length is 5 metres longer than its width. (a) Write an expression in x to represent the length of the vegetable patch. (b) Show that the area of the patch can be expressed in the form 2 x + 5x. Page 5 of 24

6 (c) If the area of the patch is 36 m, find the dimensions of the garden. Page 6 of 24

7 Question 3 (25 marks) (a) (i) Simplify 4( 2 3i) 2( i 4) i( 5 2i) +. (ii) If 4+ ti = 5, find two possible values for tt,. (b) Identify each complex number, z 1, z 2 and z 3, on the complex plane below given that: z z 1 = z 2 = i z 2 1 ( ) 3 1 Im( z) Re( z) Page 7 of 24

8 Question 4 (25 marks) (a) Differentiate 3 2 3x 2x 5x with respect to x. (b) As a plane travels down a runway its distance from 2 a marker is given by s() t = 2t + 5t 20, where s is measured in metres and t is measured in seconds. (i) How far does the plane travel in the first 10 seconds? Page 8 of 24

9 (ii) Find the speed of the plane in terms of t. (iii) After how many seconds is the speed of the plane 85 m/s? Page 9 of 24

10 Question 5 (25 marks) The graph of the function ( ) 2 f x = x 7x+ 10 is shown below in the domain 1 x 6. (a) Using the graph write down the roots of f ( x ) = 0. (b) Find f '( x ), the derivative of f ( x ). Page 10 of 24

11 (c) For what value of x will f '( x ) = 0. (d) Which of the graphs below represent f '( x ), the derivative of ( ) Explain your answer fully. f x. Answer: Reason: Page 11 of 24

12 Question 6 (25 marks) A woman has a gross yearly income of 60,000. Her standard rate cut-off point is 27,000 and she has tax credits of 3,200. The standard rate of tax is 20% of income up to the standard rate cut-off point and 41% on all income above the standard rate cut-off point. (a) Calculate the tax payable at the standard rate of tax. (b) Calculate the amount of gross tax payable for the year. Page 12 of 24

13 (c) Calculate the woman s net yearly income. (d) The woman saves 11% of her net income each month. Calculate her yearly savings correct to the nearest euro. Page 13 of 24

14 Section B Contexts and Applications 150 marks Answer all three questions from this section. Question 7 (50 marks) An indoor cycling race has a rolling start. The speed of two competing cyclists, in metres per second, as they crossed the starting line each lap was recorded as follows. Cyclist A has a starting speed of 2 m/s and accelerates uniformly by 1.5 m/s 2 during the first 5 seconds. Cyclist B has a starting speed of 1.5 m/s and accelerates uniformly by 2.5 m/s 2 during the first 5 seconds. (a) Complete the following table to show the speed of each cyclist during the first 5 seconds of the race. Time (seconds) Cyclist A Cyclist B (b) Display the change in speed of both cyclists on a suitable graph. Page 14 of 24

15 Page 15 of 24

16 (c) Use your graph to find: (i) the speed of both cyclists after 4.5 seconds. Cyclist A Cyclist B (ii) the time when cyclist B overtakes cyclist A. Page 16 of 24

17 (d) Find the equations that model the speeds of both cyclists. Cyclist A Cyclist B (e) Find algebraically the time when the speeds of the cyclists are equal. Page 17 of 24

18 Question 8 (60 marks) In the first month after opening, a mobile phone shop sold 300 phones. A model for future trading assumes that sales will increase by x phones per month for the next 35 months. (a) Write down an expression to represent the number of phones expected to be sold in the second month. (b) Write down an expression to represent the number of phones expected to be sold in the third month. (c) Write down an expression to represent the number of phones, P n, expected to be sold in the n th month. Page 18 of 24

19 (d) Paul states the sequence is arithmetic, Jake disagrees. Is Paul correct? Explain your answer fully. (e) Using this model with x = 6, calculate the number of phones sold in the 36 th month. Page 19 of 24

20 (f) Calculate the total number of phones sold over the 36 months. (g) The shop sets a sales target of 20,000 phones to be sold over the 36 months. Find the least value of x required to achieve this target. Page 20 of 24

21 Question 9 (40 marks) An open-top box is cut from a sheet of cardboard with dimensions as shown. A square of side x cm is cut from each corner. (a) Write down the length of the side of the box in terms of x. (b) Write down the width of the side of the box in terms of x. Page 21 of 24

22 (c) Write down an expression in x to represent the volume of the box. (d) Find, correct to two decimal places, the value of x that will maximise the volume of the box. Page 22 of 24

23 Page 23 of 24

24 Page 24 of 24

FUNCTIONAL SKILLS MATHEMATICS (level 1)

FUNCTIONAL SKILLS MATHEMATICS (level 1) FUNCTIONAL SKILLS MATHEMATICS (level 1) Detailed Marking Instructions Version: May 2011 Question Marking Scheme Illustrations of evidence No Give for each for awarding a mark 1 (a) Ans: 675 represent:

More information

Gears Ratios and Speed / Problem Solving

Gears Ratios and Speed / Problem Solving Teacher Mechanics Note to the teacher On this page, students will learn about the relationship between gear ratio, gear rotational speed, wheel radius, diameter, circumference, revolutions and distance.

