Why do I need to log in?
A. General Information
B. SET UP
C. Getting Decimal Answers
D. Complex Numbers
E. Solve a Quadratic or Cubic Equation
F. Solve a System of Two or Three Equations
G. Solve a System of Four Equations
H. One Variable Statistics and Frequency Distributions
I. Regression (Line of Best Fit)
J. Calculate a Derivative
K. Calculate a Definite Integral
Image from Sharp Canada
Starting in Fall 2017, the calculator that will be supported and used in all School of Technology first-year math courses is the Sharp EL-W516XGB-SL Advanced WriteView calculator. It is available in the college bookstore.
General Information about the Sharp EL-W516XGB-SL Calculator
DON’T THROW THOSE INSTRUCTIONS AWAY!!
The Sharp EL-W516XGB-SL Advanced WriteView calculator uses multiple lines to display fractions as fractions, roots as roots, integrals as integrals, matrices as matrices, and so on. This allows you to enter your calculations exactly as they are shown on your page!
Results in WriteView mode are displayed as fractions, roots, etc. An important button is the "CHANGE" button at the middle right of the keypad. Pressing "CHANGE" will change the form of your answer from mixed fraction, to improper fraction, to decimal, and back to fraction.
The calculator has eight different modes: NORMAL, STAT (statistics), TABLE (table of values), COMPLEX (complex numbers), EQUATION (to solve various types of equations), MATRIX (matrices), VECTOR, DISTRIBUTION (probability distributions), and DRILL(math drills). Each has its own purpose and will be used at different points in your course. Switch modes by hitting the MODE button and then pressing the number of the corresponding mode (e.g. 1 for STAT). Use the up/down arrows to show all of the options. In general, use NORMAL mode (MODE 0). You can also hit the HOME button in the top left corner at any time to return to NORMAL mode.
The 2ndF button allows access to secondary functions (written in orange above the buttons). For example, to find the cube root of 5 hit the 2ndF button then the square root button. A cube root sign will appear in the display. Hit 5 and then = to calculate the cube root of 5 (1.7099759...). To turn off the calculator hit 2ndF then ON/C.
Using brackets can make calculations easier to perform. Sometimes they are necessary to get the correct value. This is because the calculator follows the BEDMAS order of operations. An example of this would be dividing 1 by 2+3. The correct answer is 0.2. If you type this in as 1÷2+3 the answer will be 3.5 which is incorrect. The calculator divided 1 by 2 and then added 3 to the result. We want 1 divided by 2+3 so we enclose the 2+3 in brackets. Typing it in as 1÷(2+3) we get 0.2, the correct answer. This is a simple example of how brackets can be used in complicated calculations.
The UP/DOWN/LEFT/RIGHT keys will be used when entering more complicated calculations. These will allow you to move up to exponents, down in fractions, outside of roots, etc.
You can review previous calculations in NORMAL mode by hitting the UP arrow, or by hitting ON/C and then the UP/DOWN arrows. This is handy for going back to check that your calculation was entered correctly, or for changing a number when performing multiple calculations with the same formula.
This allows you to change which unit your calculator uses for angles, the format it uses to display numbers, and allows you to turn off the WriteView display.
To enter SET UP press the 2ndF button followed by MATH. <SET UP> should now be displayed with 7 options, 1-4 on screen and 5-7 available by pressing the DOWN arrow.
This changes what unit your calculator uses for angles: degrees, radians, or grads. There are two ways to change how your calculator displays angles.
To use the SET UP route, press 0 and then ENTER to select DRG. Now press 0 DEG, 1 RAD, or 2 GRAD to select the mode you want.
A shortcut is accessible by pressing 2ndF and then the decimal point. That accesses DRG►.
Note: You can tell which mode you are in by looking at the top of your display. It will say DEG, RAD, or GRAD.
This changes the format used to display numbers: fixed, scientific, engineering, or normal mode.
In SET UP, press 1 and then ENTER. Now press the number for the format you want.
0 - FIX. This choice fills the screen with decimal places. You will be asked to enter a TAB SETTING between 0 and 9. This allows you to choose how many decimal places you want the calculator to use for all numbers.
1 - The SCI choice changes your calculator into Scientific Notation mode. You will be asked to enter a SIG. SETTING between 0 and 9. This allow you to choose how many significant digits you want the calculator to display for all numbers.
