MENTAL EXAMINATION.
ALGEBRA.—Candidates will be required to pass a satisfactory examination in that portion of algebra which includes the following range of subjects: definitions and notation; the fundamental laws; the fundamental operations, viz.: addition, subtraction, multiplication and division; factoring; highest common factor; lowest common multiple; fractions, simple and complex; simple, or linear, equations with one unknown quantity; simultaneous simple, or linear, equations with two or more unknown quantities; involution, including the formation of the squares and cubes of polynomials; binomial theorem with positive integral exponents; evolution, including the extraction of the square and cube roots of polynomials and of numbers: theory of exponents; radicals, including reduction and fundamental operations, rationalization, equations involving radicals, operations with imaginary numbers, quadratic equations; equations of quadratic form; simultaneous quadratic equations; ratio and proportion; arithmetical and geometrical progressions. Candidates will be required to solve problems involving any of the principles or methods contained in the foregoing subjects.
The following questions were used at a recent examination:
Substitute y + 3 for x in x⁴-x³ + 2x²-3 and arrange the result in descending powers of y.
On the eve of a battle one army had 5 men to every 6 men in the other. The first army lost 14,000 men and the second 6,000 men. The first army then had 2 men to every 3 men in the other. How many men were there originally in each army?
Solve 1.2x - (.18x - .05)/.5 = .4w + 8.9
Find the lowest common multiple of 1-x, x²-1, x-2, and x²-4.
Solve √x + 9 = 2 √x - 3.
Solve (2x - 3)² = 8x.
Expand (m-3/4-m(4/3))⁴ by the Binominal Theorem.