A test for divisibility by any prime number is discussed and its proof is given. (MP)

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

The problem of rounded numbers used in computations on digital computers is discussed and examples showing the effect of round-off errors are given. (DT)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

The concept of prime factorization is discussed and two rules are developed: one for finding the number of divisors of a number and the other for finding the sum of the divisors. (MP)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…