2 - The ENG choice changes your calculator into Engineering mode. You will be asked to enter a TAB SETTING between 0 and 9. This allows you to choose how many digits you want the calculator to display for all numbers.
3, 4 - The NORM1 and NORM2 choices get your calculator out of any of these modes back to looking a “normal calculator” look. NORM1 should be your choice.
This changes the display format your calculator uses. There are two options:
0: W-VIEW - WriteView uses multiple lines to display fractions as fractions, roots as roots, and so on. You'll have two option for how to display answers in WriteView mode. The first option, 0 - EXACT, displays answers as fractions, roots, etc. You can get the decimal answer by pressing CHANGE until the decimal answer appears. The second option, 1 - APPROX, will display answers in decimal form. Pressing the CHANGE button will change the answer to fraction or root form, if possible.
1: LINE - Linear mode uses a single line so fractions are displayed as 4r5, and so on. This mode makes the calculator display just like the Sharp EL-546W. Results are displayed as decimals (unless fractions were used).
This adjusts the contrast of your calculator's display making it lighter or darker.
When turned ON, this places a bar above a decimal digit(s) that repeats (e.g. 1/3 = 0.3333... would be displayed as 0.3 with a bar above the three).
Allows you to change the decimal point to a comma instead of a dot.
Allows you to enter your name into the calculator. Your name will display under the Sharp logo when your calculator is being turned of (2ndF then ON/C).
The Sharp EL-W516XGB's WriteView displays calculation results are displayed as fractions (or with roots or pi) whenever possible. Pressing the CHANGE button repeatedly will change these to decimal answers.
If you prefer to always get decimal results you need to switch to WriteView APPROX mode. Do this by pressing the 2ndF button then MATH to enter the SET UP screen. Then press 2 for EDITOR, 0 for W-VIEW, and 1 for APPROX. Answers will now be given as decimals by default. Pressing the CHANGE button will change the answer to fraction or root form, if possible. To go back to displaying answers as fractions/roots by default, go through the same process but press 0 for EXACT.
Press 2ndF and MATH to enter SET UP. Now press 2 for EDITOR.
There are now two options: 0: W-VIEW, and 1: LINE
Press 1 for Linear display mode to disable the WriteView display, and to get decimals as your answers.
To return to the WriteView display, go through the steps above but press 0 for W-VIEW.
The MODE button allows you to enter and calculate with complex numbers in polar or rectangular form. Choose MODE and then the "3" COMPLEX option.
Once you do that, you may choose polar or rectangular formats. To choose polar format, press 2ndF and the 8 key to access →rθ. You will see an “rθ” appear on the left side of the screen. To choose rectangular format, press 2ndF and the 9 key to access →xy. You will see an “xy” appear on the left side of the screen.NOTE: In COMPLEX mode, to change from degrees to radians press 2ndF MATH to enter SETUP, then 0 for DRG, and 0 for DEG or 1 for RAD.
That means the “xy” is on the left side of the screen. This does not affect the normal arithmetic calculations you need to do, but it does activate the buttons on the calculator used for complex number calculations. One of those is the “i” key which is under the DºM'S button near the top right of the keypad.
Let’s say you want to enter 2 + 8i. You would type in 2 + 8, and then press the DºM'S key for i. Press the = key. The calculator shows both parts of the complex number: the real part "2", and the imaginary part "+8i".
To multiply (4 + 6i)(6 – 5i), enter the numbers. Make sure you use brackets as shown! Press the = key. You get 54 + 16i.
For any entry of complex numbers in rectangular form, use brackets around each complex number, as in (4 – 2i).
That means the “rθ” is on the left side of the screen. Again, this does not affect the normal arithmetic calculations you need to do, but it does activate the complex number buttons on the calculator. One of those is the angle symbol which is 2ndF then (x,y).
Let’s say you want to enter the complex number 2 angle 30^{o}. First make sure you are in degree mode (DEG is displayed at the top of the screen). Then type in 2, press 2ndF then (x,y) for the angle symbol, and then type 30. Press the = key. The calculator shows both parts of the complex number: the magnitude "2", and the angle "30".
To multiply (5 angle 30^{o})(6 angle 120^{o}), enter the numbers as shown. Press the = key. You get 30 angle 150^{o}.
