HP 40gs Graphing Calculator

The HP 40gs is Hewlett-Packard's graphing calculator targeted at students in high school who need a computer algebra system (CAS). It is the successor to the 40G, and 38G, and it is sold alongside the 39gs (equivalent with infrared but without CAS).

The 40gs is aimed directly at the TI-83 and TI-84 graphing calculators, but it is a much better choice, as it is cheaper, more powerful, and easier to use. It also provides a good alternative to the TI-89. It has a high-resolution screen and, unique among HP calculators, provides split-screen graphing and has electronic lessons known as "aplets".

Included Accessories

• Hard plastic slide-on case
• USB cable
• Calculator-to-calculator serial link cable
• Batteries
• 444-page printed user's guide
• CD with Windows-based connectivity software and PDF with 366 pages of additional documentation

Physical Characteristics

• 184 mm by 87 mm by 23.5 mm (7.2" by 3.4" by 0.93"); slide-on case is 19 mm (0.75") thick
• 247 g (8.7 oz)
• Black painted faceplate with textured black back
• Hard plastic keys with metal domes for fast and accurate typing
• 7 cm (2.7") display with anti-glare protective cover

Technical Specifications

• 131x64 pixel display with adjustable contrast, showing 7 lines with 22 characters
• 75 MHz 32-bit ARM920T processor
• 256 KB RAM
• 2 MB Flash ROM
• Four AAA batteries, providing 50 hours of typical use, and one CR2032 battery
• Piezoelectric beeper
• Powered by battery or USB
• Over 600 functions
• HP part number F2225AA ()

Calculating Environments

• EOS-style algebraic

Communications

• USB (cable included)
• RS-232 serial (; includes 40gs to 40gs link cable)

Programmability

• HP Basic programming language
• Write your own "aplets"
• Compilation and decompilation of code built-in
• Full access to all built-in commands, including branching, testing, graphics, matrices, statistics, input and output

Aplets

• Interactive history, notes, and sketch functions for aplets
• Symbolic, numeric, and graphic views available to aplets
• Built-in standard aplets: function, inference, parametric, polar, sequence, solve, finance, linear equation solver, triangle solver, statistics
• Built-in teaching aplets: Quadratic Explorer, Trigonometry Explorer

Applications

• Text editor (Notepad)
• Graphics editing (Sketch)
• Matrix editor
• Finance (time value of money and amortization)

Graphing

• 2-D function, polar, parametric, sequences, histogram, box and whisker plot, scatter plot
• Determine roots, intersections, slope, area, extrema
• Zoom, trace, find coordinates, and shade plots
• Plot multiple equations simultaneously
• Table of values

Probability and Statistics

• x, x2, y, y2, xy
• Sample standard deviation, population standard deviation, mean
• Curve fitting (linear, logarithmic, exponential, and power regression)
• Plot statistical data
• Hypothesis tests
• Confidence intervals
• Combinations, permutations, factorials, random number generation
• Upper-tail normal distribution, upper-tail chi-square distribution, upper-tail Snedecor's F-distribution, and upper-tail student's t distribution

Scientific

• Decimal hours/degrees to hours/degrees-minutes-seconds conversions
• Angle conversions
• Simple unit conversions
• Constants library, with 29 common physical constants

Mathematics

• Advanced Computer Algebra System (CAS)
• Calculus, including numeric and symbolic integration (Risch algorithm) and differentiation, integration by parts, Fourier expansion, Laplace transform
• Differential equations, including solving
• Limits and series, including Taylor expansion, Taylor polynomials, and asymptotic development
• Matrices, including cross product, determinant, dot product, eigenvalues/eigenvectors, identity, inverse, LQ factorization, least squares, LU decomposition, QR factorization, reduced row echelon form, Schur decomposition, condition number, transposition, and more
• Trigonometry, including hyperbolic and inverse sine, cosine and tangent, as well as simplification of trigonometric expressions
• Rewrite expressions, including reordering of variables and conversions between trigonometric functions, and rewriting of logarithmic and exponential terms
• Solving, including a quadratic equation solver, a root finder, a triangle solver, the Solve aplet, and a simultaneous linear equations solver
• Fractions, including powerful conversions from decimals to fractions in terms of and radicals, or between proper and improper fractions
• Decimal functions, finding the integer and fractional parts, the floor and ceiling, the mantissa and exponent, the sign, and rounding or truncating to a specified number of decimal places or significant figures
• Lists, including calculating the sum, product, and differences, and sorting
• Complex numbers
• Summation

Software Library

• Pre-loaded with twelve aplets, and many more HP-provided aplets available as separate downloads
• Hundreds of third party aplets 
• Compatible at the binary level with software written for the 39g+, 39gs, 39G, and 40G
• Compatible at the source-code level with most software written for the 38G

Standardized Exam Support

• AP Calculus
• AP Statistics
• AP Chemistry
• AP Physics
• SAT Reasoning Test
• SAT Subject Tests in Mathematics Level 1 and Level 2
• PSAT/NMSQT

HP Provided Documentation

• , 444 pages, provided in printed form with the calculator
• , 366 pages, provided in electronic form with the calculator
• Thirty , totaling 130 pages, provided as a separate download