No. 21.
133
ARITHMETIC.
CLASS III.
1. Express as decimal fractions :-
34 84–57.
X
84 1+ 2
1
1-13
2. Assuming that a year contains 365-2422 days and a lunar month 29.5306 days find to four places what decimal a lunar month is of a year and what multiple nineteen years is of a lunar mouth.
3. A pond 70 yards square is frozen over with ice 3 inches thick; find in tons to the nearest whole number the weight of the ice if a cubic foot of it weighs 57 lbs.
4. If the carriage of 3 tous 4 cwt. for 98 miles cost 16s, what will be the cost of carrying 4 tous 9 ewt, a distance of 28 miles at the same rate?
5. An estate consists of 89 ac. 3 r. 37 sq. po. of pasture, 73 uc. 2 r. 17 sq. po. of arable land, 10 ac. 1 r. 12 sq. po. of plantation.
What is its annual value at a rent 55s, an acre ?
No. 22.
GEOMETRY.
CLASS I A.
1. Prove that the opposite angles of any quadrilateral L M N P inscribed in a circle are together equal to two right angles.
2. Prove that if a straight line touch a circle and from the point of -contact a chord be-drawn the angles which this chord makes with the tangent
shall be equal to the angles in the alternate segments of the circle. (NOTE:Name the taugent L M N and the chord P M.)
3. If four common tangents are drawn to two circles external to one another; shew that the two direct and also the two transverse tangents intersect on the straight line which joins the centres of the circles.
4. Inscribe a regular pentagon (II K L M N) in a given circle.
5. An equilateral triangle is inscribed in a given circle: shew that twice the square on one of its sides is equal to three times the area of the square inscribed in the same circle.
6. From an external point A two tangents A B and A C are drawn to a given circle and the angle B A C is bisected by a straight line which meets the circumference at I and 1,. Shew that I is the centre of the circle inscribed in the triangle A B C, and 1, the centre of one of the inscribed circles.
No. 23.
CLASS I B.
GEOMETRY.
Note:-Use letters L M N P R for all work.
1. On the same base and on the same side of it there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another and also those which are terminated at the other extremity equal to one another.
2. Prove that in a quadrilateral if two opposite sides which are not parallel are produced to meet one another, the perimeter of the greater of the two triangles so formed is greater than the perimeter of the quadrilateral.
3. Prove that in a right-angled triangle the square described on the hypotenuse is equal to the sum of the squares described on the other two sides.
4. Prove that the bisectors of the angles of a triangle are concurrent. 5. What is the difference between the square on the sile subtending the obtuse angle in an obtuse-angled triangle and the square ou the sides containing the obtuse angle? Prove it.
6. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares ou the diagonals.