zilongwang/ReadingBank huggingface dataset:
Co-ordinate Geometry Straight line Gradient form: y = m + b General form: A + By + C = 0 Distance: d = (1-2)2 + (y1-y2)2 Midpoint: mp = (1 + 2 , y1 + y2 ) Gradient: m = y2-y1 2-1 Perpendicular distance P = A1 + By1 + C A2 + B2 m = tan Geometrical Properties Complementary angles add to 90 Supplementary angle add to 180 Vertically opposite angles are equal Angles at a point add to 360 Angle sum of a triangle is 180 The exterior angle of a triangle is equal to the sum of the opposite interior angles An isosceles triangle has equal base angles Equilateral triangles have all angles 60 Alternate angles on parallel lines are equal Corresponding angles on parallel lines are equal Co-interior angles between parallel lines are supplementary The angle sum of a polygon is (n-2)x180 The sum of the exterior angles of any polygon is equal to 360 The angle sum of a quadrilateral is 360 Tests for special quadrilaterals: Parallelograms: Two opposite sides equal and parallel or Opposite sides are equal or Opposite angles are equal or Diagonals bisect each other Rhombus: All sides equal or Diagonals bisect each other at right angles Rectangle: All angles are right angles or Parallelogram with equal diagonals Square: All sides equal and one angle right or All angles right and two adjacent sides equal. Tests for congruent triangles SSS SAS AAS RHS Tests for similar triangles AA Corresponding sides proportional (SSS) Two sides are proportional and included angles are equal (SAS) Applications of Differentiation First derivative dy/d - Stationary point when equals 0 - Curve increasing>0 - Curve decreasing<0 -Max turning point if second derivative negative -Minimum turning point if second derivative positive Second derivative d2y/d2 - Point of inflexion when equals 0 -Concave up when >0 -Concave down when <0 Horizontal point of inflexion if both first and second derivative equals zero. Integration
n d = n+1 + c Area between curve and axis A = ba f() d Volume of revolution V = ba [ f() ]2 d Area between two curves A = top curve - bottom curve Volume between two curves A = (top curve)2 – (bottom curve)2 Approximating integrals Simpson’s Rule A = h [ f(a) + 4 x f((a+b)/2) + f(b) ] 3 Trapezoidal Rule A = ½ h [ f(a) + f(b) ] Logarithmic and Exponential Functions Exponential functions e = e ec = cec ef() = f’() ef(x) e d = e + k ec d = ec + k Logarithmic Functions loge = logef() = d = loge = c d = logef() + c Log laws logee2 = 2logee = 2 logek = logek + loge loge = loge ½ = ½ loge loge/k = loge - logek Trigonometric Functions Arc length l = rΘ area of sector A = ½ r2Θ y = sin Period = 2 Amplitude = 1 y = cos Period = 2 Amplitude = 1 y = tan Period = = 1 Derivatives sin = cos cos = -sin tan = sec2 Integrals sina d = -1/a cos + c cosa d = 1/a sin + c sec2a d = 1/a tan + c Rates of Change
1 One mark: One mark: 1 3 2.4 x x 2 400 One mark: x After cancellations One mark: 2 400 2 2.5 x x One mark: x After cancellations One mark: 3 2.6 - x - 3-8 4 -5 4 One mark: - One mark: 3-8 4 One mark: -5 4 3 17 3 One mark: division by 5 One mark: 2 2 4 4.1 D One mark for the correct letter 1 4 4.2 C 1 4.3 C 1 4.4 B 1 5 6 20% of 50 teachers x 10 50% of R 35 = R 17,50 of R 60,00 = R 15,00 Coffee One mark: One mark: 10 One mark: R 17,50 One mark: R 15,00 One mark: Coffee 2 3 2 3
7 30% of R 125 000 x R 37 500 R125 000 – R 37 500 R 87 500 One mark: R 37 500 One Mark: subtracting. One mark: for correct answer Apply CA. 3 3 8 8.1 B One mark for the correct letter 1 3 8.2 C 1 8.3 C 1 9 3 One mark for the correct answer 1 1 10 3,3; 3,033; 3,030 One mark for the correct answer 1 1 11 11.1 2,3 0,98 +18,176 21,456 One mark: For all the correct digits One mark: For the correct answer 21,456 2 10 11.2 56,032 - 9,706 46,326 One mark: For all the correct digits One mark: For the correct answer 46,326 2 11.3 5,6 X 3,47 392 2240 + 16800 19,432 One mark: For the correct answer 19,432 One mark: For the correct arrangement of digits One mark: For multiplying correctly Apply CA. 3 11.4 18,469 ÷ 23 = 0,803 18,469 – 18,400 0,8 x 23 = 18,400 0,069 -0,069 = 0 0,003 x 23=0,069 0,8 + 0,003 = 0,803 One mark: For the correct answer One mark: for 18,4 One mark: for 0,069 Apply CA 3 12 180 000 ÷ 2 250 = 80 times One mark: For the division One mark: For the correct answer 80 Apply CA 2 2
Q5: B C Q R P S x + 5 A D x ABCD and PQRS are rectangles. Each has an area of 13cm2. AD = x cm and PS = (x + 5) cm Find in terms of x an expression for AB PQ Given that AB = 3cm greater than PQ, form an equation in x and show that it simplifies to 3x2 + 15x – 65 = 0 Solve the equation 3x2 + 15x – 65 = 0, giving each answer correct to 2 decimal places. (i) Show that the perimeter od ABCD is 14.9cm correct to 3 significant figures. Find the difference between the perimeter of two rectangles. Q6: h The length of the base of the parallelogram is 6cm more than its perpendicular height, h cm.The area of this parallelogram is 33.25 cm2. Show that h satisfies the equation 4h2 + 24h – 133 = 0 Solve the equation 4h2 + 24h – 133 = 0 Find the length of the base of the parallelogram.
