=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 + 6_xy_] - [(_x_^2 + 2_xy_) - {_x_^2 - [2_xy_ - (4_xy_ - _y_^2)]} - (-_x_^2 - 2_xy_)]. (_b_) Factor (1) _a_^9_b_^9 + 64_c_^6 (2) _x_^2 - _y_^2 - 2_y_ - 1 (3) _x_^3 - 3_x_^2 + 4. 2. Solve [sqrt]((4/_x_^2) + 5) - [sqrt]((4/_x_^2) - 5) = 2. Prove that your answers are correct. 3. How many terms will there be in the expansion of (_a_^{⅒} + _b_^{⅕}×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 5_x_^3 + 2_x_^2 - 3_x_ - 1 when _x_ = 1 - [sqrt](-4) (_b_) Simplify (5×[sqrt](_x_^{4/3})^{-3/2} 6. Two trains run toward each other from A and B, respectively, and meet at a point which is 15 miles farther from A than it is from B. After the trains meet, it takes the first train 2⅔ hours to run to B, and the second 3⅜ hours to run to A. How far is it from A to B? { (1/_a_ + 1/_b_)_x_ + (1/_a_ - 1/_b_)_y_ = 4 7. Solve { { _x_/(_a_ + _b_) + _y_/(_a_ - _b_) = 2