Heinemann VCE Zone textbook reference General Mathematics

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1 Contents Cross-reference table for TI-Nspire CAS skills required for Heinemann VCE Zone: General, Heinemann VCE Zone: Further and Heinemann VCE Zone: Specialist. Code Description TS.1 Rounding off 4 TS.2 Scientific notation 8 TS.3 Entering numbers using scientific notation 8 TS.4 Fractions, decimals and index notation 9 Heinemann VCE Zone textbook reference General Further TS.5 TVM calculations , 314, 320 TS.6 Solving equations 46, 99, 100 TS.7 Transposition 54 TS.8 Checking algebraic simplifications 61 TS.9 Finding axis intercepts 62 TS.10 Finding points of intersection 63, 70, 96, , 237 TS.11 More algebraic simplifications 64 TS.12 Generating tables of values 66 TS.13 Choosing the values for a table of values 67 TS.14 Using Solve to solve simultaneous linear equations TS.15 Simplifying algebraic expressions TS.16 Partial fractions TS.17 Solving three simultaneous equations 94 TS.18 Factorising expressions 99 TS.19 Finding relationships 103 TS.20 Entering a matrix TS.21 Adding and subtracting matrices TS.22 Matrix multiplication TS.23 Determinant and inverse of a matrix TS.24 Solving simultaneous equations using matrices TS.25 Transition matrices , 417 TS.26 Plotting graphs from a table of values 171 Specialist

2 Code TS.27 Description Finding the equation of a straight line given two points Heinemann VCE Zone textbook reference General TS.28 Graphing half-planes TS.29 Intersecting half-planes TS.30 Investigating quadratic functions TS.31 Finding a quadratic equation from a table of values 212 TS.32 Graphs of logarithmic functions 216 TS.33 Calculating percentiles 248 TS.34 Mean and median TS.35 Five-figure summary and boxplot , 17 TS.36 Standard deviation TS.37 Comparative boxplots TS.38 Random numbers TS.39 Drawing a scatterplot , 111 TS.40 Pearson's correlation coefficient (r) TS.41 Regression equations , 83 TS.42 Three-median regression line TS.43 Using linear regression 318 TS.44 Surd arithmetic 339 TS.45 Radians 366 TS.46 Trigonometry 384, 389, 394, 395 Further 174, 175, 178, 179, 180, 185, 197 TS.47 Unit vectors , 14 TS.48 Scalar (dot) product of vectors TS.49 Scalar and vector resolutes of vectors TS.50 Complex solutions TS.51 Complex arithmetic TS.52 Complex conjugates TS.53 Complex division TS.54 Polar form of complex numbers TS.55 Converting from polar form TS.56 Polar form arithmetic , 61 Specialist

3 Code Description Heinemann VCE Zone textbook reference General Further TS.57 Complex solutions to polynomial equations TS.58 Complex solutions to complex polynomial equations TS.59 Arithmetic sequences TS.60 Arithmetic series TS.61 Geometric sequences , 122 TS.62 Terms in a geometric sequence TS.63 Solving for a power TS.64 Sum of a finite geometric series TS.65 Sum of an infinite geometric series TS.66 Solving for an unknown in a ratio TS.67 Finding the derivative 585 TS.68 Area under a curve TS.69 Adding and subtracting forces 608 TS.70 Histograms 6 TS.71 Coefficient of determination 50 TS.72 Residual plots 62 TS.73 Transformation of x to x 2 65 TS.74 Transformation of x to log 10 x. 66 TS.75 Transformation of x to x 1 67 TS.76 Seasonal graphs 88, 96, 98 TS.77 Difference equations 141 TS.78 Fibonacci and Fibonacci-like sequences 146 TS.79 Heron's rule 195 TS.80 Linear modelling 217 TS.81 Step graphs 223 TS.82 Linear programming 247 TS.83 Straight line graphs 260 TS.84 Cubic graphs 261 TS.85 Rectangular hyperbolas 261 TS.86 The truncus 262 TS.87 Finding a relationship 266 Specialist

4 Code Description Heinemann VCE Zone textbook reference General TS.88 Compound interest 296 TS.89 Scalar multiplication of matrices 394 Further TS.90 Converting a vector to rectangular form 11 TS.91 Position vectors 12 TS.92 Evaluating zi n 50 TS.93 Powers of complex numbers 51 TS.94 Converting point form to polar coordinates 53 TS.95 Addition of ordinates 99 TS.96 Describing key points on graphs 100 TS.97 Reciprocal graphs 106 TS.98 Drawing an ellipse 113 TS.99 Drawing a hyperbola 120 TS.100 Reciprocal circular functions 129 TS.101 Graphs of reciprocal circular functions 135 TS.102 Graphs of inverse circular functions 159 TS.103 Derivatives of inverse circular functions 165 TS.104 Antidifferentiation 177 TS.105 Definite integrals 216 TS.106 Area between curves 224 TS.107 Volumes of solids of revolution 232 TS.108 Second derivatives 247 TS.109 First-order differential equations 263 TS.110 Second-order differential equations 268 TS.111 First-order differential equations of the type 272 dy = f (y) dx TS.112 Slope field analysis 290 TS.113 Displacement at given times 302 TS.114 Displacement, velocity and acceleration graphs Specialist TS.115 Analysing motion 328, 394 TS.116 Parametric graphs 340,

