Casio fx-991CW for Further Maths
Scientific calculator with no symbolic algebra or graph plotting. Numerical integration does not demonstrate an exact antiderivative. A calculator output does not supply required reasoning.
Use only where the selected paper permits a calculator. The CW+ UK variant has a separate manual.
Check quadratic roots with Polynomial
Solve x² − 5x + 6 = 0 and check both roots.
- Open Equation, choose Polynomial and select the quadratic coefficient form.
- Enter coefficients 1, −5 and 6, then calculate.
- Move through the displayed roots; distinguish root results from any extremum coordinates.
Expected result: The roots are 2 and 3. Substitution gives zero in each case.
Factorisation gives (x − 2)(x − 3) = 0 and explains why these are all the roots. Copy each requested variable with its value.
Use on a calculator-permitted paper. Polynomial handles degrees 2–4. The general Solver is a separate numerical method and may return only one root.
Check what Solver has actually found
Investigate x² = 4 using two starting estimates.
- In Equation, choose Solver and enter x² = 4.
- Select x as the target, supply a positive starting estimate and execute.
- Repeat with a negative starting estimate. Read the left-side minus right-side residual.
Expected result: Suitable starts can find 2 and −2. Each has residual zero mathematically.
Factor x² − 4 = (x − 2)(x + 2) to prove the complete solution set. A small residual supports a particular approximation; it does not count all roots.
Solver uses Newton iteration, returns decimal approximations and may fail or return one of several roots. Starting values can change the result.
Check a matrix product in the right order
For A = [[1,2],[0,1]] and B = [[1,0],[3,1]], calculate AB and BA.
- Open Matrix and its matrix-variable list. Define MatA with two rows and two columns and enter A.
- Define MatB with the same dimensions and enter B. Return to the calculation screen.
- Insert MatA and MatB using the Matrix catalogue and calculate MatA × MatB.
- Repeat in the reversed order and compare the entries.
Expected result: AB = [[7,2],[3,1]], whereas BA = [[1,2],[3,7]].
In a column-vector transformation, AB applies B first. Calculate one entry by hand, such as 1 × 1 + 2 × 3 = 7, to check the entered matrices.
Multiplication requires matching inner dimensions. A stored matrix can persist after leaving the app or switching the calculator off, so check the current entries. The calculator supports larger matrices than some qualifications permit.
Before accepting an answer
Check angle mode, domain and the form requested. A decimal approximation does not replace an exact result, and a list of numerical roots does not show why every required root has been found.
For matrix work, confirm dimensions and multiplication order. For a probability, choose the tail and interpret it in context before deciding what the result means.
Use the linked manufacturer instructions for the exact screen and software version. Menu names differ between models.