and the geometry thereof 10 Consolidation of number work and an extension of ratio and proportion through multiplicative reasoning and problem solving Extension of algebraic graphs, functions and equations and an extension where appropriate to areas under curves, interpreting the gradient of a curve and more complex algebraic fractions Transformations, congruence and similarity, Pythagoras’ theorem, trigonometry for right and non-right triangles Circles and circle geometry, geometric proof, similarity and congruence and bearings Averages and range, representing data and analysing and interpreting data Probability and consolidation of topics as required. 11 Consolidation and extension of GCSE number content Consolidation and extension of GCSE algebra content Consolidation and extension of GCSE shape and geometry work Consolidation and extension of GCSE data handling work Final revision and preparation for GCSE examinations At A Level we offer both maths and further maths and the new Mathematical Studies (Core Maths) course. Students study a variety of topics from both pure and applied maths in the units outlined below. A Level maths is a popular choice at Woodkirk with over 70 students studying AS maths in 2016 and 50 students on the Mathematical studies course. At Key Stage 5 we are proud of our academic track record and every year support a number of students in moving on to study maths at University. Maths Further Maths Mathematical Studies Year 12 Core 1 Core 2 Decision 1 Further Pure 1 Mechanics 1 Statistics 1 2 units made up of numerical and statistical methods applied to unfamiliar contexts offering excellent support for other subjects such as business, psychology, sciences and geography. Year 13 Core 3 Core 4 Statistics 1 Further Pure 2 Mechanics 2 Mechanics 3 Decision 2
9 Foundation Core Higher Estimation Algebraic manipulation Averages Number skills Area Ratio + proportion Sequences Probability Fractions Angles Graphs Presenting data Measures Surface area Volume Equations Percentages Transformations Decimals/Inequalities Constructions Project - algebra 9 Enhanced Upper and Lower bounds Factorise and solve quadratics Presenting Data Number skills Pythagoras’ theorem Proportion Sequences Probability Percentages Congruency and similarity Graphs Presenting data Equations Surface area Volume Simultaneous equations Trigonometry Graphs Inequalities Constructions Algebraic fractions 10 Foundation Negative numbers Manipulating expressions Averages Primes, HCF/LCM Area and perimeter Ratio Sequences Probability Fractions 2D shapes and angles Linear graphs Statistical diagrams Pie charts Timetables Travel graphs and compound measure 3D solids, volume and surface area Linear equations Percentages Transformation Decimals Constructions 10 Core Estimating and rounding Manipulating expressions Averages Standard form Area and perimeter Ratio Sequences Probability Fractions Angles Linear graphs Scatter graphs Box plots Compound measures Volume and surface area Linear equations Percentages Transformations Inequalities Constructions 10 Higher Limits and bounds Factorising quadratics Cumulative freq and box plots Indices and standard form Circles Pythagoras Proportion Proportion Sequences Probability Percentages Similarity Linear graphs Scattergraphs Linear equations Surface area and volume Simultaneous equations Trigonometry Common graphs Inequalities Loci 10 Enhanced Limits and bounds Recurring decimals Factorising quadratics Complete the square Cumulative frequency, box plots and histograms Indices and surds Circle theorems Direct and inverse proportion Sequences Probability Percentages Congruency and similarity Linear graphs Scattergraphs and time series Linear equations Expand binomials Surface area and Volume Simultaneous equations Pythagoras and Trigonometry Common graphs Loci Vectors
11 Foundation Core Algebra – equations 3D solids Percentages Algebra – formulae Polygons + bearings Transformations Inequalities Circles and cylinders Volume and SA Quadratic graphs Trial + improvement Pythagoras’ theorem Converting units Revision 11 Higher Enhanced Circles + sectors Simultaneous equations Pythagoras’ theorem Trigonometry Inequalities Trial + imp Transformations Formulae Similarity/congruency Proportion Quadratic functions Common functions Surface area + volume Limits Transform graphs Vectors Non-right angled trig Revision Revision
these methods, and provides a fascinating combination of deep and mathematically well-grounded method-building and wide-ranging applied work with data. Mathematics at Cambridge Standard Offer: A*A*A + STEP Successful: 17% Admissions Test: None More information: The Cambridge Mathematics course is often considered to be the most demanding undergraduate Mathematics course available in Britain and, correspondingly, one of the most rewarding. Two other aspects of the course that our students greatly appreciate are its flexibility and the breadth of subjects offered. The amount of choice increases each year and after Year 1 the workload isn’t fixed so you can choose the number of options you study to suit your own work pattern. Some students take as many options as they can; others take fewer and study them very thoroughly. Maths Enrichment Problems Proving Pythagoras’ Theorem In the left figure below, the blue and green regions have been formed by dropping a perpendicular as shown. How are their areas related to the red area in the right figure? How does this result prove Pythagoras's Theorem? Graph Sketching Here are descriptions of eight real-world processes. For each, try to sketch a suitable graph. If you are not familiar with the background science, then try to use what you do know to reason through what a graph might look like. You do not need to calculate or plot exact points, just sketch graphs that give the general shape. As you produce your sketches, make a list of the features that you are considering. Temperature of a cup of tea over time. Height of the valve on a bicycle tyre as the bicycle moves forwards. Height of a tennis ball thrown straight up and then caught. Distance fallen by a parachutist jumping out of a plane.
