Using A Calculator

Calculator Basics & Settings

• Check your calculator is in **MATH mode** (display shows 'MATH').
• Set **angle unit to degrees** – look for a 'D' symbol on screen.
• Use **SETUP** or **MODE** button to change settings; reset before exam.
• Switch between exact (fraction) and approximate (decimal) answers using **S⇔D** button.
• Know your specific model (e.g., Casio fx-83GT) – functions may be accessed differently.

Essential Shortcut Buttons

• Use **fraction button** (a b/c) for fractions; **square (x²)**, **cube (x³)**, **power (^)** for exponents.
• **Square root (√)** and **cube root (∛)** via SHIFT $+ \sqrt{or}$ dedicated button.
• **SHIFT** key gives access to inverse functions (e.g., sin⁻¹, cos⁻¹, tan⁻¹) and nth roots.
• **π** is often near the standard form button; may require SHIFT.
• **×10ˣ** button enters standard form; modern calculators display as '×10ⁿ'.

Using Brackets Correctly

• Always use brackets around **negative numbers** – $e.g., (-3)^{2}$ gives 9, $but -3^{2}$ gives -9.
• Use the **(-) button** for negative values, not the minus button.
• Brackets ensure correct order of operations – $e.g., (68+18)\div (9-5)$ vs $68+18\div 9-5$.
• Close all brackets after functions like sin(45°) – type sin(45) then close bracket.

Trigonometry Functions

• Use **sin, cos, tan** for finding sides; ensure calculator is in **degrees mode**.
• For angles, use **sin⁻¹, cos⁻¹, tan⁻¹** via SHIFT + sin/cos/tan.
• After typing a trig function, an open bracket appears – remember to close it.
• Example: $\sin (30) =$ 0.5; sin⁻¹(0.5) $= 30^{\circ}$.

Standard Form & π

• Enter standard form using **×10ˣ** button – e.g., 1.2×10⁻³ is 1.2 ×10ˣ (-)3.
• Modern calculators display standard form as '1.2×10⁻³'; older models may show '1.2E-3'.
• **π** is a constant; use it in calculations like area of a circle $(\pi r^{2})$.
• Combine with brackets for complex expressions: $(\pi \times 5^{2})$ gives 78.5398...

The Ans (Answer) Function

• **Ans** recalls the last calculated result – useful for multi-step calculations.
• Avoid rounding intermediate answers by using Ans in the next step.
• Example: compute $4.69^{2} = 21.9961$, then $\sqrt{Ans} = 4.689$... (but better to do in one go).
• Press **Ans** button (often above '=') to insert the previous answer.

Table Function for Graphs

• Use **TABLE mode** to generate values for functions like $y = x^{3}$ – $6x + 1$.
• Enter the function, set start/end/step, and calculator outputs a table.
• Helps reduce errors in 'complete the table' questions.
• Example: for $y = x^{3}$ – $6x + 1$, table gives $x=-3$ → $y=-8, x=-2$ → $y=5$, etc.

Time Calculations

• Use **° ' ''** button to enter time in hours/minutes/seconds – e.g., 3°45'0'' for 3h45m.
• Convert between decimal time and hh:mm:ss using the same button.
• Example: 2.7 hours $= 2^{\circ}42'0'' (since 0.7\times 60=42 minutes)$.
• Useful for speed, distance, time problems.

Worked Example Tips

• Do **one calculation at a time** and write down intermediate results with '...' to show no rounding.
• Use **fraction button** for numerator/denominator – $e.g., (4.69^{2})/(0.343+sin45^{\circ})$.
• For standard form substitution, use brackets: (1.2×10⁻³)² × (7.83×10⁵).
• Always write down more digits than needed; round only the final answer.

Calculator Key Layout (Casio fx-83GT)

Order of Operations with Brackets

Using the Fraction Button

Table Function Example