Graphin+Calculator+Standards

// Use a graphics calculator to draw scatter diagrams //  || [ These can be generated on scientific or a graphics calculator using the RND and RAN function keys.]  || (See also 10F.4.3) [Include the use of spreadsheets or a graphics calculator to explore arithmetic sequences.]  || [Graphics calculators can be used to explore a range of functional relationships.]   || // Create a display like this with your graphics calculator  //  || // ax // 2 + // bx // + // c // = 0 by reading from the graph of  // y // = // ax // 2 + // bx // + // c // the // x // -coordinate(s) of the intersection point(s) of the graph of this function and the // x // -axis. [Include the use of a graphics calculator.]     || [Include the use of a graphics calculator.]  || (See also 12F.13.1) [ These can be generated on scientific or a graphics calculator using the RND and RAN function keys.]  || (See also 12F.13.1 and 11A14.1) [ These can be generated on scientific or a graphics calculator using the RND and RAN function keys.]  ||
 * Standards Where Use of Graphics Calculator is either Required or Highly Recommended **
 * ** 10, 11 AND 12 FOUNDATION  ** ||
 * ** Grade  ** || **   Standard   ** || **   Details   ** ||
 * 10 FDN  ||   10F.4.3   ||   Sum arithmetic sequences, including the first  // n // consecutive integers, and give a ‘geometric proof’ for the formulae for these sums.   ||
 * ^  ||   10F.9.1   ||   Draw scatter diagrams between two random variables associated with some common context; identify through elementary qualitative discussion positive and negative correlation; where there appears to be correlation, draw a line of best fit, judging by eye the line about which the data points are most evenly distributed.
 * 11FDN  ||   11F.5.01   ||   Use a graphics calculator to plot and interpret a range of functional relationships, some continuous and others discontinuous, arising in familiar contexts    ||
 * ^  ||   11F.5.10   ||   Model a range of situations with appropriate quadratic functions.   ||
 * ^  ||   11F.5.13   ||   Find approximate solutions of the quadratic equation // ax // 2 + // bx // + // c // = 0 by reading from the graph of // y // = // ax // 2 + // bx // + // c // the // x // -coordinate(s) of the intersection point(s) of the graph of this function and the // x // -axis.   ||
 * ||  11F.5.14   ||   Find exactly by algebraic means, and approximately from the points of intersection of a straight line with the graph of a quadratic function, the solution set of two simultaneous equations L 1 and Q 1 //, // where L 1 represents a linear relation for // y // in terms of // x // , and Q 1 a quadratic function of // y // in terms of // x //   ||
 * ^  ||   11F.5.16   ||   Understand the statement // y is inversely proportional to x // and set up the corresponding equation // y // = // k/x // ; know some characteristics, including that // x // ≠    0 and that // x // = 0 is an // asymptote // to the curve, as is // y // = 0; study examples of inverse proportionality.   ||
 * 12FDN  ||   12F.5.1   ||   Use a graphics calculator, including the trace function, to show approximate solutions to physical problems requiring the location and physical interpretation of the intersection points of two or more graphs.   ||
 * ^  ||   12F.5.8   ||   Understand the ideas of exponential growth and decay and the forms of the associated graphs //y// = //a// // x //, where //a ≠//0; use a graphics calculator to plot the graphs of the exponential function, e // x // , and the natural logarithm function, ln //x//; know that one is the inverse function of the other and use this to find solutions to physical problems; solve for //x// the equation //y// = //a// // x // and use this in problems; use the log function (logarithm in base 10) on a calculator.   ||
 * ^  ||   12F.13.1   ||   Use coins, dice or random numbers to generate models of random data.
 * ** 10, 11 AND 12 ADVANCED  ** ||
 * 10ADV  ||   10A.4.3   ||   Identify and sum arithmetic sequences, including the first // n // consecutive positive integers, and give a ‘geometric proof’ for the formulae for these sums.
 * ^  ||   10A.5.4    ||   Use a graphics calculator or graph plotter and pencil and paper methods to plot and interpret a range of functional relationships, some continuous and others discontinuous, arising in familiar contexts.
 * ^  ||   10A.5.19   ||                   Recognise a second-order polynomial in one variable, // y // = // ax // 2 + // bx // + // c //, as a quadratic function; plot graphs of such functions (recognising that these are all parabolas) and identify the intercepts with the coordinate axes, the axis of symmetry and the coordinates of the maximum or minimum point; understand when quadratic functions are increasing, when they are decreasing and when they are stationary.
 * 11ADV  ||   11A.5.5   ||   Find approximate solutions of the quadratic equation
 * ^  ||   11A.5.8   ||   Find exactly by analytical methods and approximately by graphical methods, the solution set of two simultaneous equations L 1 and Q 1 //, // where L 1 represents a linear relation for // y // in terms of // x // , and Q 1 a quadratic function of // y // in terms of // x // .    ||
 * ^  ||   11A.5.10   ||   Understand the statement // y is inversely proportional to x // and set up the corresponding equation // y // = // k/x // ; know some characteristics, including that // x≠ // 0 and that // x // = 0 is an // asymptote // to the curve, as is // y // = 0; study examples of inverse proportionality.
 * ||  11A.5.11   ||   Use a graphics calculator, including use of the trace function, to show approximate solutions to physical problems requiring the location and physical interpretation of the intersection points of two or more graphs.   ||
 * ^  ||   11A.5.18   ||   Understand the ideas of exponential growth and decay and the forms of the associated graphs // y // = // a //// x //, where // a // > 0; use a graphics calculator to plot the graphs of the exponential function, e // x // , and the natural logarithm function, ln // x // ; know that one is the inverse function of the other and use this to find solutions to physical problems; solve for // x // the equation // y // = // a //// x // and use this in problems; use the log function (logarithm in base 10) on a calculator.    ||
 * ^  ||   11A.14.1   ||   Use coins, dice or random numbers to generate models of random data.
 * 12 ADV  ||   12A.5.1   ||   Use a graphics calculator to plot exponential functions of the form // y // = e // kx // ; describe these functions, distinguishing between cases when // k // is positive or negative, and the special case when // k // is zero.   ||
 * ||  12A.16.1   ||   Use coins, dice or random numbers to generate models of events described by random variables and to calculate probabilities and frequencies.
 * 12SC  ||   12SC.5.1   ||   Use a graphics calculator to plot exponential functions of the form // y // = e // kx // ; describe these functions, distinguishing between cases when // k // is positive or negative, and the special case when // k // is zero.   ||