W1 W2 W3 W4 - A W5 - A W6 - S W7 - S W8 - M W9 - M W10 - D W11 - D W12 W13 W14 Number – place value Count in multiples of 6, 7, 9. 25 and 1000. Find 1000 more or less than a given number. Count backwards through zero to include negative numbers. Recognise the place value of each digit in a four digit number (thousands, hundreds, tens and ones) Order and compare numbers beyond 1000. Identify, represent and estimate numbers using different representations. Round any number to the nearest 10, 100 or 1000. Solve number and practical problems that involve all of the above and with increasingly large positive numbers. Number- addition and subtraction Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate. Estimate and use inverse operations to check answers to a calculation. Solve addition and subtraction two step problems in contexts, deciding which operations and methods to use and why. Number – multiplication and division Recall and use multiplication and division facts for multiplication tables up to 12 x 12. Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers. Recognise and use factor pairs and commutativity in mental calculations. Multiply two digit and three digit numbers by a one digit number using formal written layout. Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects. Measurement- Area Find the area of rectilinear shapes by counting squares.
W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 Measures: Perimeter and Length Convert between different units of measure eg kilometre to metre. Measure and calculate the perimeter of a rectilinear figure (including squares) in cm and m Measurement: Area and Perimeter Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres Convert between different units of measure [for example, kilometre to metre] Find the area of rectilinear shapes by counting squares. Geometry: Angles Identify acute and obtuse angles and compare and order angles up to two right angles by size. Geometry: Shape and symmetry Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes. Identify lines of symmetry in 2D shapes presented in different orientations. Complete a simple symmetric figure with respect to a specific line of symmetry. Geometry- Position and Direction Describe positions on a 2D grid as coordinates in the first quadrant. Describe movements between positions as translations of a given unit to the left/ right and up/ down. Plot specified points and draw sides to complete a given polygon. Statistics Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs. Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. Revisit objectives not yet secure across all strands
Assessment design criteria The Assessment design criteria are based on the learning requirements and are used by teachers to: clarify for the students what he or she needs to learn design opportunities for the student to provide evidence of his or her learning at the highest level of achievement. The assessment design criteria consist of specific features that: students need to demonstrate in their evidence of learning teachers look for as evidence that students have met the learning requirements. For this subject, the assessment design criteria are: • Concepts and Techniques • Reasoning and Communication The specific features of these criteria are described below. The set of assessments, as a whole, give students opportunities to demonstrate each of the specific features by the completion of study. Assessment Design Criteria Continued Mathematics The specific features of the criteria are described below: Concepts and Techniques Reasoning and Communication CT1 Knowledge and understanding of concepts and relationships CT2 Selection and application of mathematical techniques and algorithms to find solutions to problems in a variety of contexts CT3 Development and/or application of mathematical models CT4 Use of electronic technology to find solutions to mathematical problems RC1 Interpretation of mathematical results RC2 Drawing conclusions from mathematical results, with an understanding of their reasonableness and limitations RC3 Use of appropriate mathematical notation, representations, and terminology RC4 Communication of mathematical ideas and reasoning to develop logical arguments RC5 Development and testing of valid predictions Numeracy The specific features of the criteria are described below: Concepts and Techniques Reasoning and Communication CT1 Knowledge and understanding of mathematical information and concepts RC1 Interpretation of mathematical results
6 During this term students will: identify and describe prime, composite, square and triangular numbers compare fractions with related denominators and represent them on a number line add and subtract fractions with related denominators add and subtract decimals sequence whole numbers, fractions and decimals and describe the rule used connect and convert metric units of length, mass and capacity construct prisms and pyramids revise and consolidate Year 5 concepts as required. Exemplar unit: The importance of zero During this term students will: revise and consolidate Term 1 concepts as required use efficient mental and written strategies for all four operations with whole numbers investigate positive and negative numbers investigate fractions of a quantity multiply and divide decimals by powers of ten investigate order of operations solve length and area problems construct and interpret data displays interpret secondary data. During this term students will: revise and consolidate Terms 1 and 2 concepts as required multiply decimals by whole numbers and perform divisions with terminating decimals investigate fractions, decimals and percentage (equivalence) calculate percentage discounts investigate angles describe probability (using fractions, decimals and percentage) conduct chance experiments (observed and expected frequency). During this term students will: revise and consolidate Terms 1, 2 and 3 concepts as required connect volume and capacity interpret and use timetables investigate translations, reflections and rotations be introduced to the Cartesian coordinate system.