Say you want to change 30 angle 150^{o} to rectangular format. There are two ways to do this depending on what complex mode you are in.
If you are in polar format mode (rθ), enter 30 angle 150^{o} and press =. Now change this to rectangular format by pressing 2ndF 9 to switch to rectangular format mode. The calculator tells you -25.98... + 15i. So 30 angle 150^{o } = 25.98... + 15i.
If you are in rectangular format mode (xy), enter 30 angle 150^{o} and press =. The calculator displays this in rectangular format as -25.98... + 15i.
Say you want to change 4 – 7i into polar format. Using one of the two methods above, you should get 8.06 angle -60.26^{o}.
Let's say you want to solve a quadratic equation. It must be written in descending order, like 5x^{2} − 8x − 1 = 0.
Press MODE and then 4 for EQUATION . You are solving a quadratic equation so press 2 for QUAD.
The calculator now wants you to enter a value for a, b, and c. These are the coefficients on the quadratic equation ax^{2} + bx + c =0.
So for a, type in 5 and press the = key.
For b, it is negative so start by pressing the negative key (–), then 8, and then the = key.
For c, it is also negative so start with (–), then 1, and press the = key.
The calculator states the answers: X= 1: 1.716515139 2: –0.116515139
These are the two real solutions to the quadratic equation. Pressing the DOWN arrow will show the coordinates of the quadratic's vertex, X-Value being the x-coordinate and Ymin or Ymax the y-coordinate. For 5x^{2} − 8x − 1, the result is X-Value: 0.8 and Ymin: –4.2 meaning the vertex is at the point (0.8, –4.2).
Let’s say you want to solve a cubic equation. It also must be written in descending order, like 4x^{3} + 3x^{2} – 2x – 1 = 0. Press MODE and then 4 for EQUATION. You are solving a cubic equation so press 3 for CUBIC.
The calculator will lead you through the solution by asking for a, b, c, and d. These are the coefficients for the general cubic equation ax^{3} + bx^{2} + cx + d = 0.
For 4x^{3} + 3x^{2} – 2x – 1 = 0 enter 4, 3, –2, and –1 in that order, pressing the = button to move from one choice to the next.
The calculator gives you the answers: X 1: -1 2: 0.640388203 3: -0.-390288203
These are the three solutions to the cubic equation.
Say the equation was 4x^{3} + 3x^{2} – 4x + 1 = 0.
The calculator gives you the answers: X= 1: -–1.517526486 2: 0.383763242 ± 0.132164836i
Notice there is only a 1 and 2 on the left side of the screen. There is no 3.
This means there is only one real solution (X1 = –1.517526486) and two complex number solutions! The two complex solutions are X2 = 0.383763242 + 0.132164836i and X3 = 0.383763242 – 0.132164836i.
Let’s say that you are working with two linear equations. They must be in this format:
4x + 5y = 35 2x – 6y = 23
Press MODE and then 4 for EQUATION. We are working with a system of two variable linear equations so press 0 for 2-VLE (2-variable linear equations).
The calculator will lead you through the solution by asking for the coefficients for each equation moving left to right (a1, b1, c1, a2, b2, and c2).
a1 is the coefficient on the first variable in the first equation. So a1 = 4. Press 4 and hit =. It nows asks for b1 which is the coefficient on the second variable in the first equation. So b1 = 5. Press 5 and hit =. We do the same for c1 which is the constant value on the right side of the equation. Type 35 and hit =.
Go through the same process for the second equation working left to right (a2 = 2, b2 = -6, and c2 = 23).
Pressing = after entering c2 will give you the solution to the equation. X = 9.6 and Y = -0.6 (these are rounded to one decimal place). D represents the determinant of the matrix for this system of equations, and generally will not be used your math course.
The calculator stays in this mode until you hit the HOME button.
If you were solving a system of three linear equations you would press MODE, then 4 for EQUATIONS, followed by 1 for 3-VLE (3-variable linear equations). The process is the same except there will be three equations, and there will be a d1 for each equation (this will now be the constant)
CAUTION: The variables in your equations must be in the same order, and the constant term must always be on the right side. X represents the solution for the first variable in your equations, Y the second variable, and Z the third variable.
The Sharp EL-W516XGB calculator will solve a system of two or three linear equations using the 2-VLE and 3-VLE commands in MODE → EQUATION, but solving a system of four equations is not possible through this method.