More information

Algebra I: A Fresh Approach. By Christy Walters

Algebra I: A Fresh Approach. By Christy Walters Algebra I: A Fresh Approach By Christy Walters 2005 A+ Education Services All rights reserved. No part of this publication may be reproduced, distributed, stored in a retrieval system, or transmitted,

More information

The Pythagorean Theorem Diamond in the Rough

The Pythagorean Theorem Diamond in the Rough The Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Shared Reading, Activating Prior Knowledge, Visualization, Interactive Word Wall Cameron is a catcher trying out for the school baseball team. He

More information

Teaching Notes. Contextualised task 35 The 100 Metre Race

Teaching Notes. Contextualised task 35 The 100 Metre Race Contextualised task 35 The 100 Metre Race Teaching Notes This activity involves interpreting data presented in different forms to compare speed, distance and time. The aim is to find who might win a race

More information

The Bruins I.C.E. School

The Bruins I.C.E. School The Bruins I.C.E. School Lesson 1: Addition & Subtraction Word Problems Lesson 2: Extend the Counting Sequence Lesson 3: Extend the Counting Sequence Lesson 4: Understand Place Value Lesson 5: Represent

More information

Formula One Race Strategy

Formula One Race Strategy Formula One Race Strategy McLaren Racing Limited Sports Technology McLaren is a registered trademark of McLaren Racing Limited INTRODUCTION Figure 1: A Vodafone McLaren Mercedes driven by Lewis Hamilton

More information

March Madness Basketball Tournament

March Madness Basketball Tournament March Madness Basketball Tournament Math Project COMMON Core Aligned Decimals, Fractions, Percents, Probability, Rates, Algebra, Word Problems, and more! To Use: -Print out all the worksheets. -Introduce

More information

Year 10 Mathematics, 2007

Year 10 Mathematics, 2007 Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 lgebra Use straightforward algebraic methods and sketch and interpret features of linear graphs Time: 20 minutes. Check that you have entered

More information

2018 School Competition Sprint Round Problems 1 30

2018 School Competition Sprint Round Problems 1 30 Name 08 School Competition Sprint Round Problems 0 0 4 5 6 7 8 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. 9 This section of the competition consists of 0 problems. You will have 40 minutes to complete

More information

GRADE 8 BASELINE TEST 2013 MATHEMATICS. 1 Hour 30 Minutes

GRADE 8 BASELINE TEST 2013 MATHEMATICS. 1 Hour 30 Minutes GRADE 8 BASELINE TEST 2013 GRADE 8 BASELINE TEST MATHEMATICS 2013 MATHEMATICS 1 Hour 30 Minutes 1 Hour 30 Minutes SCHOOL:. LEARNER:.. CLASS: 1 Baseline Assessment Instrument Gr 8 (135 marks) Read the questions

More information

Math 6 EQT Study Guide Quarter 3. and a package of 12 golf balls. The package with 3 golf balls costs $4.59, and the package with 12 golf balls

Math 6 EQT Study Guide Quarter 3. and a package of 12 golf balls. The package with 3 golf balls costs $4.59, and the package with 12 golf balls Math EQT Study Guide Quarter 3 1. How will the surface area of the figure represented by the net change if the length increases by 7 feet? The original figure has dimensions of l = 12 feet, w = feet, and

More information

, Candidate Name Number

, Candidate Name Number , Candidate Name Centre Number 0 Candidate Number GCSE MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED HIGHER TIER 2 nd SPECIMEN PAPER SUMMER 2017 1 HOUR 45 MINUTES ADDITIONAL MATERIALS A calculator

More information

POST TEST KEY. Math in a Cultural Context*

POST TEST KEY. Math in a Cultural Context* Fall 2007 POST TEST KEY Building a Fish Rack: Investigation into Proof, Properties, Perimeter and Area Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: POST TEST KEY Grade: Teacher:

More information

Monday Tuesday Wednesday Thursday

Monday Tuesday Wednesday Thursday Name: Weekly Math Homework - Q1:1 Teacher: Monday Tuesday Wednesday Thursday Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of Operations to simplify. Use Order of

