Shape, Space and Measure
|
|
|
- Bathsheba Clarissa Adams
- 7 years ago
- Views:
Transcription
1 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 and circumference of circles Circle Theorems Congruency and Similarity Surface Area Spheres, Cones and Pyramids Transformations: Translations Enlargements Density, Mass, Volume Bearings Constructions Loci Vectors
2 Q1 - Pythagoras. ABCD is a trapezium. AD = 10 cm AB = 9 cm DC = 3 cm Angle ABC = angle BCD = 90 Calculate the length of AC. Give your answer correct to 3 significant figures.... (Total for Question is 5 marks)
3 Q2 Pythagoras and SOHCAHTOA. The diagram shows a quadrilateral ABCD. drawn Diagram NOT accurately AB = 16 cm. AD = 12 cm. Angle BCD = 40. Angle ADB = angle CBD = 90. Calculate the length of CD. Give your answer correct to 3 significant figures cm (Total for Question is 5 marks) Q3 SOHCAHTOA missing angle.
4 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. Diagram NOT accurately drawn Q4 Cosine Rule (Total for Question is 3 marks) Calculate the length of PR. Give your answer correct to 3 significant figures cm (Total for Question is 3 marks)
5 Q5 Sine rule. ABCD is a parallelogram. Diagram NOT accurately drawn AC = 9 cm DC = 11 cm Angle DAC = 100 Calculate the area of the parallelogram. Give your answer correct to 3 significant figures....cm 2 (Total for Question is 5 marks)
6 Q6 ½ ab sin C & cosine rule. ABC is a triangle. (a) Work out the area of triangle ABC. Give your answer correct to 3 significant figures. (b) Work out the length of the side AB. Give your answer correct to 3 significant figures cm 2 (2)... (3) (Total for Question is 5 marks)
7 Q7 Trig graphs. A sketch of the curve y = sin x for 0 < x < 360 is shown below. y 2 1 O x 1 2 (a) Using the sketch above, or otherwise, find the equation of each of the following two curves. (i) y 2 1 O x 1 2 (i) Equation y =...
8 (ii) y 2 1 O x 1 2 (ii) Equation y =... (2) (b) Describe fully the sequence of two transformations that maps the graph of y = sin x onto the graph of y = 3 sin 2x (3) (Total 5 marks)
9 Q8 Trig graphs. Diagram 1 is a sketch of part of the graph of y = sin x. (a) Write down the coordinates of (i) P, (, ) (ii) Q. (, ) (2) Diagram 2 is a sketch of part of the graph of y = 3 cos 2x. (b) Write down the coordinates of (i) R, (, ) (ii) S (, ) (2) (Total 4 marks)
10 Q9 3D Pythag/Trig. The diagram represents a cuboid ABCDEFGH. AB = 5 cm. BC = 7 cm. AE = 3 cm. (a) Calculate the length of AG. Give your answer correct to 3 significant figures. E 3 cm A 5 cm F B H D 7 cm G C Diagram NOT accurately drawn... cm (2) (b) Calculate the size of the angle between AG and the face ABCD. Give your answer correct to 1 decimal place. (2) (Total 4 marks)
11 Q10 Plans and Elevations. The diagram shows a solid prism. On the centimetre square grid, draw the side elevation of the solid prism from the direction shown by the arrow. (Total for Question is 2 marks)
12 Q11 Circumference of a Circle. * Saphia is organising a conference. People at the conference will sit at circular tables. Each table has a diameter of 140 cm. Each person needs 60 cm around the circumference of the table. There are 12 of these tables in the conference room. A total of 90 people will be at the conference. Are there enough tables in the conference room? (Total for question = 4 marks)
13 Q12 Area of circles. *Mr Weaver's garden is in the shape of a rectangle. In the garden there is a patio in the shape of a rectangle and two ponds in the shape of circles with diameter 3.8 m. The rest of the garden is grass. Diagram NOT accurately drawn Mr Weaver is going to spread fertiliser over all the grass. One box of fertiliser will cover 25 m 2 of grass. How many boxes of fertiliser does Mr Weaver need? You must show your working. (Total for Question is 5 marks)
14 Q13 Sector Area. OAB is a sector of a circle, centre O. The radius of the circle is 15 cm. The angle of the sector is 30. Calculate the area of sector OAB. Give your answer correct to 3 significant figures cm 2 (Total for Question is 2 marks)
15 Q14 Circle Theorems. * S and T are points on the circumference of a circle, centre O. PT is a tangent to the circle. SOP is a straight line. Angle OPT = 32 Work out the size of the angle marked x. Give reasons for your answer.... (Total for Question is 5 marks)
16 Q15 - Circle Theorems. A, B, C and D are points on the circumference of a circle, centre O. AC is a diameter of the circle. AC and BD intersect at E. Angle CAB = 25 Angle DEC = 100 Work out the size of angle DAC. You must show all your working.... (Total for question = 4 marks)
17 *Q16 Circle Theorems/Congruent Triangles. AOC and BOD are diameters of a circle, centre O. Prove that triangle ABD and triangle DCA are congruent. (Total for Question is 3 marks)
