SHARP EL-546XTBSL Scientific Calculator Examples

Introduction

This document provides examples for operating the SHARP EL-546XTBSL scientific calculator. It covers various modes and functions to help users understand and utilize the calculator's capabilities effectively.

Calculator Modes

The EL-546XTBSL supports several operational modes:

• COMP (Computer/Calculation) Mode: For general calculations, including arithmetic, fractions, powers, roots, logarithms, trigonometric functions, hyperbolic functions, factorials, permutations, and combinations.
• STAT (Statistics) Mode: For statistical calculations, including single-variable and two-variable statistics.
• MTR (Matrix) Mode: For matrix operations, allowing calculations with matrices up to 3x3.
• BASE Mode: For calculations involving different number bases such as decimal (DEC), hexadecimal (HEX), binary (BIN), and octal (OCT).
• MLT (Multi-Variable) Mode: For vector operations.
• CPLX (Complex Number) Mode: For calculations involving complex numbers.

COMP Mode Examples

Basic Arithmetic and Fractions

Example: Calculate (12 + 34) × 5.

( 12 + 34 ) × 5 = 220

Example: Calculate 1/2 + 1/3.

1 / 2 + 1 / 3 = 5 / 6

Example: Convert 5/6 to decimal.

[SHIFT] [→] (fraction to decimal conversion) = 0.8333333333

Powers and Roots

Example: Calculate 3⁴.

3 [x^y] 4 = 81

Example: Calculate the square root of 144.

[√] 144 = 12

Example: Calculate the cube root of 27.

[³√] 27 = 3

Example: Calculate 2^-1.5.

2 [x^y] ( - 1.5 ) = 0.3535533906

Logarithms and Exponentials

Example: Calculate log₁₀(100).

[log] 100 = 2

Example: Calculate ln(e⁵).

[ln] [ALPHA] [e^x] 5 = 5

Example: Calculate 10³.

[10^x] 3 = 1000

Example: Calculate e².

[e^x] 2 = 7.389056099

Trigonometric and Hyperbolic Functions

Ensure the calculator is in the correct angle mode (DEG, RAD, GRAD).

Example (DEG mode): Calculate sin(30°).

[DRG] [DEG]

[sin] 30 = 0.5

Example (RAD mode): Calculate cos(π/3).

[DRG] [RAD]

[cos] [ALPHA] [π] / 3 = 0.5

Example: Calculate sinh(1).

[sinh] 1 = 1.175201194

Factorials, Permutations, and Combinations

Example: Calculate 5! (5 factorial).

5 [x!] = 120

Example: Calculate ₅P₂ (5 permutations of 2).

5 [nPr] 2 = 20

Example: Calculate ₅C₂ (5 combinations of 2).

5 [nCr] 2 = 10

Scientific Notation

Example: Enter 1.23 × 10⁴.

1.23 [EXP] 4 (Displays as 1.23E4)

Example: Convert 1.23E4 to standard notation.

[SHIFT] [→] (scientific to standard) = 12300

Memory Functions

Example: Store 50 in memory, add 25, recall, and clear.

50 [STO] [M+] (Stores 50 in memory)

25 [M+] (Adds 25 to memory, total 75)

[RCL] [M] (Recalls memory value: 75)

[MR] [C] (Clears memory value)

STAT Mode Examples

Single Variable Statistics

Example: Calculate mean and standard deviation for the data set: 10, 12, 15, 11, 13.

[MODE] [STAT] [1] (for SD mode)

10 [DATA]

12 [DATA]

15 [DATA]

11 [DATA]

13 [DATA]

[SHIFT] [S-VAR] (Accesses statistics variables)

[n] = 5 (Number of data points)

[x̄] = 12.2 (Mean)

[σn-1] = 1.923538406 (Sample standard deviation)

[σn] = 1.719027978 (Population standard deviation)

Two Variable Statistics

Example: Calculate correlation coefficient for the data set:

[MODE] [STAT] [2] (for LINE mode)

1 [SHIFT] [x,y] 2 [DATA]

3 [SHIFT] [x,y] 5 [DATA]

4 [SHIFT] [x,y] 7 [DATA]

6 [SHIFT] [x,y] 10 [DATA]