More information

The Rabbit Pen Problem Created by: Angeli Tempel George Mason University, COMPLETE Math Spring 2016

The Rabbit Pen Problem Created by: Angeli Tempel George Mason University, COMPLETE Math Spring 2016 The Rabbit Pen Problem Created by: Angeli Tempel George Mason University, COMPLETE Math Spring 2016 The Task Ms. Brown s class will raise rabbits for their spring science fair. They have 24 feet of fencing

More information

Sum Fun Tournament Meeting (Multiple Topics)

Sum Fun Tournament Meeting (Multiple Topics) Sum Fun Sum Fun Tournament Meeting (Multiple Topics) Sum Fun Topic There are a wide range of topics and difficulty levels covered during this meeting. Materials Needed The first four items listed below

More information

Transform Your Classroom and Construct Learning with Geometry Golf

Transform Your Classroom and Construct Learning with Geometry Golf Transform Your Classroom and Construct Learning with Geometry Golf Nancy Norem Powell nancynpowell@gmail.com 2012 Conference Common Core State Standards for Mathematics Practice Standards: This lesson

More information

Teacher s Resource Pack

Teacher s Resource Pack Teacher s Resource Pack Stage 4 & Stage 5 Mathematics Book your excursion today! Call (02) 8251 7801 Welcome to SEA LIFE Sydney Aquarium s Mathematics Student Resources Teacher Notes A trip to SEA LIFE

More information

A Study of Olympic Winning Times

A Study of Olympic Winning Times Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ A Study of Olympic Winning Times Objective: Students will graph data, determine a line that models

More information

Mini-Golf Course Description. 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants.

Mini-Golf Course Description. 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. Algebra 1 Mrs. Blake B256 Mini-Golf Course Description Guidelines for your creation: 1. You must draw your design on a piece of graph paper so that it will cover all four quadrants. 2. On the graph paper

More information

Acceleration: Galileo s Inclined Plane

Acceleration: Galileo s Inclined Plane Teacher s Notes Main Topic Subtopic Learning Level Technology Level Activity Type Motion Acceleration High Low Student Description: Use a water clock to measure a ball s acceleration as it rolls down an

More information

USE INEQUALITY NOTATION TO SPECIFY SIMPLE ERROR INTERVALS DUE TO TRUNCATION OR ROUNDING (foundation and higher tier)

USE INEQUALITY NOTATION TO SPECIFY SIMPLE ERROR INTERVALS DUE TO TRUNCATION OR ROUNDING (foundation and higher tier) N15 USE INEQUALITY NOTATION TO SPECIFY SIMPLE ERROR INTERVALS DUE TO TRUNCATION OR ROUNDING (foundation and higher tier) You should be able to find least and greatest value of a number that has been rounded

More information

National Quali cations Forename(s) Surname Number of seat. Date of birth Day Month Year Scottish candidate number

National Quali cations Forename(s) Surname Number of seat. Date of birth Day Month Year Scottish candidate number N5 X744/75/02 FRIDAY, 9 MAY 2:10 PM 3:50 PM FOR OFFICIAL USE National Quali cations 2014 Mark Lifeskills Mathematics Paper 2 *X7447502* Fill in these boxes and read what is printed below. Full name of

More information

2018 Chapter Competition Countdown Round Problems 1 80

2018 Chapter Competition Countdown Round Problems 1 80 2018 Chapter Competition Countdown Round Problems 1 80 This booklet contains problems to be used in the Countdown Round. 2018 MATHCOUNTS National Competition Sponsor National Sponsors Raytheon Company

More information

BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL 4

BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL 4 BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL Rounding 1. Round these numbers to the nearest 10: a) 238 b) 719 c) 682 3 2. Round these numbers to the nearest 100: a) 6783 b) 13295 c) 199 3 3. Round these

More information

100-Meter Dash Olympic Winning Times: Will Women Be As Fast As Men?

100-Meter Dash Olympic Winning Times: Will Women Be As Fast As Men? 100-Meter Dash Olympic Winning Times: Will Women Be As Fast As Men? The 100 Meter Dash has been an Olympic event since its very establishment in 1896(1928 for women). The reigning 100-meter Olympic champion

More information

1. Identify the sample space and the outcome shown for spinning the game spinner.

1. Identify the sample space and the outcome shown for spinning the game spinner. 2014-2015 6 th Grade Compacted Spring Semester Review Name: 1. Identify the sample space and the outcome shown for spinning the game spinner. Z W Y X a. Sample space: {W, X, Y, Z} Outcome shown: Z b. Sample

More information

Special Right Triangle Task Cards

Special Right Triangle Task Cards Special Right Triangle Task Cards 45-45-90 and 30-60-90 Special Right Triangle Task Cards 45-45-90 and 30-60-90 Teachers: I have included 2 sets of task cards. The first set (slides 3-9) asks for the answer

More information

Montréal Canadiens 100th Anniversary

Montréal Canadiens 100th Anniversary Situational Problem End of Secondary Cycle One Year One Montréal Canadiens 100th Anniversary Student Answer Booklet Name: Group: Evaluation Grid Solves a situational problem Observable indicators corresponding

More information

Figure 1. What is the difference between distance and displacement?

