The candidate is given all assistance needed to insure the proper filling out of these papers.
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; graphical representation and solution of linear equations with two unknowns; 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:
1. (a) Simplify [(x - y)2 + 6xy] - [(x2 + 2xy) - {x2 - [2xy - (4xy - y2)]} - (-x2 - 2xy)].
(b) Factor (1) a9b9 + 64c6 (2) x2 - y2 - 2y - 1 (3) x3 - 3x2 + 4.
2. Solve √((4/x2) + 5) - √((4/x2) - 5) = 2. Prove that your answers are correct.
3. How many terms will there be in the expansion of (a⅒ + b⅕×15) by the binomial formula?
Write the 6th term in the simplest form.
What other term will have the same coefficient?
Write down this term and simplify it.
4. A number of workmen, who receive the same wages, earn together a certain sum. Had there been 7 more workmen, and had each one received 25 cents more, their joint earnings would have increased by $18.65. Had there been 4 fewer workmen, and had each one received 15 cents less, their joint earnings would have decreased by $9.20. How many workmen are there, and how much does each one receive?
5. (a) Find the value of 5x3 + 2x2 - 3x - 1 when x = 1 - √(-4)