TASK 6 Division Work through: Mymaths – number – multiply divide written – short division Examples: 168 ÷ 4 = 2782 ÷ 13 = 0 4 2 0 2 1 4 4 1 6 8 13 2 7 8 2 Now try these: 155 ÷ 5 = 234 ÷ 3 = 438 ÷ 6 = 2520 ÷ 8 = 1452 ÷ 11 = 5894 ÷ 14 = TASK 7 Add and subtract fractions Work through: Mymaths – number – fractions – adding subtracting fractions (pages 1-4 only) Examples: If the denominators are different, find a common denominator. If possible, simplify your answer. Now try these, leaving your answers in their simplest form: TASK 8 Fractions of amounts Work through: Mymaths – number – fractions – fractions of amounts
Mathematics year 9 Assessment summary for parents (Extension) Date Assessment Descriptions Assessment 1 September to mid-November Topic 1: Number: limits and bounds 25% Formal 1 hour exam Topic 2: Algebra: straight line graphs 25% Topic 3: Statistics: Diagrams and charts 25% Topic 4: Number: Indices and standard form 25% Nov 2014 School Assessment 1 (Based on topics 1 - 4) Not part of summative Assessment 2 to end of January Topic 5: Geometry: Circles and Pythagoras 25% Formal 1 hour exam Topic 6: Number: Proportion 25% Topic 7: Algebra: Sequences 25% Topic 8: Probability 25% Jan 2015 School Assessment 2 (Based on topics 5 - 8) Not part of summative Assessment 3 February - mid April Topic 9: Number : Percentages 25% Formal 1 hour exam Topic 10: Geometry: Congruency and similarity 25% Topic 11: Algebra: Simultaneous equations 25% Topic 12: Statistics: Diagrams and charts 25% April 2015 School Assessment 3 (Based on topics 9 - 12) Not part of summative Summative Assessment Mid-April to July End of Year Assessment: Covering all topics covered since September Non-calculator paper 50% Formal 2 x 1 hour exam
Calculator paper 50% 100% of summative June 2015 School Summative Assessment Mathematics year 9 Assessment summary for parents (Core) Date Assessment Descriptions Type of assessment Assessment 1 September to mid-November Topic 1: Number: rounding and calculator skills 25% Formal 1 hour exam Topic 2: Algebra: Algebraic manipulation 25% Topic 3: Statistics: Averages 25% Topic 4: Number: Indices and standard form 25% Nov 2014 School Assessment 1 (Based on topics 1 - 4) Not part of summative Assessment 2 to end of January Topic 5: Geometry: Perimeter/area inc Circles 25% Formal 1 hour exam Topic 6: Number: Ratio and Proportion 25% Topic 7: Algebra: Sequences 25% Topic 8: Probability 25% Jan 2015 School Assessment 2 (Based on topics 5 - 8) Not part of summative Assessment 3 February - mid April Topic 9: Number : Fractions 25% Formal 1 hour exam Topic 10: Geometry: Angles 25% Topic 11: Algebra: Graphs 25% Topic 12: Statistics: Diagrams and charts 25% April 2015 School Assessment 3 (Based on topics 9 - 12) Not part of summative
ASPECT 3 Number Properties Understands the structural properties of numbers including how to regroup when operating with numbers. For example, 9x6=6x6+3x6, 27+38+3=(27+3)+38 ASPECT 4 System Place Value Recognises that the place value system can be extended indefinitely in two directions – to the left and right of the decimal point Recognises the relationship between values of adjacent places (units) in a numeral ASPECT 6 Reforms the Whole When iterating a fraction part such as one-third beyond the whole, re-forms the whole ASPECT 7 Composite Area Creates the row-column structure of the iterated composite unit of area Uses the row-column structure to find the number of units to measure area Repeated Layers Creates the row-column-layer structure of the iterated layers when measuring volume Uses the row-column-layer structure to find the number of units to measure volume Measurement and Geometry Students - identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems Term 1 Term2 Term 3 Term 4 Position MA3-17MG locates and describes position on maps using a system Use a grid-reference system to describe locations Find locations on maps, including maps with legends, given their grid references Describe particular locations on grid-referenced maps, including maps with a legend Describe routes using landmarks and directional language Find a location on a map that is in a given direction from a town or landmark Describe the direction of one location relative to another Follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map Use a given map to plan and show a route from one location to another Use a street directory or online map to find the route to a given location
I-NOTE NO. NAME DELIVERY ADDRESS 44 Tehsildar Mathura NIC Computer Sadar,Dist-Mathura. 228 Chaata Tehsil Office , ChaataTehsil, Dist -Mathura. 229 Maath Tehsil Office , MaathTehsil, Dist 441 Chaata Tehsil Office , ChaataTehsil, Dist -Mathura. 442 Maath Tehsil Office , MaathTehsil, Dist 864 Chaumuha BDO ,Chaumuha Block, ChaataTehsil, Dist -Mathura 865 Nandgaon BDO ,Nandgaon Block, ChaataTehsil, Dist -Mathura 866 Naujhil BDO ,Naujhil Block, MaathTehsil, Dist -Mathura 867 Raya BDO ,Raya Block, MaathTehsil, Dist -Mathura 868 Baldeo BDO ,Baldeo Block, Mathura SadarTehsil, Dist -Mathura 869 Farah BDO ,Farah Block, Mathura SadarTehsil, Dist -Mathura 870 Goverdhan BDO ,Goverdhan Block, Mathura SadarTehsil, Dist -Mathura 999 Zila Viklang Kalyan Adhikari, Vikas Bhawan sri.Arun Kumar