Figure 1. What is the difference between distance and displacement? Q1.A train travels from town A to town B. Figure 1 shows the route taken by the train. Figure 1 has been drawn to scale. Figure 1 (a) The distance the train travels between A and B is not the same as the

More information

Perimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below.

Perimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below. Perimeter Reteaching 1-1 Find the perimeter of the figure below. 15 m x 4 ft 4 ft 2 ft y 2 ft 5 ft 6 m 20 ft Reteaching 1-1 By using a formula: There are two equal lengths and equal widths, so you can

More information

Grade 8 / Scored Student Samples ITEM #5 SMARTER BALANCED PERFORMANCE TASK

Grade 8 / Scored Student Samples ITEM #5 SMARTER BALANCED PERFORMANCE TASK Grade 8 / Scored Student Samples ITEM #5 SMARTER BALANCED PERFORMANCE TASK Focus Standards and Claim Stimulus Claim 4 7.EE.B.4 Stacks of Cups Your science classroom uses cups for many experiments. Your

More information

Vectors. Wind is blowing 15 m/s East. What is the magnitude of the wind s velocity? What is the direction?

Vectors. Wind is blowing 15 m/s East. What is the magnitude of the wind s velocity? What is the direction? Physics R Scalar: Vector: Vectors Date: Examples of scalars and vectors: Scalars Vectors Wind is blowing 15 m/s East. What is the magnitude of the wind s velocity? What is the direction? Magnitude: Direction:

More information

The Cycle Shop Performance Task

The Cycle Shop Performance Task The Cycle Shop Performance Task Did you enjoy this activity? Why or why not? How do you think this type of activity compares to more traditional math practice problems? Do you think this type of activity

More information

Pre-Algebra Chapter 3 Decimals and Equations

Pre-Algebra Chapter 3 Decimals and Equations Pre-Algebra Chapter 3 Decimals and Equations SOME NUMBERED QUESTIONS HAVE BEEN INTENTIONALLY DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU

More information

Basketball Packaging. Basketball Packaging. 1 of 10. Copyright 2008, Exemplars, Inc. All rights reserved.

Basketball Packaging. Basketball Packaging. 1 of 10. Copyright 2008, Exemplars, Inc. All rights reserved. The Bouncing Basketball Company is looking to design a new carton to ship 24 basketballs. Each basketball comes in a box that measures 1 foot on every side, and the company wants to put 24 of these boxes

More information

CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES

CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES 317 Recalling The Pythagorean Theorem a 2 + b 2 = c 2 a c 90 b The 90 angle is called the right angle of the right triangle. The other two angles of the right

More information

Common Core State Standards

Common Core State Standards 0 03 Pacing Guide for Sixth Grade Common Core State Standards Math Content Standards Ratios and Proportional Relationships RP Understand ratio concepts and use ratio reasoning to solve problems. The Number

More information

Tying Knots. Approximate time: 1-2 days depending on time spent on calculator instructions.

Tying Knots. Approximate time: 1-2 days depending on time spent on calculator instructions. Tying Knots Objective: Students will find a linear model to fit data. Students will compare and interpret different slopes and intercepts in a context. Students will discuss domain and range: as discrete

More information

Perimeter. Perimeter is the distance around a shape. You can use grid. Step 1 On grid paper, draw a rectangle that has a length

Perimeter. Perimeter is the distance around a shape. You can use grid. Step 1 On grid paper, draw a rectangle that has a length Lesson 13.1 Perimeter Perimeter is the distance around a shape. You can use grid paper to count the number of units around the outside of a rectangle to find its perimeter. How many feet of ribbon are

More information

Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 1. Pythagorean Theorem; Task 3.1.2

Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 1. Pythagorean Theorem; Task 3.1.2 Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic. Pythagorean Theorem; Task 3.. TASK 3..: 30-60 RIGHT TRIANGLES Solutions. Shown here is a 30-60 right triangle that has one leg of length and