18 Q17 Similar shapes lengths. Diagram NOT accurately drawn Quadrilaterals ABCD and LMNP are mathematically similar. Angle A = angle L Angle B = angle M Angle C = angle N Angle D = angle P (a) Work out the length of LP. (b) Work out the length of BC....cm (2)...cm (2) (Total for Question is 4 marks)
19 Q18 Similar shapes volume. A frustrum is made by removing a small cone from a similar large cone. The height of the small cone is 20 cm. The height of the large cone is 40 cm. The diameter of the base of the large cone is 30 cm. Work out the volume of the frustrum. Give your answer correct to 3 significant figures cm 3 (Total for Question is 4 marks)
20 Q19 Surface area. Here is a cuboid. The cuboid is 6 cm by 1.5 cm by 1.5 cm. Work out the total surface area of the cuboid cm 2 (Total for Question is 3 marks)
21 Q20 - Volume of Pyramid. The diagram shows a pyramid. BCDE is a square with sides of length 10 cm. The other faces of the pyramid are equilateral triangles with sides of length 10 cm. (a) Calculate the volume of the pyramid. Give your answer correct to 3 significant figures. (b) Find the size of angle DAB cm 3 (4)... (2) (Total for Question is 6 marks)
22 Q21 Hemisphere and cone volume. The diagram shows a solid made from a hemisphere and a cone. Diagram NOT accurately drawn The radius of the hemisphere is 4 cm. The radius of the base of the cone is 4 cm. Calculate the volume of the solid. Give your answer correct to 3 significant figures....cm 3 (Total for Question is 3 marks)
23 Q22 Hemisphere and bounds. A clay bowl is in the shape of a hollow hemisphere. 8.2 cm 7.7 cm Diagram NOT accurately drawn The external radius of the bowl is 8.2 cm. The internal radius of the bowl is 7.7 cm. Both measurements are correct to the nearest 0.1 cm. The upper bound for the volume of clay is kπ cm 3. Find the exact value of k. k =.. (Total 4 marks)
24 Q23 - Transformations. Describe fully the single transformation that maps triangle P onto triangle Q (Total for Question is 2 marks)
25 Q24 - Transformations. Enlarge triangle B by scale factor 3, centre (1, 2). (Total for Question is 3 marks) Q25 - DMV. 3.8 cm 2.5 cm Diagram NOT accurately drawn An ice hockey puck is in the shape of a cylinder with a radius of 3.8 cm, and a thickness of 2.5 cm. It is made out of rubber with a density of 1.5 grams per cm 3. Work out the mass of the ice hockey puck. Give your answer correct to 3 significant figures.... grams (Total 4 marks)
26 Q26 - Bearings. The diagram shows the positions of two villages, Beckhampton (B) and West Kennett (W). Scale: 4 cm represents 1 km. (a) Work out the real distance, in km, of Beckhampton from West Kennett.... The village, Avebury (A), is on a bearing of 038 from Beckhampton. On the diagram, A is 6 cm from B. (b) On the diagram, mark A with a cross ( ). Label the cross A. (2) (2) (Total for Question is 4 marks) Q27 - Bearings. Work out the bearing of (i) B from P,... (i) P from A, N P A Diagram NOT accurately drawn... B (Total 3 marks)
27 Q28 - Bearings. N Diagram NOT accurately drawn N Hospital Cinema 72 Art gallery The diagram shows the position of each of three buildings in a town. The bearing of the Hospital from the Art gallery is 072. The Cinema is due East of the Hospital. The distance from the Hospital to the Art gallery is equal to the distance from the Hospital to the Cinema. Work out the bearing of the Cinema from the Art gallery. (Total 3 marks)
28 Q29 SAS accurate drawing. Make an accurate drawing of this triangle. The line AB has been drawn for you. (Total for Question is 2 marks) Q30 SSS accurate drawing. Here is a sketch of a triangle Diagram NOT accurately drawn 3.6 cm 6 cm 7.5 cm
29 In the space below, use ruler and compasses to construct the triangle accurately. You must show all construction lines. (Total 3 marks) Q31 Angle bisector. A B C Use ruler and compasses to construct the bisector of angle ABC. You must show all construction lines. (Total 2 marks)
30 Q32 Construct given angle. In the space below, use ruler and compasses to construct an angle of size 30. You must show all construction lines. (Total 3 marks) Q33 Perpendicular bisector. A B Use ruler and compass to construct the perpendicular bisector of the line segment AB. You must show all construction lines. (Total 2 marks)
31 Q34 - Perpendicular bisector through point on line. Use the ruler and compasses to construct the perpendicular to the line segment AB that passes through the point P. You must show all construction lines. B P A (Total 2 marks) Q35 Perpendicular from external point. A B C On the grid, draw a line from the point C perpendicular to the line AB. (Total 1 marks) Q36. The diagram represents a triangular garden ABC. The scale of the diagram is 1 cm represents 1 m. A tree is to be planted in the garden so that it is nearer to AB than to AC, within 5 m of point A. On the diagram, shade the region where the tree may be planted.
