Using A Calculator

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Notes de leçon

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.

The Casio fx-83GTX Classwiz

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 + √ 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'.

Calculator shortcut buttons

Using Brackets Correctly

Always use brackets around negative numbers – e.g., (-3)² gives 9, but -3² gives -9.
Use the (-) button for negative values, not the minus button.
Brackets ensure correct order of operations – e.g., (68+18)÷(9-5) vs 68+18÷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°.

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 (πr²).
Combine with brackets for complex expressions: (π × 5²) 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 4.69² = 21.9961, then √(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 = x³ – 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 = x³ – 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°42'0'' (since 0.7×60=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., (4.69²)/(0.343+sin45°).
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.

Diapos

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Questions d'entraînement

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1.Find the value of \√{3481}.
Easy
- A59
- B61
- C49
- D69
2.Find the value of 3\√{2744}.
Easy
- A14
- B16
- C12
- D18
3.Find the value of \√{70}.
Easy
- A8.3666...
- B7.0711...
- C8.6023...
- D8.4261...
4.Find the value of 5^-2.
Easy
- A0.04
- B0.2
- C0.4
- D0.008
5.Find the value of \√{196}.
Easy
- A14
- B16
- C12
- D18
6.Calculate 15³.
Easy
- A3375
- B225
- C45
- D3376
7.Edelgard tries to calculate \frac{68+18}{9-5}. She types into her calculator 68+18 \div 9-5. Explain why this does not give Edelgard the correct answer.
Medium
- AThe calculator performs division before addition and subtraction, so it computes 68 + (18 \div 9) - 5.
- BThe calculator performs addition before division, so it computes (68+18) \div 9 - 5.
- CThe calculator performs subtraction before division, so it computes 68 + 18 \div (9-5).
- DThe calculator performs operations from left to right without order of operations.
8.Work out the correct answer to \frac{68+18}{9-5}.
Easy
- A21.5
- B65
- C17.2
- D86