This is where matrices come in. A matrix (plural: matrices) is an array of numbers, and they are often used to represent and solve systems of equations.
Let’s say we want to solve the system of equations 2p + q + 5r + s = 5 p + q – 3r – 4s = -1 3p + 6q – 2r + s = 8 2p + 2q + 2r – 3s = 2
The terms on the left side of the equal signs display an array of numbers. These numbers are the “coefficients” of the letter variables. These are highlighted in bold. 2p + 1q + 5r + 1s 1p + 1q – 3r – 4s 3p + 6q – 2r + 1s 2p + 2q + 2r – 3s
NOTE: The variables must be in the same order for all of the equations.
They will become this matrix on your calculator:
To enter this matrix in your calculator you need to be in matrix mode. Press MODE and then 5 for MATRIX (press the DOWN arrow to see this option).
Next press MATH and 1 for EDIT. A screen will appear with "matrix: 2 x 2" above a matrix with four blanks. The "2x2" represents the number of rows and columns required for the matrix. The cursor should be on the first 2, which represents the number of rows in the matrix. Our matrix has 4 rows so type 4. The cursor will move to the second 2, which represents the number of columns. Our matrix has 4 columns so type 4. Press = to move down to the matrix.
Notice that the matrix on the screen has increased its number of blanks to represent our 4x4 matrix (the last row and last column are off of the screen).
Enter these numbers in the matrix above into your calculator exactly as you see them. Start by typing 2 and then pressing =. A 2 goes into the first blank (row 1, column 1) and the cursor advances to the next blank. Type 1 and press =, then 5 and press =. The screen now shifts to show the last column. Type 1 and press =. The first row is now filled and the cursor advances to the first blank in the second row.
Continue entering the rest of the numbers, including the negative signs. If you make a mistake, you can use the arrow keys to scroll back to the mistake and type over it.
Once all of the values have been entered, press the ON/C button to exit out of the number entry for the matrix.
Press the MATH key and choose number 3 for STORE. This is to store the matrix numbers in the calculator’s memory. You have four choices. Let’s choose matA. Press 0 to make that choice. "STORED!" will briefly display and you will return to the main "MATRIX MODE" screen..
If you think you made an entry error, you can always go back to survey your entries. Press the MATH key and then choice 0 for MATRIX. Choose matA by pressing the 0 key. matA shows on your screen. Press = to show the matrix. Use the arrows to scroll through the values. Correct any if necessary, and then go through the STORE procedure again.
Now to enter the numbers that are on the right side of the equal sign in the equations. You will enter those in another matrix. This will be a matrix with 4 rows and 1 column.
Press the MATH key, and then 1 for EDIT. The 4x4 matrix you just finished entering will display, and the cursor will be on the first 4. You want to enter the matrix above. It has 4 rows so we type 4. This moves us to the second 4 which is the number of columns. Our new matrix only has 1 column so type 1 and hit =. The matrix displayed is now 4 rows by 1 column.
Replace the values currently in the matrix with the values in the matrix above. Type 5 and press =. Type –1 and press =. Type 8 and press =. Type 2 and press =. The matrix should now contain all of the values.
Press the ON/C button to exit. We need to save this matrix as well. Press MATH and STORE (number 3). Let’s save this as matB. Press 1. "STORED!" will briefly display and you will return to the main "MATRIX MODE" screen.
We have now entered all the equation numbers in matrix form. Think of the 4 equations now in matrix form like this:
To solve for these 4 variables, we will need to move the large matrix on the left to the other side of the equation. In algebra, we would be moving it over by dividing since it is attached to the variables by multiplication. Dividing is the same as multiplying by its inverse (using the exponent of -1). This all looks like this:
In terms of the calculator, we need to multiply matA^{-1} x matB.
Press the MATH key and then press 0 for MATRIX. Press 0 for matA. Press 2ndF and then x^{2} button to access the x^{-1}. Your screen should now show matA^{-1}. Press the multiplication key. Press the MATH key and then press 0 for MATRIX. Press 1 for matB. Press the = key.
The calculator now provides the answers in matrix form. First it tells you that there are 4 rows and 1 column. The matrix is displayed below with the the numbers 2, 0.2, 0, and 0.8 (you'll need to use the down arrow to see the 0.8). In matrix form, this would look like this:
So you can see that p = 2, q = 0.2, r = 0, and s = 0.8. These are the solutions to the equations.