More information

Ball Toss. Vernier Motion Detector

Ball Toss. Vernier Motion Detector Experiment 6 When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would

More information

STRATEGIES ACHIEVE MATHEMATICS SUCCESS

STRATEGIES ACHIEVE MATHEMATICS SUCCESS STAMS SERIES D STRATEGIES TO ACHIEVE MATHEMATICS SUCCESS PROVIDES INSTRUCTIONAL ACTIVITIES FOR 12 MATHEMATICS STRATEGIES USES A STEP-BY-STEP APPROACH TO ACHIEVE MATHEMATICS SUCCESS PREPARES STUDENTS FOR

More information

13.7 Quadratic Equations and Problem Solving

13.7 Quadratic Equations and Problem Solving 13.7 Quadratic Equations and Problem Solving Learning Objectives: A. Solve problems that can be modeled by quadratic equations. Key Vocabulary: Pythagorean Theorem, right triangle, hypotenuse, leg, sum,

More information

Pythagorean Theorem in Sports

Pythagorean Theorem in Sports Name Date Pythagorean Theorem in Sports Activity 1: Pythagorean Theorem in Baseball Directions: Measure the distance between each of the bases using the yard stick provided. Then convert your measurements

More information

Candidate Number. General Certificate of Secondary Education Higher Tier March 2013

Candidate Number. General Certificate of Secondary Education Higher Tier March 2013 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier March 2013 Pages 2 3 4 5 Mark Mathematics

More information

MATHCOUNTS State Competition Target Round Problems 1 and 2 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.

MATHCOUNTS State Competition Target Round Problems 1 and 2 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. MATHCOUNTS Name School Chapter 2006 State Competition Target Round Problems 1 and 2 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This round of the competition consists of eight problems, which will

More information

Name Date PD. Pythagorean Theorem

Name Date PD. Pythagorean Theorem Name Date PD Pythagorean Theorem Vocabulary: Hypotenuse the side across from the right angle, it will be the longest side Legs are the sides adjacent to the right angle His theorem states: a b c In any

More information

Quali cations. Forename(s) Surname Number of seat

Quali cations. Forename(s) Surname Number of seat FOR OFFICIAL USE Quali cations N5National 015 X744/75/01 WEDNESDAY, 9 APRIL 1:00 PM 1:50 PM Mark Lifeskills Mathematics Paper 1 (Non-Calculator) *X7447501* Fill in these boxes and read what is printed

More information

GCSE Mathematics Practice Tests: Set 5

GCSE Mathematics Practice Tests: Set 5 GCSE Mathematics Practice Tests: Set 5 Paper 2H (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser,

More information

MORE TRIGONOMETRY

MORE TRIGONOMETRY MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram

More information

Motion. 1 Describing Motion CHAPTER 2

Motion. 1 Describing Motion CHAPTER 2 CHAPTER 2 Motion What You ll Learn the difference between displacement and distance how to calculate an object s speed how to graph motion 1 Describing Motion 2(D), 4(A), 4(B) Before You Read Have you

More information

ACTIVITY: Finding a Formula Experimentally

ACTIVITY: Finding a Formula Experimentally 8.1 Volumes of Cylinders How can you find the volume of a cylinder? 1 ACTIVITY: Finding a Formula Experimentally Work with a partner. a. Find the area of the face of a coin. b. Find the volume of a stack

More information

Distance-time graphs

Distance-time graphs Distance-time graphs Name & Set 1 Someone runs a race at a steady speed. The runner s motion is plotted as a distance-time graph below. distance /m 100 80 60 40 20 0 0 2 4 6 8 10 12 time /s (i) Over what

More information

Physics: 3. Velocity & Acceleration. Student Notes

Physics: 3. Velocity & Acceleration. Student Notes Physics: 3. Velocity & Acceleration Please remember to photocopy 4 pages onto one sheet by going A3 A4 and using back to back on the photocopier Syllabus OP1 Perform simple calculations based on speed,

More information

Pacific Charter Institute Pacing Guide Grade(s): _5 Subject Area: _Math in Focus grade 5 CP: yes _X no

Pacific Charter Institute Pacing Guide Grade(s): _5 Subject Area: _Math in Focus grade 5 CP: yes _X no Week 1 Pre-requisite skills review Chapter 1 pre-test Assessment 5 chapter pre-test pp. 1-4 or MIF Student book 5A pp. 1-4 Reteach 4A (1.1, 1.2, 2.1, 3.2, 3.4) NWEA Kids start Wed. Week 2 1.1 Writing numbers

More information

Candidate Name Centre Number Candidate Number MATHEMATICS - NUMERACY UNIT 2: CALCULATOR-ALLOWED FOUNDATION TIER SPECIMEN PAPER SUMMER 2017