Plus de questions

9.Find the value of \√{265.69}.
Easy
- A16.3
- B16.2
- C16.4
- D15.9
10.Find the value of 8³.
Easy
- A512
- B64
- C24
- D256
11.Calculate \√{0.0025}.
Easy
- A0.05
- B0.5
- C0.005
- D0.0005
12.Write 2^-4 as a decimal.
Easy
- A0.0625
- B0.125
- C0.25
- D0.5
13.Calculate \frac{1}{0.01} - 8².
Medium
- A36
- B84
- C64
- D100
14.Calculate (8 + 4 \times 7)^0.6.
Medium
- A12.96
- B36
- C8.64
- D15.59
15.Calculate \frac{3.142 - 52163}{16604} and give your answer in standard form correct to 2 significant figures.
Hard
- A-3.1 \times 10⁰
- B-3.14 \times 10⁰
- C-3.1 \times 10¹
- D-3.14 \times 10¹
16.Calculate 3 - 4.3 \times 6.72 and write down all the figures shown on your calculator.
Medium
- A-25.896
- B25.896
- C-26.896
- D26.896
17.A rectangle has length 8.2 cm and width 5.6 cm. Calculate the area of the rectangle. Give your answer correct to 3 significant figures.
Medium
- A45.9 cm²
- B45.92 cm²
- C46.0 cm²
18.A car travels 150 miles on 12 gallons of petrol. Calculate the number of miles per gallon the car travels.
Easy
- A12.5
- B0.08
- C162
- D138
19.Calculate \frac{4.85 \times 6.14}{8.91 + 3.89}. Give your answer correct to 2 decimal places.
Medium
- A2.33
- B2.34
- C2.32
- D2.35
20.The formula for the volume of a sphere is V = \frac{4}{3} \π r³. Calculate the volume of a sphere with radius 6 cm. Give your answer correct to 3 significant figures.
Medium
- A905 cm³
- B904 cm³
- C904.78 cm³
- D905.0 cm³
21.The area of a circle is 50 cm². Calculate its radius. Give your answer correct to 3 significant figures. (Use π = 3.142)
Medium
- A3.99 cm
- B4.00 cm
- C3.98 cm
- D4.01 cm
22.Calculate \frac{16.379 - 0.879}{4.2 \times 1.241}. Give your answer correct to 2 significant figures.
Medium
- A3.0
- B2.9
- C3.1
- D2.8
23.Given that a = \frac{p + q}{p² q}, find the value of a when p = 1.2 × 10^-3 and q = 7.83 × 10⁵. Give your answer to 3 significant figures.
Medium
- A694000
- B694
- C6940000
- D69.4
24.The formula for the area of a trapezium is A = \frac{1}{2}(a + b)h. Calculate the area of a trapezium with parallel sides of length 8 cm and 12 cm, and height 5 cm.
Easy
- A50 cm²
- B100 cm²
- C25 cm²
- D40 cm²
25.What is the value of \√{729}?
Easy
- A27
- B23
- C33
- D29
26.What is the value of 18³?
Easy
- A5832
- B5830
- C5834
- D5836
27.The 'Ans' button on a calculator recalls the last answer calculated.
Easy
True or false?
28.Which button should you use to enter a negative number on a calculator?
Easy
- AThe minus button (-)
- BThe '(-)' button
- CThe subtraction button
- DThe shift button
29.When using trigonometric functions on a calculator, the calculator should be in radians mode.
Easy
True or false?
30.What does the 'S ⇔ D' button on a Casio calculator do?
Easy
- ASwitches between degrees and radians
- BSwitches between exact and approximate answers
- CStarts the table function
- DChanges the number of decimal places
31.Calculate 4.85 \times 6.14 on your calculator. Which of the following is the correct result?
Easy
- A29.779
- B29.7790
- C29.78
- D29.8
32.To enter the time 3 minutes 45 seconds on a calculator using the degrees/minutes/seconds function, which of the following is correct?
Easy
- A0°3'45''
- B3°45'0''
- C3°0'45''
- D0°45'3''
33.A student enters the calculation 68+18 \div 9-5 into their calculator. Why is this incorrect for the expression \frac{68+18}{9-5}?
Medium
- AThe calculator does not follow the order of operations.
- BThe student should have used brackets around the numerator and denominator.
- CThe division symbol is wrong.
- DThe calculator cannot handle fractions.
34.Which of these is the correct way to enter (3.2 \times 10⁵) \times (4.1 \times 10^-2) into a calculator?
Medium
- A3.2 \times10^x 5 \times 4.1 \times10^x (-)2
- B(3.2 \times10^x 5) \times (4.1 \times10^x (-)2)
- C3.2 \times 10 ^ 5 \times 4.1 \times 10 ^ -2
- D3.2 EXP 5 \times 4.1 EXP -2
35.The cube root function is accessed by pressing 'SHIFT' then the square root button on most scientific calculators.
Easy
True or false?
36.Calculate \frac{19.8 + 11.53}{-1.43 + \√[3]{42.875}}. Give your answer correct to 2 decimal places.
Hard
37.Use your calculator to find the value of \√{70} correct to 3 decimal places.
Easy
38.Calculate \frac{19.8 + 11.53}{-1.43 + \√[3]{42.875}}. Give your answer correct to 2 decimal places.
Medium
- A16.13
- B14.13
- C15.13
- D17.13
39.Use your calculator to find the value of \√{70} correct to 3 decimal places.
Easy
- A8.367
- B9.367
- C7.367
- D10.367