32 B A C (Total 3 marks) Q37. A B D C ABCD is a rectangle. Shade the set of points inside the rectangle which are both and more than 4 centimetres from the point A more than 1 centimetre from the line DC. (Total 4 marks)
33 Q38 - Vectors. A B 6a Diagram NOT accurately drawn P O OABC is a parallelogram. 6c C P is the point on AC such that AP = 2 3 AC. OA = 6a. OC = 6c. (a) Find the vector OP. Give your answer in terms of a and c.... (3) The midpoint of CB is M. (b) Prove that OPM is a straight line. (2) (Total 5 marks)
34 Q39 - Vectors. Diagram NOT accurately drawn OAB is a triangle. = a = b (a) Find in terms of a and b.... (1) P is the point on AB such that AP : PB = 3 : 1 (b) Find in terms of a and b.give your answer in its simplest form.... (3) (Total for Question is 4 marks)
35 Mark Scheme Shape, Space and Measure Q1. Q2.
36 Q3.
37 Q4. Q5.
38 Q6. 7. (a) (i) y = 1 + sin x 2 B1 for y = 1 + sin x (ii) y = 2sin x B1 for y = 2sin x SC both (i) f(x) + 1, (ii) 2f(x) B1 (b) Stretch parallel to y-axis scale factor Stretch parallel to x-axis scale factor 2 M1 for stretch A1 for Stretch parallel to y-axis scale factor 3 oe 1 A1 for Stretch parallel to x-axis scale factor 2 oe 1 SC if M0 award BI for sf 3 vertically and sf horizon. 2 [5] 8. (a) (i) (90, 1) 2 B1 cao could be indicated on diagram (ii) (180, 0) B1 cao could be indicated on diagram (b) (i) (45, 0) 2 B1 cao could be indicated on diagram (ii) (90, 3) B1 cao could be indicated on diagram [4] 9. (a) = 83 M1 for correct use of 3D Pythagoras formula or 2 correct applications of the 2D formula A1 for 9.11 to 9.12
39 (b) Tan GAC = 3 ( ) M1 correct trig expression for angle GAC A1 for 19.2 to 19.3 [4] Q10. Q11. Q12. Q13.
40 Q14.
41 Q15. Q16. Q17.
42 Q18. Q19.
43 Q20.
44
45 Q = ( ) = B1 for 8.25 or 7.65 seen M1 for expression using r = 8.25 minus same expression using r = M1 for R r used A1 cao [4] Q23. Q24.