Candidate Name Centre Number Candidate Number MATHEMATICS - NUMERACY UNIT 2: CALCULATOR-ALLOWED FOUNDATION TIER SPECIMEN PAPER SUMMER 2017 GCSE MATHEMATICS - NUMERACY Specimen Assessment Materials 107 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS - NUMERACY UNIT 2: CALCULATOR-ALLOWED FOUNDATION TIER SPECIMEN PAPER SUMMER

More information

8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary 8-1 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg

More information

Analysis of Shear Lag in Steel Angle Connectors

Analysis of Shear Lag in Steel Angle Connectors University of New Hampshire University of New Hampshire Scholars' Repository Honors Theses and Capstones Student Scholarship Spring 2013 Analysis of Shear Lag in Steel Angle Connectors Benjamin Sawyer

More information

Virginia - Mathematics Standards of Learning (2009): 4.3 b, 4.3 c,

Virginia - Mathematics Standards of Learning (2009): 4.3 b, 4.3 c, 1 Lesson Plan Round Decimals Age group: 5 t h Grade Virginia - Mathematics Standards of Learning (2009): 4.3 b, 4.3 c, 5.1 Virginia - Mathematics Standards of Learning (2016): 4.3.b, 5.1 Fairfax County

More information

MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED INTERMEDIATE TIER 1 HOUR 45 MINUTES

MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED INTERMEDIATE TIER 1 HOUR 45 MINUTES Candidate Name Centre Number 0 Candidate Number GCSE MATHEMATICS - NUMERACY UNIT 2: CALCULATOR - ALLOWED INTERMEDIATE TIER 2 nd SPECIMEN PAPER SUMMER 2017 1 HOUR 45 MINUTES ADDITIONAL MATERIALS A calculator

More information

PATTERNS & FUNCTIONS

PATTERNS & FUNCTIONS PATTERNS & FUNCTIONS University of Houston Central Campus September 23, 2006 1 Warm-up Activity Test your knowledge by answering the following questions. No calculations or finger counting allowed. Good

More information

National Qua li ncations ' ' '

National Qua li ncations ' ' ' FOR OFFICIA USE National Qua li ncations 2014 MarkO X744/75/02 ifeskills Mathematics Paper 2 FRIDAY, 9 MAY 2:10 PM - 3:50 PM 1111111111111111111111111 11111111 11111111111111 * X 7 447 5 0 2 * Fill in

More information

Note! In this lab when you measure, round all measurements to the nearest meter!

Note! In this lab when you measure, round all measurements to the nearest meter! Distance and Displacement Lab Note! In this lab when you measure, round all measurements to the nearest meter! 1. Place a piece of tape where you will begin your walk outside. This tape marks the origin.

More information

The Science of Golf. Test Lab Toolkit The Score: Handicap. Facilitator Guide Grades 6-8

The Science of Golf. Test Lab Toolkit The Score: Handicap. Facilitator Guide Grades 6-8 The Science of Golf Test Lab Toolkit The Score: Facilitator Guide Grades 6-8 Science Technology Engineering Mathematics Table of Contents Welcome to the Test Lab 02 How to Use the Toolkit 03 Investigate:

More information

Name: Class: Date: ID: A

Name: Class: Date: ID: A Class: Date: Chapter 7.1-7.2 Essentail Skills REVIEW 1. The Sharks Aquatic Club recently held a fundraiser to raise money for a local charity. The swimmers received money for each lap that they swam during

More information

BASICS OF TRIGONOMETRY

BASICS OF TRIGONOMETRY Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 09-10-015 Mathematics Revision

More information

Piecewise Functions. Updated: 05/15/10

Piecewise Functions. Updated: 05/15/10 Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ Objectives: Students will review linear functions and their properties and be introduced to piecewise

More information

Applications of Mathematics

Applications of Mathematics Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 1: Applications 1 For Approved Pilot Centres ONLY Foundation Tier Wednesday

More information

Exam 1 Kinematics September 17, 2010

Exam 1 Kinematics September 17, 2010 Physics 16 Name KEY Exam 1 Kinematics September 17, 21 This is a closed book examination. You may use a 3x5 index card that you have made with any information on it that you would like. You must have your

More information

a. Cari s first tank is 4 feet wide, 8 feet long and 5 feet high. How many cubic feet of water can her tank hold?

a. Cari s first tank is 4 feet wide, 8 feet long and 5 feet high. How many cubic feet of water can her tank hold? 5.MD Cari's Aquarium Alignments to Content Standards: 5.MD.C.5.b Task Cari is the lead architect for the city s new aquarium. All of the tanks in the aquarium will be rectangular prisms where the side

More information

Operations with Fractions. reciprocals (recíprocos) ESSENTIAL QUESTION. How can you use operations with fractions to solve real-world problems?