I-NOTE NO. NAME DELIVERY ADDRESS 1069 District Employment officer Districk Employment Office,Civil Line,MDDA Bulding,Near Collectret, Mathura Sri.S.R Sharama 1131 Zila Parivecha Adhikari, Collectrate Parisar Mukesh Chandani 1196 Zila Samaj Kalyan Adhikari, Rajeev Bhawan, Mathura Sanjai Vyas 1310 District Informatics Officer, NIC District Centre, Collectorate,Mathura Mr. Ramprakash 1333 CMO, District Hospital Chief Medical Officer
Math Websites Unit 1: Place Value Topic: Envisions Lesson: Website: Counting/Understanding Number Lines 1-5A/1-5B Rounding 2-4 Estimating Sums 2-5 Adding 2-digit numbers 2-6 Adding with Expanded Algorithm 2-7A Adding 3-digit numbers 2-8 Problem Solving: Draw a picture 2-10 Making Sense of Addition & Subtraction Equations 4-1A Subtracting 3-digit numbers 4-3 Subtracting with an Expanded Algorithm 4-3A Problem Solving: Draw a picture & write a number sentence 4-6 Unit 1B: Graphs Topic: Envisions Lesson: Website: Organizing Data 20-1 http://www. .com/numbers/mathdata.html Reading Pictographs & Bar Graphs 20-2 Pictographs: Bar Graphs: Making Pictographs 20-3 http://www.ixl.com/math/grade-3/ -pictographs
Algebra 2 Pearson High School Algebra 2 Pearson 978-0-133-31805-0 Algebra 2 Honors Pearson High School Algebra 2 Pearson 978-0-133-31805-0 Geometry Pearson High School Geometry Pearson 978-0-133-23961-4 Geometry Honors Pearson High School Geometry Pearson 978-0-133-23961-4 Pre-Calculus Demana, Precalculus: Graphical, Numerical, Algebraic, 9th Edition Pearson 978-0-133-13548-0 Pre-Calculus Honors Sullivan Precalculus: Enhanced with Graphing Utilities, 6th Edition Pearson 978-0-133-13548-0 Probability and Statistics with Applications with Applications Larson, Elementary Statistics: Picturing the World 6th edition Pearson 978-0-133-13548-0 Probability and Statistics with Applications Honors Larson, Elementary Statistics: Picturing the World 6th edition Pearson 978-0-133-13548-0 Course eBook Title Publisher ISBN Link Calculus Lial, Calculus with Applications, Brief Version 10th edition Pearson 978-0-132-96237-7 Calculus Honors Briggs, Calculus Early Transcendentals 2nd Edition Pearson 978-0-132-96237-7 AP Calculus BC Finney Calculus: Graphing, Numerical, Algebraic 5th Edition Pearson 978-0-133-13548-0
Tab 7: Dilation of a figure (Triangle, quadrant 3) Record the coordinates of the vertices and the side length and height of the pre-image. Then record the coordinates of the vertices and the side length and height of the image. Example 1 Vertex Pre-Image Vertex Image Ratio Scale Factor Motion Rule C C’ E E’ F F’ Pre-Image Image Side EF Side E’F’ Height GC Height G’C’ How did the figure’s side length, height, and coordinates change? ___________________________ What is the scale factor being used to create the image? _________________________________ What is the motion rule for this dilation? Example 2 Vertex Pre-Image Vertex Image Ratio Scale Factor Motion Rule C C’ E E’ F F’ Pre-Image Image Side EF Side E’F’ Height GC Height G’C’ How did the figure’s side length, height, and coordinates change? ___________________________ What is the scale factor being used to create the image? _________________________________ What is the motion rule for this dilation?
Dilations Foldable Image Dilations (x, y) (2x, 2y) Enlargement Pre-Image Image Dilations (x, y) Reduction Pre-Image Name: ______________________
_____7. If the figure shown on the graph is dilated using the scale factor of 2, what are the coordinates of C’? A. (−2, 2) C. (−1, 2) B. (−2, 4) D. (2, −1) _____8. Triangle XYZ, is dilated using the scale factor of . Choose the correct ordered pair of vertex X’ and the side length of . A. X’ (3, 3) C. X’ (9, 9) = 2 = 18 B. X’ (1, 1) D. X’ (1, 1) = 2 = 6 _____9. Which motion rule describes the dilation below, with the origin as the center of dilation? _____10. Use the motion rule to draw the new vertices of the figure on the coordinate plane below. Which of the following is the correct new set of ordered pairs? (2, 0), (0, −2), (−2, 0), (0, 2) (3, 0), (0, −2.5), (−6, 0), (0, −6) C. (3, 0), (0, −3), (−3, 0), (0, 3) D. (0, 3), (3, 0), (0, 3), (3, 0)
7/5 10.7The Distance Formula, the Midpoint Formula, and Other Applications 10.8 The Complex Number 10.7:7,11,23,45,29,33,51,55,65,69 10.8: 9,13,19,27,31,35,41,49,65,69,75,83 7/6 11.1 Quadratic Equations 11.2 The Quadratic Formula Review for Midterm 2 11.1:7,11,17,39,45,51,57,59,63,75,79 11.2:7,11,15,19,27,29,33,37,41,43,49 7/7 Midterm 2 5 7/11 11.4 Applications Involving Quadratic Equations 11.3 Studying Solutions of Quadratic Equations 11.5 Equations Reducible to Quadratic 11.4:5,9,13,17,23,27,31,37,51 11.3:7,11,13,17,21,31,35,41,53,55,59 11.5:5,11,17,27,31,35,43,47,53 7/12 11.6 Quadratic Functions and Their Graphs 11.7 More About Graphing Quadratic Functions 11.8 Problem Solving and Quadratic Functions 11.6:5,13,21,31,37,47,51,57 11.7:9,11,13,15,17,21,25,31,43,47,49 11.8:7,11,15,21,23,27,29,35,37 7/13 7/14 12.1 Composite Functions and Inverse Functions 12.2 Exponential Functions 12.3 Logarithmic Functions 12.4 Properties of Logarithmic Functions 12.5 Common Logarithms and Natural Logarithms 12.2:7,13,17,39,41 12.5:13,17,35,39,47,53
6—7/18 7/19 7/20 12.6 Solving Exponential Equations and Logarithmic Equations 12.7 Applications of Exponential Functions and Logarithmic Functions 12.6:9,13,17,19,29,33,41,53,61 12.7:5,13,19,27,33,35,37,39,41,43,47 7/21 13.1 Conic Sections: Parabolas and Circles 13.1: 13,19.25,27,33,41,45,53,55 7/25 13.2 Conic Sections: Ellipses 13.3 Conic Sections: Hyperbolas 13.2:9,13,19,21,27,31,33 13.3:7,9,15,17,21,25-43(odd) 7/26 13.4 Nonlinear Systems of Equations Chatper Review 13.4:7-25(odd);27,31,37,41,47,51,57 8/18 Final Review