[SHIFT] [S-VAR]

[r] = 0.998889966 (Correlation coefficient)

[a] = 0.5 (Regression coefficient Y = aX + b)

[b] = 1.2 (Regression intercept)

MTR Mode Examples

Example: Perform matrix addition: A + B

Matrix A:

Matrix B:

[MODE] [MTR] [2] (for 2x2 matrices)

[DIM] [1] (Define Matrix A size) [2] [ENTER] [2] [ENTER]

1 [ENTER] 2 [ENTER] 3 [ENTER] 4 [ENTER]

[DIM] [2] (Define Matrix B size) [2] [ENTER] [2] [ENTER]

5 [ENTER] 6 [ENTER] 7 [ENTER] 8 [ENTER]

[RCL] [M1] [ + ] [RCL] [M2] [ = ]

Resulting Matrix (A+B):

Example: Perform matrix multiplication: A × B

[RCL] [M1] [×] [RCL] [M2] [ = ]

Resulting Matrix (A×B):

Example: Calculate the determinant of Matrix A.

[SHIFT] [DET] [RCL] [M1] [ = ]

Determinant of A: -2

BASE Mode Examples

Example: Convert decimal 255 to hexadecimal and binary.

[MODE] [BASE] [DEC]

255 [ = ]

[SHIFT] [HEX] (Displays as FF)

[SHIFT] [BIN] (Displays as 11111111)

Example: Add two binary numbers: 1011 + 1101.

[MODE] [BASE] [BIN]

1011 [ + ] 1101 [ = ]

Result in binary: 11000

Convert result to decimal: [SHIFT] [DEC] (Displays as 24)

MLT Mode Examples

Example: Perform vector addition: V1 + V2

Vector V1: (1, 2, 3)

Vector V2: (4, 5, 6)

[MODE] [MLT] [3] (for 3-dimensional vectors)

[DIM] [1] (Define Vector V1) [3] [ENTER]

1 [ENTER] 2 [ENTER] 3 [ENTER]

[DIM] [2] (Define Vector V2) [3] [ENTER]

4 [ENTER] 5 [ENTER] 6 [ENTER]

[RCL] [V1] [ + ] [RCL] [V2] [ = ]

Resulting Vector (V1+V2): (5, 7, 9)

Example: Calculate the dot product of V1 and V2.

[RCL] [V1] [DOT] [RCL] [V2] [ = ]

Dot Product: 32

CPLX Mode Examples

Example: Calculate (2 + 3i) + (4 - 5i).

[MODE] [CPLX] [a+bi]

( 2 [ + ] 3 [i] ) [ + ] ( 4 [ - ] 5 [i] ) [ = ]

Result: (6 - 2i)

Example: Calculate (1 + i) × (2 - i).

( 1 [ + ] 1 [i] ) [ × ] ( 2 [ - ] 1 [i] ) [ = ]

Result: (3 + i)

Example: Convert polar form (r=5, θ=30°) to rectangular form (a+bi).

[SHIFT] [CPLX] [POL] 5 [ , ] 30 [ = ]

Result (a): 4.330127019

[SHIFT] [CPLX] [ANS] [ = ] (To get b)

Result (b): 2.5

Diagram Descriptions

Normal Distribution Curve: This diagram typically shows a bell-shaped curve, symmetrical around the mean. The horizontal axis represents values, and the vertical axis represents frequency or probability density. The peak of the curve is at the mean, and the curve tapers off towards the tails, indicating that values further from the mean are less frequent. The area under the curve represents probabilities.

Scatter Plot: This diagram displays individual data points on a two-dimensional plane, with one variable plotted on the horizontal (X) axis and another on the vertical (Y) axis. It is used to visualize the relationship or correlation between two variables.

Calculator Layout: The calculator features a multi-line display at the top, showing input and results. Below the display are various function keys, including numeric keys (0-9, decimal point), arithmetic operators (+, -, ×, ÷), special function keys (e.g., sin, cos, log, ln, !, √, x^y), mode selection keys (MODE, DRG), memory keys (M+, M-, MR, MC), and control keys (ON/C, AC, DEL, INS). SHIFT and ALPHA keys are used to access secondary functions printed above the primary keys.