Operations with Fractions. reciprocals (recíprocos) ESSENTIAL QUESTION. How can you use operations with fractions to solve real-world problems? UNIT Study Guide MODULE MODULE? Review Operations with Fractions Key Vocabulary reciprocals (recíprocos) ESSENTIAL QUESTION How can you use operations with fractions to solve real-world problems? EXAMPLE

More information

A Pyramid of Crunchkins

A Pyramid of Crunchkins Pictured below you will see Nestle Crunchkins stacked in a triangular pyramid. Each layer is in the shape of an equilateral triangle, and the top layer is a single Nestle Crunchkin. How many Nestle Crunchkins

More information

Functional Skills Mathematics Level 2 (Set 3)

Functional Skills Mathematics Level 2 (Set 3) PLEASE SIGN AND DATE BELOW TO CONFIRM DETAILS AND YOU UNDERSTOOD THE INSTRUCTIONS First name: Joe Family name: Blogs Student number (ULN): 0 Centre number: 0 Date of birth: 06/05/1972 Signature: Today's

More information

Unit 3 Day 7. Exponential Growth & Decay

Unit 3 Day 7. Exponential Growth & Decay Unit 3 Day 7 Exponential Growth & Decay 1 Warm Up - Zombies SCENARIO 1 A pack of zombies is growing exponentially! After 1 hour, the original zombie infected 5 people, and those 5 zombies went on to infect

More information

1) Solve for x. Round answers to the nearest tenth. (1 mark each = 2 marks)

1) Solve for x. Round answers to the nearest tenth. (1 mark each = 2 marks) WorkPlace Math 20 Chapter 1 Review Name /60 1) Solve for x. Round answers to the nearest tenth. (1 mark each = 2 marks) 3 x 4.3 2 a) = b) = 0 8 x 2) Calculate the slope. Express our answers as a fraction

More information

HOW DO SPORTS USE MATHEMATICS?

HOW DO SPORTS USE MATHEMATICS? MATHS IN SPORT LEVELS 6 YEARS 9 HOW DO SPORTS USE MATHEMATICS? 1 Key concept Mathematics is involved in sport in many ways. LEVELS 6 YEAR 9 Focusing questions 1. How do sports use mathematics? 2. How is

More information

Performance Task # 1

Performance Task # 1 Performance Task # 1 Goal: Arrange integers in order. Role: You are a analyzing a Julie Brown Anderson s dive. Audience: Reader of article. Situation: You are interviewing for a job at a sports magazine.

More information

Velocity. Translational Motion. Date:

Velocity. Translational Motion. Date: Translational Motion Velocity Name: Date: 1. A caterpillar travels across the length of a 2.00-meter porch in 6.5 minutes. What is the average velocity of the caterpillar in m/s? v ave = 2. A hiker is

More information

Midterm Exam: Making a Study Guide

Midterm Exam: Making a Study Guide Name: Class: Physics Teacher: Mr. Szopiak Date: Midterm Exam: Making a Study Guide This worksheet will help you and your classmates put together a pretty comprehensive guide to your midterm studying. Your

More information

Homework Packet Week #16

Homework Packet Week #16 Name Chapter 6 Homework Packet Week #16 Write a system of equations to represent each problem situation. Solve the system of equations using the substitution method or linear combinations method. Then,

More information

Lesson 22: Getting the Job Done Speed, Work, and Measurement Units

Lesson 22: Getting the Job Done Speed, Work, and Measurement Units Lesson 22: Getting the Job Done Speed, Work, and Measurement Units Student Outcomes Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula.

More information

Unit 1 Summary. License Math: Basic Math in Real Estate. Converting fractions to decimals

Unit 1 Summary. License Math: Basic Math in Real Estate. Converting fractions to decimals Converting fractions to decimals Some real estate math problems will contain fractions. While it is possible to solve the problem using fractions, it s typically easier to convert the fraction to a decimal

More information

Pneumatic Reservoir Analysis Work Sheet

Pneumatic Reservoir Analysis Work Sheet Pneumatic Reservoir Analysis Work Sheet Getting Started Use a pair of dial calipers to measure the length and diameter dimensions of the: 1. End Cap 2. Threaded Boss 3. Stainless Steel Tube Record these

More information

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 4 Hydraulics Jumps Lecture - 4 Features of Hydraulic Jumps (Refer Slide

More information

How many square feet of paper are needed to cover the outside of the square pyramid?