Notes de révision

## Using a Calculator - IGCSE Maths Core ### Key Functions - **Square root (√)**: e.g., √3481 = 59 - **Cube root (³√)**: use SHIFT then √ button - **Powers**: x², x³, x^y (e.g., 5⁻² = 0.04) - **Standard form**: use ×10^x button; e.g., 1.2×10⁻³ - **Trigonometry**: sin, cos, tan (degrees mode); inverse: SHIFT sin⁻¹ etc. - **π**: often near standard form button - **Fraction button**: for fractions and mixed numbers - **Ans button**: recalls last answer - **S⇔D**: toggle between exact (fraction) and decimal ### Important Settings - **Mode**: MATH (default) - **Angle unit**: degrees (D symbol on screen) - **Reset before exam** to avoid errors ### Brackets & Negative Numbers - Use brackets for numerators/denominators: (68+18)÷(9-5) - Use (-) button for negative numbers, not minus sign - Example: (-3)² = 9, but -3² = -9 ### Order of Operations - Calculator follows BIDMAS; use brackets to override - Write down intermediate steps to avoid mistakes ### Worked Examples 1. **√(4.69) / (0.343 + sin45°)** = 2.901406085 (full display) 2. **a = (p + q) / (p²q)** with p=1.2×10⁻³, q=7.83×10⁵ → a = 694000 (3 s.f.) 3. **Table for y = x³ - 6x + 1**: use brackets for negative x ### Examiner Tips - Do one calculation at a time - Write down more digits than needed; round only final answer - Use table function for plotting graphs ### Common Questions - Square roots: √196 = 14, √265.69 = 16.3 - Cube roots: ³√2744 = 14, ³√0.729 = 0.9 - Powers: 18³ = 5832, 2⁻⁴ = 0.0625 - Mixed operations: (16.379 - 0.879) / (4.2 × 1.241) = 2.97 (2 s.f.)

Square root: A value that when multiplied by itself gives the original number; e.g., √3481 = 59.
Cube root: A value that when multiplied by itself three times gives the original number; e.g., ³√2744 = 14.
Standard form: A way of writing very large or small numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer.
BIDMAS: Order of operations: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
S⇔D button: Toggles between exact (fraction/surd) and decimal answers on a calculator.
(-) button: Used to enter negative numbers; distinct from the minus sign for subtraction.
Ans button: Recalls the last calculated answer to use in further calculations.
Table function: A calculator mode that generates a table of values for a given function, useful for plotting graphs.

Cartes mémo

How do you switch between exact (fraction) and approximate (decimal) answers on a Casio fx-83GT?

Press the 'S ⇔ D' button while in MATH mode.

What button should you use to enter a negative number on a calculator?

Use the '(-)' button, not the minus button.

Why is it important to use brackets around negative numbers in calculations?

Because −3² gives a different result than (−3)². Brackets ensure correct order of operations.

How do you access cube root and nth root functions on a typical scientific calculator?

Use the 'SHIFT' (or 2nd/INV) button to access cube roots and nth roots.

What does the 'Ans' button do on a calculator?

It recalls the last answer calculated, allowing you to use it in further calculations without rounding.

How do you enter a number in standard form on a modern calculator?

Use the ×10^x button. For example, 2 × 10⁵ is entered as 2 ×10^x 5.

What should you check before using trigonometric functions on your calculator?

Ensure the calculator is in degrees mode (a 'D' symbol should appear on the display).

How do you enter time in hours/minutes/seconds on a calculator?

Use the ° ' '' button. For example, 3 minutes 45 seconds is entered as 0°3'45''.

Calculate: √3481

Calculate: ∛2744

Calculate: 7⁰

Calculate: 5⁻²

0.04 or 1/25

Calculate: √196

Calculate: 15³

3375

Calculate: ∛729

Calculate: 18³

5832

Calculate: √265.69

16.3

Calculate: 8³

512

Calculate: √(0.0025)

0.05

Calculate: √4489

Calculate: 4³

Calculate: ∛274625

Calculate: 2⁻³ × √242

1/8 × √242 = √242/8 ≈ 1.9445 (exact: 11√2/8)

Calculate: 2⁻⁴ as a decimal

0.0625

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