Book Sections Chapter 1 Chapter 1 is mainly for reading and terminology. 1.1 Descriptive and Inferential Statistics 1.2 Variables and Type of Data 1.3 Data Collection 1.4 Observational and Experimental Studies 1.5 Uses and Misuses 1.6 Computers and Calculators Chapter 2 2.1 Organizing Data 2.2 Histograms, Frequency Polygons and Ogives 2.3 Other Types of Graphs 2.4 Paired Data and Scatter Plots Chapter 3 3.1 Measures of Central Tenancy 3.2 Measures of Variation 3.3 Measures of Position 3.4 Exploratory Data Analysis Chapter 4 4.1 Sample Spaces and Probability 4.2 The Addition Rules 4.3 The Multiplication Rules 4.4 Counting Rules 4.5 Probability and Counting Rules Chapter 5 5.1 Probability Distributions 5.2 Mean, Variance, Standard Deviation and Expectation 5.3 The Binomial Distribution Chapter 6 6.1 Normal Distributions 6.2 Applications of the Normal Distribution 6.3 The Central Limit Theorem Chapter 7 7.1 Confidence Intervals for the Mean Standard Deviation Known 7.2 Confidence Intervals for the Mean, Standard Deviation Unknown 7.3 Confidence Intervals for Proportions 7.4 Confidence Intervals for Variances and Standard Deviation Chapter 8 8.1 Hypothesis Testing Traditional 8.2 z Test for a Mean 8.3 t Test for a Mean 8.4 z Test for a Proportion 8.5 Chi-Squared Test for a Variance and Standard Deviation Chapter 10 10.1 Correlation 10.2 Regression Chapter 11 11.1 Test for Goodness of Fit 11.2 Tests Using Contingency Tables 11.3 Analysis of Variance (ANOVA)
Math 140 Notes and Activity Packet (Word) Sampling Variability, Sampling Distributions, Standard Error and Confidence Intervals Confidence Intervals Act 1 Exploring Sampling Variability for Mean Averages with a Sampling Distribution The goal of this activity is to explore how well random samples approximate population values. Normally we do not know population values and we must use a sample value to approximate the population value. This is called a “point estimate”. For this activity we will look at some population data from International Coffee Organization (ICO). We will be using the “Columbian Mild” price data in U.S. cents per pound. The population mean average price was 134.338 cents per pound. Again, in real data analysis we often do not know the population value, but for this activity it is useful for comparison purposes. Open the “Confidence Interval Act 1 Data Set A” in Excel. 81 random samples have been taken from the Columbian Mild data. All the data sets have 30 coffee prices. Each person in the class will be finding the mean of a few of these data sets. Once you find the mean, you will put a magnet up or draw a dot on the board to represent the sample mean you found. When everyone’s magnets or dots are up on the board, we will have generated a “sampling distribution”. Answer the following questions: 1. The population mean was 134.338 cents. How many cents was the sample mean you calculated from the population mean of 134.338 cents? (If you calculated more than one sample mean, answer the question for all the sample means you calculated.) 2. Look at the dots or magnets on the board. Did all the sample means come out to be the same as the population mean of 134.338 cents? Why do you thing this happened? Aren’t random samples supposed to be good approximations of the population? What does this tell you about sampling variability? 3. Normally we may have only one random sample. If all you knew was one of the random samples on the board, how difficult would it be to determine that the population mean is really 134.338 cents? What does this tell us about the difficulty in determining population values from 1 random sample?
Supplemental e-resources, including MyLab, will be made available to all MATH 1630 students. The use of these resources will be at the discretion of each instructor. Curriculum Chair, Academic Assessment Specialist, and Math Faculty November 2016 For co-requisite students, content in MATH 0630, LS for Finite, will be updated to more closely align the material with content in MATH 1630. Curriculum Chair and Math Faculty November 2016 Content in MATH 1630 will be reviewed to determine its relevance to the SLO’s with a focus on building in remediation work to supplement the material based on the enrollment of LS for Finite students in MATH 1630. Curriculum Chair and Math Faculty August 2017 The Math department will create/provide an e-resource for specific questions that had lower benchmark scores. Curriculum Chair and Math Faculty August 2017 Assessment Instrument: pre/post-tests
Derivative Rules and Graphing Supplemental Instruction Iowa State University Leader: Anna Steffensmeier Course: Math 165 Instructor: Paul Barloon Date: February 8, 2018 What were the two derivative rules that we discussed in class on Monday? What are the general formulas for these two rules? Grab a partner and move to the board before we begin our activity. Derive the following functions using the derivative rules that we know. Once finished graph both the function and its derivative *on two separate graphs*. Reflect on the following. When does my f(x) have a positive slope? Negative slope? A slope of zero? Give an interval(s) or x-value of this. When does my f’(x) have positive values? Negative values? A value of zero? Give an interval(s) or x-value of this. What comparisons can you make about the two? Given the following derivative graphs, graph its corresponding f(x) function.
