Canterbury Provincial Gazette – 1874 – No. 20

Page 125

✨ Teacher Examination Questions



125

  1. Solve (1) 125-7x=145-12x.
    (2) (x+7)(x-3)=(x-5)(x-15).

  2. Divide 50 into two such parts that the double of one part may be three times as great as the other part.

  3. A bill of £100 was paid with guineas and half-crowns, and 48 more half-crowns than guineas were used. How many of each were paid?

  4. Reduce to lowest terms a-b/a^2+ab + a^2-b^2/a^2-ab

  5. Find the sum of x/y + x/x+y + x^2+xy.

  6. Solve (1) 3x-5y=51
    2x+7y=3
    (2) mx+ny=e
    px+qy=f

  7. The sum of two digits composing a number is 10, and if 54 be added to the number the digits will be inverted. What is the number?

  8. Solve (1) x^2+18x-243=0.
    (2) x^2-x=16.
    (3) 1/x + 1/y = 2/9
    1/x^2 - 1/y^2 = 1/9

  9. A cistern can be filled by two pipes running together in 2 hours 55 minutes. The larger pipe by itself will fill it sooner than the smaller by 2 hours. What time will each pipe take separately to fill it?

(2) The note.—12 and 13 are for first class men only.

GEOMETRY.
FIRST AND SECOND CLASSES.

  1. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

  2. If a straight line falling on two other straight lines make the alternate angles equal to each other, these two straight lines shall be parallel.

Female candidates of the first class are to write out here the three other theorems on parallel straight lines:

  1. Triangles upon equal bases and between the same parallels, are equal to one another.

  2. From two given points on the same side of a straight line given in position, draw two lines which shall meet in a point in that line, and make equal angles with it.

  3. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part.

NOTE.—Female candidates need not go beyond the 5th question.



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🎓 Examination for Certificates, January 1874: Algebra (continued from previous page)

🎓 Education, Culture & Science
Education, Examination, Teachers, Certificates, Algebra, Mathematics

🎓 Examination for Certificates, January 1874: Geometry

🎓 Education, Culture & Science
Education, Examination, Teachers, Certificates, Geometry, Theorems