How to make a table of values on the Casio fx-CG50
Fill in "complete the table" questions in seconds and spot sign changes for roots. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
Sign-change arguments in numerical methods ("show that there is a root between 0.3 and 0.4"), the trapezium rule's y values, and sketching.
Practise it: Numerical methods · Integration (trapezium rule).
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Tables of values on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 7 (TABLE).
- Type Y1 = X² − 3X + 1 and EXE.
- F5 (SET): Start −1 EXE, End 4 EXE, Step 0.5 EXE, then EXIT.
- F6 (TABLE). Scroll with ▼. Change any X value in the table to see y there.
- Two functions (Y1, Y2) give two columns: handy for comparing a model with data or for f(x) and g(x).
Tables of values on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- y=: Y1 = X² − 3X + 1.
- 2nd window (TBLSET): TblStart = −1, ΔTbl = 0.5, Indpnt: Auto.
- 2nd graph (TABLE). Scroll with the arrow keys.
- Set Indpnt: Ask to type in your own x values (useful for uneven tables).
Tables of values on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Graphs page: f1(x) = x² − 3x + 1.
- ctrl T shows the table next to the graph.
- menu → Table → Edit Table Settings: Table Start −1, Table Step 0.5.
Tables of values on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 9 (Table).
- Type f(x) = X² − 3X + 1, = (press = again to skip g(x)).
- Start −1 =, End 4 =, Step 0.5 =. The table appears.
- With both f(x) and g(x) the table holds up to 30 rows; with f(x) only, 45.
Tables of values on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Table.
- Enter the function after f(x)=, then set Table Range: Start −1, End 4, Step 0.5.
- Choose Execute (or EXE) to show the table.
Worked example
Complete a table of y = x² − 3x + 1 for x = −1 to 4 in steps of 0.5, and find two intervals that contain a root.
Answers (checked with Python)
For example f(0) = 1, f(0.5) = −0.25, f(2.5) = −0.25, f(3) = 1. The sign changes between 0 and 0.5 and between 2.5 and 3, so there are roots in [0, 0.5] and [2.5, 3] (they are x ≈ 0.382 and 2.618).
Common calculator mistakes
- Squaring negatives: typing −1² gives −1. The table uses X² correctly, but when you check a value by hand, bracket it: (−1)².
- Step too large: a step of 1 can jump straight over two roots close together.
- A sign change shows a root only if the function is continuous there: y = 1/x changes sign at 0 with no root.
- Plot points from the table accurately and join them with a smooth curve, not straight lines.
Do it in Desmos
Not in the exam. Desmos is not allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- Define f(x) = x^2 − 3x + 1.
- Add a table (+ → table), put x₁ values −1, −0.5, … and f(x₁) as the second column heading: Desmos fills it in.
- The points appear on the graph; the curve shows where it crosses the axis.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
f(x)=x^{2}-3x+1a table of the data
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.