1925 MATHEMATICS A-ELEMENTARY ALGEBRA COMPLETE-NEW REQUIREMENT Monday, June 15 9:30 a.m. Three hours For separate question papers in Mathematics A1 and A2—New Requirement, see pages 7 and 8. New and Old Requirement papers in Mathematics A differ only in Questions 1, 5, 7, and 9. 1. a) What are the factors of 21+4x-x2? b) What are the factors of x-16y8? c) Simplify 2x2-x(−6+2x)—x. 2. Copy the statements below and write after each one "yes" if the statement is true and "no" if it is false. 4. Solve the equation x2+8x-17=0, leaving the answers in radical form. Use the relations between the roots and the coefficients as a check on your results. 5. a) Given the formula s=vt, find t in terms of the other letters. Substitute this value of t in the formula s=at2, and thence derive a formula for a in terms of v and s. b) Find a if v=24 and s=8. (THIS EXAMINATION IS CONTINUED ON PAGE 6) 6. a) Plot the graph of y=3-2x. b) Plot the graph of y=x2-4x, using the same axes as in (a). c) Obtain from the figure the values of x and y which satisfy both equations. 7. The load that a beam can carry varies as the square of the depth of the beam. If a beam 6 inches deep can carry 1,800 pounds, how much could it carry if it were 8 inches deep? 9. A stay wire 147.6 feet long from the top of an iron chimney makes an angle of 58° with the level ground. Using logarithms, find the height of the chimney. 10. A farmer has enough wire netting to build a rectangular inclosure with the length 2 feet more than seven times the width. He finds, however, that if he builds a square inclosure, using the same amount of netting, the area of the inclosure will be increased 361 square feet. How many feet of netting has he? MATHEMATICS A1-ALGEBRA TO QUADRATICS NEW REQUIREMENT Monday, June 15 1925 9:30 a.m. Two hours New and Old Requirement papers in Mathematics A1 differ in Questions 1, 3, 4, and 5. 1. a) What are the factors of 21+4x-x2? b) What are the factors of x4-16y3 ? c) Simplify 2x2−x(−6+2x)—x. 2. Copy the statements below and write after each one "yes" if the statement is true and "no" if it is false. = c) If a and b 0.4, what is the value of 8a2-10ab? = d) Given √2=1.414, find the value of √50. 4. a) Given the formula s= =vt, find t in terms of the other letters. Substitute this value of t in the formula s=at2, and thence derive a formula for a in terms of v and s. b) Find a if v=24 and s=8. 5. A 10-foot ladder leaning against a stone wall just reaches the top of the wall and makes an angle of 64° with the level ground. How high is the wall? 6. There were two-thirds as many women as there were men on a train. At the next station six men and eight women got off the train and nine men and two women got on. There were then twice as many men as women on the train. How many men and how many women were on the train at first? MATHEMATICS A2-QUADRATICS AND BEYOND NEW REQUIREMENT 1925 Monday, June 15 9:30 a.m. Two hours New and Old Requirement papers in Mathematics A2 differ only in Questions 2 and 5. 1. Solve the equation x2+8x-17=0, leaving the answers in radical form. Use the relations between the roots and the coefficients as a check on your results. 2. The load that a beam can carry varies as the square of the depth of the beam. If a beam 6 inches deep can carry 1,800 pounds, how much could it carry if it were 8 inches deep? 3. a) Plot the graph of y=3-2x. b) Plot the graph of y=x2-4x, using the same axes as in (a). c) Obtain from the figure the values of x and y which satisfy both equations. 4. a) What kind of progression is 23, 4, 53, b) Obtain by formula the tenth term. ? c) Obtain by formula the sum of the first ten terms. 5. A stay wire 147.6 feet long from the top of an iron chimney makes an angle of 58° with the level ground. Using logarithms, find the height of the chimney. 6. A farmer has enough wire netting to build a rectangular inclosure with the length 2 feet more than seven times the width. He finds, however, that if he builds a square inclosure, using the same amount of netting, the area of the inclosure will be increased 361 square feet. How many feet of netting has he? MATHEMATICS B-ADVANCED ALGEBRA Wednesday, June 17 1925 2 p.m. Two hours For question paper in Mathematics B-New Requirement, see page 2. 1. Locate between two consecutive integers a positive root of the equation 2. A rectangular box has a volume of 30 cubic feet, and a base whose dimensions are 1 and 3 feet, respectively, greater than the height. Prove that there is only one such box. Find its dimensions. 3. By means of determinants solve the following system of equations for y. x+y-z+ u=0, 2x +2z- u=6, 3y+z+2u=3, 3x−y+z+ u=0. 4. Prove that if a+bi is a root of an algebraic equation with real coefficients, then a-bi is also a root. 5. From thirty members of a society a committee of five is to be appointed, including the president, P. If A will serve only when B is a member of the committee, how many different committees can be formed? 6. Show that the roots of the equation x3+7x2+15x+13=0 are equal to the roots of the equation x3+x2-x+3=0, each diminished by the same amount, h. |