How many square feet of paper are needed to cover the outside of the square pyramid? 17 cm 16 cm How many square feet of paper are needed to cover the outside of the square pyramid? company plans to store boxes that measure 15 feet x 2 feet x 25 feet in a storage space that is 20 feet

More information

The Math and Science of Bowling

The Math and Science of Bowling The Report (100 : The Math and Science of Bowling 1. For this project, you will need to collect some data at the bowling alley. You will be on a team with one other student. Each student will bowl a minimum

More information

Bathymetry Data Collection for Subaqueous Soil Mapping. Maggie Payne 2 nd National Workshop on Subaqueous Soils Rhode Island August 9-12, 2010

Bathymetry Data Collection for Subaqueous Soil Mapping. Maggie Payne 2 nd National Workshop on Subaqueous Soils Rhode Island August 9-12, 2010 Bathymetry Data Collection for Subaqueous Soil Mapping Maggie Payne 2 nd National Workshop on Subaqueous Soils Rhode Island August 9-12, 2010 Overview of Method Collect tide data Collect bathymetry data

More information

Box-and-Whisker Plots

Box-and-Whisker Plots 7.2 Box-and-Whisker Plots Essential Question How can you use a box-and-whisker plot to describe a data set? Drawing a Box-and-Whisker Plot 3 9 23 62 3 Numbers of First Cousins 0 3 9 3 45 24 8 0 3 3 6 8

More information

Have bonus questions or something available for early finishers.

Have bonus questions or something available for early finishers. Instructions Print one answer sheet per team (plus a few spares) and one set of question cards. Arrange the question cards around the classroom / maths block / playground in the order of the reference

More information

Math 146 Statistics for the Health Sciences Additional Exercises on Chapter 2

Math 146 Statistics for the Health Sciences Additional Exercises on Chapter 2 Math 146 Statistics for the Health Sciences Additional Exercises on Chapter 2 Student Name: Solve the problem. 1) Scott Tarnowski owns a pet grooming shop. His prices for grooming dogs are based on the

More information

MATHCOUNTS 2005 State Competition Target Round Problems 1 and 2

MATHCOUNTS 2005 State Competition Target Round Problems 1 and 2 MATHCOUNTS 2005 State Competition Target Round Problems 1 and 2 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This round of the competition consists of eight problems, which will

More information

Algebra Break Apart Ones to Subtract

Algebra Break Apart Ones to Subtract Lesson 5.1 Algebra Break Apart to Subtract To subtract a one-digit number, break it apart. Break apart ones in 7. Use 4 because 44 has a 4 in the ones place. The other part is 3. 44-7 =? 4 3 Start at 44.

More information

Level 3 Mathematics and Statistics (Statistics), 2013

Level 3 Mathematics and Statistics (Statistics), 2013 91586 915860 3SUPERVISOR S Level 3 Mathematics and Statistics (Statistics), 2013 91586 Apply probability distributions in solving problems 9.30 am Wednesday 20 November 2013 Credits: Four Achievement Achievement

More information

4.8 Applications of Polynomials

4.8 Applications of Polynomials 4.8 Applications of Polynomials The last thing we want to do with polynomials is, of course, apply them to real situations. There are a variety of different applications of polynomials that we can look

More information

Parametric Ball Toss TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Parametric Ball Toss TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System Math Objectives Students will be able to use parametric equations to represent the height of a ball as a function of time as well as the path of a ball that has been thrown straight up. Students will be

More information

Math 081 Worksheet Section 5.4 v01 Spring 2011 Dressler. Name

Math 081 Worksheet Section 5.4 v01 Spring 2011 Dressler. Name Math 081 Worksheet Section 5. v01 Spring 2011 Dressler Name Solve. 1) The ratio of a quarterback's completed passes to attempted passes is 5 to 6. If he attempted 2 passes, find how many passes he completed.

More information

Level 3 Mathematics and Statistics (Statistics), 2013

Level 3 Mathematics and Statistics (Statistics), 2013 91585 915850 3SUPERVISOR S Level 3 Mathematics and Statistics (Statistics), 2013 91585 Apply probability concepts in solving problems 9.30 am Wednesday 20 November 2013 Credits: Four Achievement Achievement

More information

The field of play must be rectangular and marked with lines. These lines belong to the areas of which they are boundaries.

The field of play must be rectangular and marked with lines. These lines belong to the areas of which they are boundaries. LAW 1: THE FIELD OF PLAY Field surface Matches may be played on natural or artificial surfaces, according to the rules of the competition The colour of artificial surfaces must be green. Where artificial

More information