Math 165: Limits! Supplemental Instruction Iowa State University Leader: Riley B Course: Math 165 Instructor: Johnston Date: 1/18/17 If , , and , use the limit laws to find the limits: b. –66 6 c. d. 17 –7 –6 50 –3/5 12 –6 Math 165: Limits! Supplemental Instruction Iowa State University Leader: Riley B Course: Math 165 Instructor: Johnston Date: 1/18/17
GRADE 10 TEST 1 2018 MEMORANDUM STATEMENT/ANSWERS DESCRIPTION OF MARKS and Any two correct numbers (2) ; 0,23…. or Any two correct numbers (2) 1.2.1 -3 1.2.2. 3 4 (2) 3 4 correct value (2) 1.3.1. a 2 – a(c - 5) - 5c a 2 – ac - 5a - 5c a(a - c) + 5 ( a - c) ( a + 5 )( a- c) 1.3.2. a 3 - 27 b 3 ( a – 3b) (a 2 + 3ab + 9 b 2 ) 1.3.3. 9 a 2 + 6ab + b 2 (3a+ b) ( 3a + b ) removing brackets/multiplying factorizing/grouping answer (3) for each factor (2) factors (2) 1.4.1. (5a - 2b) ( -2a - 3b ) - 10a 2 - 15 a b + 4ab + 6 b 2 - 10 a 2 – 11ab + 6 b 2 1.4.2 (5a2 - 2b) ( 10 a 4 + 20 a 3b - 35 a 2 b 2 – 4a2b-8ab2 + 14b3 1.4.3. (2p2 + 3q2)(5p -6pq + 2q 2 ) 10p3 - 12 p3q + 4 p2q2+ 15pq2 - 18 pq2 + 6q4 10p3 - 12 p3q + 4 p2q2 - 3pq2 + 6q4 removing brackets/multiplying answer (2) Simplification (3) Expansion Answer (3)
QUESTION 2 2.2.1 - 2.2.2. 2.2.3. = 2.2.4. numerator and LCM simplifying numerator answer (4) numerator and LCM Answer (3) manipulation Answer (3) Numerator Denominator Simplification Factorisation
Simplification Manipulation Answer (7) QUESTION 3 3.1.1. = = = = - 4 3.1.2 2. = 18 = 9 = = 2 3.1.3 or Equation answer (3) dividing Simplifying answer (3) Method Simplification Manipulation Answer (4)
MALS6-4 explores contexts of everyday measurement MS11-4 performs calculations in relation to figures MS1-12-4 analyses simple two-dimensional models to solve practical problems MS2-12-4 analyses two-dimensional and models to solve practical problems MALS6-5 demonstrates understanding of money MALS6-6 explores money management and financial decision-making MS11-5 models relevant financial situations using appropriate tools MS1-12-5 makes informed decisions about financial situations likely to be encountered MS2-12-5 makes informed decisions about financial situations, including annuities and loan repayments MALS6-7 demonstrates understanding of number and patterns in a range of contexts MALS6-8 solves problems using number and patterns in real-life situations MS11-6 makes predictions about everyday situations based on simple mathematical models MS1-12-6 represents the relationships between changing quantities in algebraic and graphical forms MS2-12-6 solves problems by representing the relationships between changing quantities in algebraic and graphical forms school dimensional
Midterm Exam Review Supplemental Instruction Iowa State University Leader: Rosalie Course: Calc II Instructor: All Date: 2/21/2016 Instructions: This is the packet prepared for the SI exam review for the Midterm exam. You may work through this at your own pace, do as many or as few problems as you like, work on it ahead of time or at my review session, whatever floats your boat. The review session time is intended for students to come, work through problems, and ask any questions about material covered so far (on this packet or otherwise). Wow, I’m impressed you read this far in the directions. Go you. Give yourself a high five or fist bump or something. Since you read this far, you get the bonus hint: There are 2 especially tricky problems in the trig section. Go forth and do math. Volumes using integrals: You need to draw pictures. I would suggest one of the shape, and one of the cross section used to find the volume of the shape, at the very minimum. You also need to use a partition and a sum to find the volume A curved wedge is cut from a circular cylinder of radius 4 by 2 planes. On plane is perpendicular to the axis of the cylinder. The second plane crosses the first plane at a 45 degree angle at the center of the cylinder. Find the volume of the wedge. (hint, think orange slice on its side as far as the shape of the wedge) A pyramid 3 m high sits on its side with the x axis straight down the center. The base of the pyramid is a square with a width and length of x m. Find the volume of the pyramid.
