Compiled, Classified, and Graduated by W. J. DICKINSON, FORMERLY LECTURER ON GRAMMAR AND EUCLID AT THE BATTERSEA TRAINING COLLEGE. AUTHOR OF 'FRACTICAL ENGLISH GRAMMAR AND ANALYSIS,' THE DIFFICULTIES OF GRAMMAR AND ANALYSIS SIMPLIFIED,' 'HOW TO TEACH GRAMMAR AND ANALYSIS,' AND THE DIFFICULTIES OF EUCLID SIMPLIFIED.' LONDON: JOSEPH HUGHES, THREE TUNS PASSAGE, PATERNOSTER SQUARE, E.C. Problems leading to Simple Equations of One Unknown, Cube Root, Simultaneous Equations of the First Degree of Two Unknowns, Quadratic Equations (involving One Unknown Quantity), . Miscellaneous Equations, Answers, N.B.-The Equations here designated as Miscellaneous are so designated in order to avoid the breaking up of questions, as in very many instances there are in one question simple equations of one and two unknowns and a quadratic to be solved. Were the questions broken up and each equation referred to its proper class, the purpose of the present idea would be thwarted, and pupils would not know how much to expect in one question. MALE PUPIL TEACHERS' EXAMINATION QUESTIONS IN ALGEBRA. QUESTIONS ON INTRODUCTORY PARTS (Signs, etc.). 1. Write the algebraic signs of addition, subtraction, multiplication, division, and equality. Explain the use of a vinculum. 2. Give the meaning of each of the following algebraical signs:,,, ×, +, =, <, >, N. 3. Write down the algebraic signs for addition, subtraction, multiplication, and division, equality, greater than, less than, therefore, because. 4. Write down the principal signs used in algebra, and explain the use and effect of a vinculum or bracket. 5. Express algebraically :-The fourth power of the sum of two numbers, together with twice the product of their squares, is equal to the sum of their fourth powers together with four times the product of their product and the square of their Also verify the equality, taking 2 and 3 as the numbers. BRACKETS (Simplification). 1. Simplify (a-b−c)+(b+c−d)~(c−d-f)-(f+g−c). 2. Simplify 3a-[a+b−{a+b+c(a+c+b+d)}]. 3. Simplify 1+x-[1+x+{1−x−(1 + x) − (1 − x + 1)}]. 4. Simplify as much as possible the expression, 8(a2+x2) — 7(a2 — x2)+6(a2 — 2x2). |