SOME CAUTIONS: • Since there are 4 variables, there are 4 equations and each variable in each equation MUST have a number attached to it. If a variable is missing, assume the number is a zero. • Make sure you keep the letter variables in the same order in each equation. • In each equation, there must be the number by itself on the right side of the equal sign.
Let’s say we want to calculate statistics for single variable data (e.g. 90, 80, 70, 60,and 50).
Press MODE and then 1 for STAT. Now press 0 for SD (single variable data).
First you need to make sure the memory is cleared out. Press 2ndF and then the MODE button to access CA to clear everything. To begin typing in the date press the CHANGE button. This will display the data entry table.
To enter 90, 80, 70, 60, and 50 as data, start by typing in 90 and then press the = key. The calculator will now show 90 under the X in the first row. The FRQ( frequency) value is 1 by default. We'll use that for frequency distributions later. For now, we'll leave it as 1.
Now type in 80 and press the = key.Type in 70 and then press the = key.Type in 60 and then press the = key. Type in 50 and then press the = key.
After 50 was typed in, the calculator screen should show five rows with the data values, and a sixth row that's empty.
Now to access the statistics, press the ON/C key. Next press ALPHA then 8 for STAT, then 0 for STATISTICS VAL. The calculator will now list all of the statistical values for the data you entered. Pressing the DOWN arrow will show more statistical values.
What if you made a mistake? Let’s say that 90 should have been 30. Press the ON/C button then the CHANGE button to return to the data entry table. Use the up and down arrows to scroll through the list of data. Scroll through to find when X: 90 appears. Make sure the cursor is on the 90. Type in the corrected value of 30 and press the = key. Pressing ON/C will return you to the main screen without erasing your data.
Let’s say we are working with a frequency distribution. A frequency distribution tells us how many times each data value appears in the data set. For example, in the data below 90 occurred 5 times, 80 appeared 2 times, 70 only once, and so on.
As before, go into MODE and choose STAT and SD. Clear the memory to enter this new data (2ndF MODE). You will be entering these pairs of numbers in a table format with the first column being the X values and the second column the frequency (FRQ). The data will be entered in ordered pairs in the form (X, FRQ). To do this, we'll use the (x, y) key.
To enter 10 with a frequency of 5, start by typing 10 and then press the (x, y) key. This (x, y) key inserts a comma. Now type 5 as the frequency. It should appear after the comma. Press =. You should now see 10 in the X column and 5 in the FRQ column. Your cursor will have moved down to the next line. Type 20, press (x,y), then 2 followed by =. In the second row of the table, you'll see 20 in the X column and 2 in the FRQ column.
Continue doing the same thing for the rest of the data. Make sure to press = after entering in the last piece of data (your cursor should be on a blank row).
To calculate the statistics, first press ON/C. Next press ALPHA then 8 (STAT in green above it). For a summary of the statistics for the frequency distribution, press 0 STATISRICS VAL. The calculator will display the n value (total number of values), the mean, sample standard deviation, and sample variance. Pressing the DOWN arrow will show the population standard deviation and variance, the sum of the x and x^{2} values. Pressing the DOWN arrow again will show the minimum x value, the first and third quartile, the median, and the maximum value (press DOWN to see this). If you prefer to calculate each statistics separately, press ALPHA then 8 then 2 for VARIABLE. Press the number of the desired statistical value and press =. To show the sums, press ALPHA 8 then 3 for SUM. To show the quartiles, min/max, and median press ALPHA 8 then 4 for MIN/MAX(QUARTILE).
To return to the main STAT screen, hit the ON/C button. To return to the data you entered, press the CHANGE button. You can then use the arrows to move around the table. To make edits, move the cursor to the value you want to change, type in the new value, and press =.
The table below compares the time T in seconds with distance D in cm of an object rolling down an inclined plane.
Say you want the linear line of best fit through the points below. This will give an equation relating the time T (the independent variable) with the distance D (the dependent variable).
Press MODE, followed by 1 for STAT and then 1 for a+bx, the equation of a straight line with y-intercept of a and slope of b.