5 Introduction This Supplement has been designed specifically for students using any of Heinemann VCE Zone: General, Heinemann VCE Zone: Further or Heinemann VCE Zone: Specialist. The Supplement: covers all TI-Nspire CAS skills for use in General, Further and Specialist includes keystrokes and screen dumps for the TI-Nspire CAS is clearly linked to textbook sections and worked examples. The instructions are written in an abbreviated format. Where there is a key to press on the keyboard the symbol for that key is shown, such as b. Where you need to make a selection from one of the menus that appear on the screen, the title of the option is given, such as Actions. Where you need to perform a number of things in order, they are separated by a >, such as b > Actions > Define. In these menus, the items have a number or letter beside them. You can either arrow down to select the item or you can press the appropriate number or letter to go there directly. In some of the screen dumps the menu system is shown. As the software version changes, so, sometimes, do the numbers or letters beside menu choices. The instruction tells you which one to choose: use this rather than just blindly pressing the number. Students are reminded to download the latest upgrades for the software from the TI site. In some of the sections, alternative methods are shown so students can make a decision as to which method suits them best. Other methods for completing some of the tasks included may be possible. What is presented is an attempt to familiarise students (and teachers) with this piece of technology. As the user becomes more familiar with the CAS then, no doubt, many other options will present themselves. Also available are: CAS Supplements Heinemann VCE Zone: Mathematical Methods 1&2/3&4 CAS TI-Nspire CAS Supplement Heinemann VCE Zone: General/Further/Specialist Casio ClassPad Supplement Heinemann VCE Zone: Mathematical Methods 1&2/3&4 CAS Casio ClassPad OS Version 3 Supplement Worked Solutions Heinemann VCE Zone: General Student Worked Solutions Heinemann VCE Zone: General Teacher Worked Solutions Heinemann VCE Zone: Further Student Worked Solutions Heinemann VCE Zone: Further Teacher Worked Solutions Heinemann VCE Zone: Specialist Student Worked Solutions Heinemann VCE Zone: Specialist Teacher Worked Solutions

6 TS.1 Rounding off Use the following instructions to round numbers. 1. In the Calculator application, press b > Number > Number Tools > Round. 2. Enter the number to be rounded (in this case ), followed by a comma and then the number of decimal places required (in this case 3), close the bracket and press. The number is then displayed with the correct number of decimal places. 3. If we need to round more than one number, it is better to set our CAS to the specified number of decimal places. We change this setting by pressing c > System Info > Document Settings, to get the screen shown at right. Pressing enables us to see our choices. We highlight the number of decimal places we want (we need to choose Fix 3 because Float 3 is significant figures) and press to confirm the choice, then e down to Apply to System and press, then again to confirm. (If there is no reason to arbitrarily limit the number of digits displayed, Float seems to be a good option.) TI-Nspire CAS Supplement 1

7 TS.2 Scientific notation 1. Unlike graphics calculators, our TI-Nspire CAS will not automatically convert numbers into scientific form because it has the capacity to scroll across an otherwise full screen to show the answers. If we want the answer in scientific form, we hold down / while we press. For instance if we wanted in scientific form, we would enter , hold down the / and press. The calculator gives us the answer 4.56E -5, this is short hand for Of course we could change the number of decimal places displayed as well. TS.3 Entering numbers using scientific notation 1. To enter figures in standard form or scientific notation we use the i key. We do not need r before the i. If we want our answers to appear in scientific form, we must change the document settings. To do this, we press c > System Info > Document Settings and change Exponential Format to Scientific. We press to bring us back to the screen. With this setting changed, we can perform calculations involving standard form and get answers in that form. (If the exponent is negative, we press v before entering the exponent.) 2 Heinemann VCE Zone: General/Further/Specialist

8 TS.4 Fractions, decimals and index notation 1. If our CAS is set to Auto (we can check this by looking at the middle word at the top of the screen), then our CAS will decide whether fraction or decimal is the better way to display the answer to our calculation. We can change the setting by pressing c > System Info > Document Settings As an example, calculate as shown. This 4 was entered as a fraction, so it gives a fraction answer. 3. If we want a decimal equivalent to this then we press / To enter a mixed number, such as 3, press 5 3+2p5. Notice that this displays the 17 answer in improper fraction form as There are some fraction options available. Press b > Number > Fraction Tools > Proper Fraction > /v). Notice that the display shows the fraction with the + between the whole number part and the fraction part. TI-Nspire CAS Supplement 3

9 6. To raise a number to a power use the l key. Be careful because the cursor stays on the index line. If we were going to enter other parts of an expression, we would need to press to bring the cursor back to the base line. Press to display the answer. 7. Our CAS has built-in algebraic logic. This means the order of operations rule has been built in. We need to use brackets accurately to indicate the calculation we require. As an example, gives an answer of when we may have been 4 expecting 1. To get 1, we would enter (1 + 3) 4. Also, in calculations such as 2(5 + 9), we do not need to put a multiplication sign ( ) outside the bracket. TS.5 TVM calculations Our TI-Nspire has a TVM (Time, Value, Money) Solver built into it. The following uses the data from Worked Examples 14 and 15 on Heinemann VCE Zone: General pp. 24 and To access the TVM Solver press b > Algebra > Finance Solver. 4 Heinemann VCE Zone: General/Further/Specialist

10 2. First we calculate the value of an investment. We make: N = 48 (the number of payments) I(%) = 6 (the interest rate) PV = 0 (the present value of the investment) Pmt = -200 (we are paying out $200 each month) FV = 0 (this is what we want to find; 0 holds the place) PpY = 12 (12 payments per year) CpY = 12 (interest is calculated 12 times per year) PmtAt = END (the calculations are done at the end of the month) To move from one line to the next press. 3. When we have entered all of the values, we scroll back to FV (keep pressing ) and then press. Note that the answer is the same as was calculated in the Worked Example. 4. Here we calculate the monthly deposit required to reach a specified final value (in this case $6000). We enter the given information, putting 0 beside Pmt and 6000 beside FV then press with Pmt highlighted. TI-Nspire CAS Supplement 5