46 Q26. Vol = π = π = = Mass = = M1 for π r where r = is 3.8 or 7.6 A1 if r = 3.8 M1 for A1 for cao [4] 27. (i) = 222 M1 for or 159 seen or for or 42 seen A1 cao (ii) (180 63) B1cao for 243 [3] or 81 3 H C A y x = y = 81 M1 for (AHC=) (=162) accept x marked as 72 and CHS as 90 or symbol ( y )180 "162" M1 dep for (= 9) 2 A1 cao
47 ALTn Draws line from A parallel to HC M1 for z = w and y + z = (= 18) "18" M1 for y (or z) = 2 A1 cao [3] Q B1 for base 7.5 cm (± 0.1 cm) M1 for 1 correct arc (± 0.1 cm) A1 for 3 rd vertex within tolerance [3] 31. Bisector 2 M1 pair of relevant arcs on line segments and corresponding relevant pair of intersecting arcs within guidelines A1 bisector line within guidelines [2] 32. Correct construction 3 B1 for 60 construction (with construction arcs seen) M1 for angle bisector construction (intersecting arcs) A1 for 30 within tolerance [3] 33. Correct construction 2 M1 for relevent intersecting arcs aligned vertically A1 for straight line within guidelines [2] 34. Perpendicular from P to intersecting arcs (within tramlines); perpendicular at least 2 cm long 2 M1 relevant pair of arcs crossing within tramlines
48 A1 SC M1A0 for full construction of a line perpendicular to AB not through P [2] 35. (a) Draws perp. 1 B1 for correctly drawing perp must touch line or cut line AB ± 2mm (b) Sketches a cylinder 1 B1 for sketching cylinder [2] 36. See overlay 3 Bisector of BAC Arc around A Region B3 cao (B2 for either two correct boundaries, no shading/ wrong shading or one correct boundary, one incorrect boundary with valid shading) (B1 for either two incorrect boundaries but one drawn from A and one intersection, with valid shading or one correct boundary) Ignore shading outside the triangle [3] 37. overlay 4 M1 quarter circle drawn centre A inside rectangle (ignore lines outside the rectangle) A1 radius 4 cm ±2mm B1 line drawn 1 cm ±2mm from DC. B1 ft (dep on two loci attempts drawn) region shaded [4] 38. (a) 2a + 4c 3 OP OA AP 2 = OA (6c 6a) 3 = 6a + 4c 4a M1 for OP OA AP or any correct vector journey involving OP 2 1 M1 for AP (6c 6a) oe or CP = ( 6c + 6a) oe or reverse 3 3 vectors A1 for 2a + 4c oe (accept unsimplified)
49 (b) OM 1. 5OP so OPM is a straight line 2 Q39. Eg OM OC CM = 6c + 3a OM 1. 5OP 1 B1 for OM = 6c + (6a) or PM = 2c + a unsimplified or reverse 2 vectors B1 for a fully correct proof. [5]
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
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
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
Mathematics 2540 Paper 5540H/3H
Edexcel GCSE Mathematics 540 Paper 5540H/3H November 008 Mark Scheme 1 (a) 3bc 1 B1 for 3bc (accept 3cb or bc3 or cb3 or 3 b c oe, but 7bc 4bc gets no marks) (b) x + 5y B for x+5y (accept x+y5 or x + 5
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
DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
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:
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
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
Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
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
MENSURATION. Definition
MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters
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
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC
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
GEOMETRIC MENSURATION
GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the
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
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 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 28, 2015 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. 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
Mathematics A *P44587A0128* Pearson Edexcel GCSE P44587A. Paper 2 (Calculator) Higher Tier. Friday 7 November 2014 Morning Time: 1 hour 45 minutes
Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Friday 7 November 2014 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper
Instructions. Information. Advice
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
1MA0/3H Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 3H (Non-Calculator) Set C Higher Tier Time: 1 hour 45 minutes
1MA0/H Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper H (Non-Calculator) Set C Higher Tier Time: 1 hour 45 minutes Materials required for examination Ruler graduated in centimetres and millimetres,
16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
Conjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical
New York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
MATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
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
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
1MA0/4H Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 4H (Calculator) Set A Higher Tier Time: 1 hour 45 minutes
1MA0/4H Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 4H (Calculator) Set A Higher Tier Time: 1 hour 45 minutes Materials required for examination Ruler graduated in centimetres and millimetres,
Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
Section 1: How will you be tested? This section will give you information about the different types of examination papers that are available.
REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help
Conjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
Geometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes
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
Comprehensive Benchmark Assessment Series
Test ID #1910631 Comprehensive Benchmark Assessment Series Instructions: It is time to begin. The scores of this test will help teachers plan lessons. Carefully, read each item in the test booklet. Select
Chapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
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
Geometry Enduring Understandings Students will understand 1. that all circles are similar.
High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Monday 6 June 2011 Afternoon Time: 1 hour 45 minutes
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 6 June 2011 Afternoon Time: 1 hour 45
Angles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
GEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
Solutions to Practice Problems
Higher Geometry Final Exam Tues Dec 11, 5-7:30 pm Practice Problems (1) Know the following definitions, statements of theorems, properties from the notes: congruent, triangle, quadrilateral, isosceles
GCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.
Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How
Tuesday 6 November 2012 Morning
H Tuesday 6 November 2012 Morning GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) *A516821112* 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. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications
Unit 2: Number, Algebra, Geometry 1 (Non-Calculator)
Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics B Unit 2: Number, Algebra, Geometry 1 (Non-Calculator) Friday 14 June 2013 Morning Time: 1 hour 15 minutes Candidate Number
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
Additional Topics in Math
Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are
2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
CIRCLE COORDINATE GEOMETRY
CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle
Friday 13 June 2014 Morning
H Friday 13 June 2014 Morning GCSE MATHEMATICS B J567/04 Paper 4 (Higher Tier) * 3 0 5 9 4 6 2 0 7 5 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical
9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
SURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
GEOMETRY COMMON CORE STANDARDS
1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,
Example Practice Papers for Cambridge IGCSE Mathematics Extended Practice Book. Example Practice Paper 4 17
Eample Practice Papers for Cambridge IGCSE Mathematics Etended Practice Book Eample Practice Paper Mark scheme for Paper 13 Eample Practice Paper 4 17 Mark scheme for Paper 4 36 NAME Cambridge IGCSE Mathematics
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
Mathematics (Project Maths)
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 12:00 300 marks Examination
CIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
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
Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Friday 10 June 2011 Morning Time: 1 hour 45 minutes
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 10 June 2011 Morning Time: 1 hour 45 minutes
Geometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
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 Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
Mark Scheme (Results) Summer 2014. Pearson Edexcel GCSE In Mathematics A (1MA0) Higher (Calculator) Paper 2H
Mark Scheme (Results) Summer 2014 Pearson Edexcel GCSE In Mathematics A (1MA0) Higher (Calculator) Paper 2H Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK
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
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 1FR Centre Number Tuesday 6 January 2015 Afternoon Time: 2 hours Candidate Number Foundation Tier Paper Reference
Algebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test
Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan
Geometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
General Certificate of Secondary Education January 2014. Mathematics Unit T3 (With calculator) Higher Tier [GMT31] FRIDAY 10 JANUARY, 9.15am 11.
![General Certificate of Secondary Education January 2014. Mathematics Unit T3 (With calculator) Higher Tier [GMT31] FRIDAY 10 JANUARY, 9.15am 11.](/thumbs/40/20949623.jpg "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,
Geometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
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
Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper
The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving
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
Thursday 8 November 2012 Afternoon
H Thursday 8 November 2012 Afternoon GCSE MATHEMATICS B J567/04 Paper 4 (Higher Tier) *J517181112* 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, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
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
Shape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
2014 2015 Geometry B Exam Review
Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists
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
CAMI Education linked to CAPS: Mathematics
- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4
of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the
High School Geometry Test Sampler Math Common Core Sampler Test
High School Geometry Test Sampler Math Common Core Sampler Test Our High School Geometry sampler covers the twenty most common questions that we see targeted for this level. For complete tests and break
Geometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.
Class-10 th (X) Mathematics Chapter: Tangents to Circles
Class-10 th (X) Mathematics Chapter: Tangents to Circles 1. Q. AB is line segment of length 24 cm. C is its midpoint. On AB, AC and BC semicircles are described. Find the radius of the circle which touches
San Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS
San Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS Recall that the bisector of an angle is the ray that divides the angle into two congruent angles. The most important results about angle bisectors
SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
Area of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
ME 111: Engineering Drawing
ME 111: Engineering Drawing Lecture # 14 (10/10/2011) Development of Surfaces http://www.iitg.ernet.in/arindam.dey/me111.htm http://www.iitg.ernet.in/rkbc/me111.htm http://shilloi.iitg.ernet.in/~psr/ Indian
Geometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
CIRCLE THEOREMS. Edexcel GCSE Mathematics (Linear) 1MA0
Edexcel GCSE Mathematics (Linear) 1MA0 CIRCLE THEOREMS Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may
Unit 3: Circles and Volume
Unit 3: Circles and Volume This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,
PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
Geometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
CHAPTER 8 QUADRILATERALS. 8.1 Introduction
CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is
2, 3 1, 3 3, 2 3, 2. 3 Exploring Geometry Construction: Copy &: Bisect Segments & Angles Measure & Classify Angles, Describe Angle Pair Relationship
Geometry Honors Semester McDougal 014-015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 1-1 MAFS.91.G-CO.1.1 1 Use Segments & Congruence, Use Midpoint & 1-/1- MAFS.91.G-CO.1.1,
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target