The data will be entered in ordered pairs in the form (T, D). T is first because it is the independent variable, and D is second because it is the dependent variable (the distance the object rolls depends on how long it has been rolling for). So the first ordered pair is (1,6), the second is (2, 23), and so on. The data will appear in table form on your calculator with a column for the X (independent variable), a column for the Y (dependent variable), and the frequency. NOTE: If there is already data in the calculator, press 2ndF then MODE to clear the data. To get back to the data entry table, press the CHANGE button.
To enter (1, 6) type 1, press (x, y) to insert a comma, and then type 6. Press = to enter the pair. The calculator will now show one row of data: 1 in the X column, 6 in the Y column, and 1 in the FRQ column. We'll leave the frequency as 1.
Next enter (2, 23). Type 2, press (x, y), type 23, then press =. Continue like this with the rest of the data. Once it has all been entered the calculator should show five rows with data and the cursor on the 6th row.
The equation of the straight line of best fit is y = a + bx, where x represent the independent variable and y represents the dependent variable.
To find the values of a and b, start by pressing the ON/C key. Next press ALPHA and 8 for STAT. Press 1 REGRESSION VAL to display the regression values. The calculator will now show the form of the equation a+bx and a list of the regression values.
a = -41.7, b = 35.9, and r = 0.9837 (these numbers are all rounded). So the equation of the line of best fit is D = -41.7 + 35.9T. To see the coefficient of determination, r^{2}, press the DOWN arrow
The other forms of regression work the same way.
For exponential regression of the form y = a e^{bx}, press MODE followed by 1 for STAT, and then 3 for a e^bx^{}. Enter the data as above. The equation of the line of best fit is y = a e^{bx}. [The e in this equation is the value 2.718....] Find the values of a, b, and r in the same way.
a = 3.84, b = 0.786, r = 0.9734 (these numbers are all rounded). So the equation of the line of best fit using exponential regression is D = 3.84e^{0.786}^{T}.
For exponential regression of the form y = a b^{x}, press MODE followed by 1 for STAT, and then 7 for a b^x^{}. Enter the data as above. The equation of the line of best fit is y = a b^{x}.
a = 3.84, b = 2.19, r = 0.9734 (these numbers are all rounded). The equation of the line of best fit is D = 3.84(2.19)^{T}.
You can find the power line of regression in the same fashion. Choose MODE, STAT, and then 5 for a x^b. Enter the data as above. The equation of the line of best fit is y = a x^{b}.
a = 5.93, b = 2.01, r = 0.9998 (these numbers are all rounded). So the equation of the line of best fit using power regression is D = 5.93T^{2.01}.
Your Sharp EL-W516XGB calculator can find the value of a first derivative for you. The calculator should be in NORMAL mode for this.
Say you wanted the value of the derivative of y = 4x^{2} + 8x – 3 at the point where x = 5.
Start by getting the d/dx command on your screen. Press ALPHA followed by the ) button above the division button.
Type the equation 4x^{2} + 8x – 3 into the brackets in the numerator of the fraction. To type the x, press the green ALPHA button and then RCL button, or hit RCL twice. Type the entire equation in.
Once the entire equation has been entered between the brackets, press the right arrow to enter the value for x. We want the value of the derivative at x = 5, so type in 5 next to the "X =" and press the = key.
The answer we get is 48.
The calculator is using an approximation formula to come up with this value. See the calculator instructions for the formula. The formula works well for smooth continuous functions.
Your Sharp EL-W516XGB calculator can find the value of a definite integral for you. The calculator should be in NORMAL mode for this.
Say you wanted the value of the integral of y = 5x + 1 between x = 1 and x = 2.
To use this feature, first press ALPHA followed by the ( button above the multiplication button to get the integral command ∫dx. An integral will appear with blanks for the lower and upper limits, and the equation.
The cursor starts in the box for the lower limit. The lower limit is x = 1, so type 1. Press the up arrow to move to the upper limit. The upper limit is x = 2, so type 2. Press the right arrow to move to the box for the equation. The integral should now show the lower and upper limits.
Next, you need to type in the equation. Start by typing 5. To type the x, use the green ALPHA button and then press the RCL button to access x. Or, press the RCL button twice. Type the entire equation in.
Once everything is typed in you can press the = key. The calculator will show "BUSY" near the top right of the screen while it calculates the answer.
The answer we get is 8 1/2.