Content Area Mathematics Grade Level 1st Grade Course Name/Course Code Standard Grade Level Expectations (GLE) GLE Code Number Sense, Properties, and Operations The whole number system describes place value relationships within and beyond 100 and forms the foundation for efficient algorithms MA10-GR.1-S.1-GLE.1 Number relationships can be used to solve addition and subtraction problems MA10-GR.1-S.1-GLE.2 Patterns, Functions, and Algebraic Structures Expectations for this standard are integrated into the other standards at this grade level. Data Analysis, Statistics, and Probability Visual displays of information can be used to answer questions MA10-GR.1-S.3-GLE.1 Shape, Dimension, and Geometric Relationships Shapes can be described by defining attributes and created by composing and decomposing MA10-GR.1-S.4-GLE.1 Measurement is used to compare and order objects and events MA10-GR.1-S.4-GLE.2 Colorado 21st Century Skills Critical Thinking and Reasoning: Thinking Deeply, Thinking Differently Information Literacy: Untangling the Web Collaboration: Working Together, Learning Together Self-Direction: Own Your Learning Invention: Creating Solutions Mathematical Practices: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Unit Titles Length of Unit/Contact Hours Unit Number/Sequence What’s in a shape? 3 weeks Count, Collect, Compare 6-7 weeks Should come before “Is it a ten or a one?” and “What’s faster than counting?” units Is it a ten or a one? 6 weeks What’s Faster than Counting? 6-10 weeks Should come after “Is it a ten or a one?” unit Keeping track 4 weeks
12 07.09A Equations for Proportional Relationships Advanced 07.10A Applications with Ratios Advanced 07.11A Applications with Percentages Advanced 07.12 Module Seven Practice Review Test 4/05 65% 13 07.12 Module Seven Practice Test 07.13 Discussion-Based Assessment 07.14 Module Seven Test 07.15A Module Seven Advanced Test 4/12 70% 14 08.00 Module Eight Pretest 08.01 Statistical Questioning 08.02 Measurements of Data 4/19 76% 15 08.03 Dot Plots and Histograms 08.04 Box Plots 08.05 Summarizing Data 4/26 82% 16 08.06 Data with Outliers 08.07 Module Eight Practice Test 08.08 Discussion-Based Assessment 5/03 86% 17 08.09 Module Eight Test 08.10 Segment Two Practice Test 08.12A Segment Two Advanced Exam 5/10 90% 18 Floating Vacation Week 5/17 94% 19 Floating Vacation Week 5/24 98% 20 Floating Vacation Week 5/31 100%
1. Mother made 8 cookies. Bob ate 3 cookies. How many cookies are left? 2. Andy picked 15 apples. Eight of the apples were green. How many of the apples were not green? 3. Six apples were in the bowl on the table. Eight bananas were in the same bowl. How many more bananas than apples were in the bowl? 4. The baker made 13 cupcakes. He sold 8 cupcakes. How many cupcakes did he have left? 5. Andre ate three carrots for lunch and five carrots for dinner. How many carrots did he eat? 6. Dad drank 5 sodas. He drank 3 more sodas. How many sodas did he drink?
Type of Graph Advantages Disadvantages Circle Graph -compares “part to whole” data is displayed as a percent -size of sector can be easily compared to other sectors -does not show actual amount or number for each category -more difficult to draw data must have “part to whole” relationship -too many categories makes it look crowded Line Graph -shows change over a period of time -can easily see trends -can be used to interpolate and extrapolate -easy to draw -limited to continuous data -may be difficult to read accurately depending on scale -comparisons between categories are not identified as quickly Bar Graph -shows number of items in specific categories -easy to compare data -easy to draw -may be difficult to read accurately depending on scale -trends are identifiable but not for purposes of interpolating and extrapolating Histogram -displays the shape of distribution -trends are easily recognizable -frequency count of items in each bin -cannot read exact values -more difficult to compare two data sets -used only with continuous data
Section 7.3.1 Supplemental Instruction Iowa State University Leader: Ben V. Course: Math 266/267 Instructor: Dr. Basnet Date: 11/9/17 In the following problems find either F(s) or f(t) as indicated
Section 4.2 Supplemental Instruction Iowa State University Leader: Ben V. Course: Math 266/267 Instructor: Dr. Basnet Date: 10/01/17 The indicated function is a solution of the given differential equation. Use reduction of order or the formula to find a second solution .
Weeks 24–26 (9 hours) Topic 2.3: Introduction to differential calculus Computation and properties of derivatives (2.3.10 – 2.3.15) estimate numerically the value of a derivative for simple power functions examine examples of variable rates of change of non-linear functions establish the formula for non-negative integers expanding or by factorising understand the concept of the derivative as a function identify and use linearity properties of the derivative calculate derivatives of polynomials Weeks 26–29 (12 hours) Topic 2.3: Introduction to differential calculus Applications of derivatives and anti-derivatives (2.3.16 – 2.3.22) determine instantaneous rates of change determine the slope of a tangent and the equation of the tangent construct and interpret position-time graphs with velocity as the slope of the tangent recognise velocity as the first derivative of displacement with respect to time sketch curves associated with simple polynomials, determine stationary points, and local and global maxima and minima, and examine behaviour as and solve optimisation problems arising in a variety of contexts involving polynomials on finite interval domains calculate anti-derivatives of polynomial functions Week 29–30 Revision and end of course assessment
Content Area Mathematics Grade Level 2nd Grade Course Name/Course Code Standard Grade Level Expectations (GLE) GLE Code Number Sense, Properties, and Operations The whole number system describes place value relationships through 1,000 and forms the foundation for efficient algorithms MA10-GR.2-S.1-GLE.1 Formulate, represent, and use strategies to add and subtract within 100 with flexibility, accuracy, and efficiency MA10-GR.2-S.1-GLE.2 Patterns, Functions, and Algebraic Structures Expectations for this standard are integrated into the other standards at this grade level. Data Analysis, Statistics, and Probability Visual displays of data can be constructed in a variety of formats to solve problems MA10-GR.2-S.3-GLE.1 Shape, Dimension, and Geometric Relationships Shapes can be described by their attributes and used to represent part/whole relationships MA10-GR.2-S.4-GLE.1 Some attributes of objects are measurable and can be quantified using different tools MA10-GR.2-S.4-GLE.2 Colorado 21st Century Skills Critical Thinking and Reasoning: Thinking Deeply, Thinking Differently Information Literacy: Untangling the Web Collaboration: Working Together, Learning Together Self-Direction: Own Your Learning Invention: Creating Solutions Mathematical Practices: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Unit Titles Length of Unit/Contact Hours Unit Number/Sequence Ruling with Rulers 6 weeks 1 Are you odd or even? 8 weeks 2 Do all halves look the same? 4 weeks 3 What does 10 have to do with 1000? 12 weeks 4