Arithmetic. Junior, Senior, and Higher Local. Junior Work, Nos. 1-10 inclusive." Senior Work, Nos. 4-13 inclusive. Higher Local Work, Nos. 6-17 inclusive. 1. Divide two billion, six million, one thousand and thirty-six by fifty-four, using short division. 2. A servant's wages average 1s. 4d. per day, what does he receive during the year?. 3. A man dies in 1884 aged 89; 19 years ago he was twice the age of his son; how old is the latter at his father's death? 4. Find by practice the value of 72 acres, 3 roods, 30 poles, 22 sq. yards at £3 3s. per acre. 49 2 5. Express as decimals, 43, To Show clearly the process by which you would reduce £5 188. 44d. to the decimal of £10. (ii) 1 ÷ 3 + 21 × 2 × 1 ÷ 1 + 2/9 × (iii) 4000002 +0065 × 3·025 + 41·75 ÷ 2·5. 7. If a block be 4 ft. 9 in. long, 4 ft. 2 in. wide, and 2 ft. 2 in. deep, what are its cubic contents? 8. What sum will amount to £4,408 2s., in 5 years at 4% simple interest? What would be the discount on that sum for the same time and at the same rate? 5 9. If a man own of a ship, and sell 224 of his share, what share in the ship has he left? And what would be the value of his share if the ship be worth £2,997 ? W 10. What is the value of £7,250 in the 3% at 88? 11. What must be the price of 3 per cent. stock, that by investing £3,678 68., my income may be £120? 12. At what time are the hands of a clock at right angles to each other between 6 and 7 o'clock? 13. If 20 horses consume 15 bus. of oats in 9 days, in what time will 27 horses consume 8 qrs. 3 bus. 2 pk. at the same rate? 14. If by selling 2 horses at £68 16s., I lose 20 per cent., what did I give for each horse? 16. What would be the length of a diagonal path across a field of 47 ac. 2 ro. 16 po. 16 sq. yds.? 17. The sides of the base of a triangular pyramid are 3, 4, and 5 feet, and its height is 6 feet; find its solid contents. Geometry. Junior, Senior, and Higher Local. Junior Work, Nos. 1-8 inclusive. Higher Local Work, Nos. 9-16 inclusive. 1. Define angle, parallel lines, rectangle, sector, angle in a segment, angle of a segment, similar segments. 2. Any two sides of a triangle are together greater than the third side. 3. Find the centre of a given circle. 4. At a given point in a given straight line, make a rectilineal angle equal to a given rectilineal angle. 5. In every triangle, the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fail on it from the opposite angle and the acute angle. 6. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles. 7. If from a point without a circle there be drawn two straight lines, one of which cuts the circle and the other meets it; if the rectangle contained by the whole line which cut the circle and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle. 8. Inscribe an octagon in a given circle. 9. Write out the postulates of Euclid and the geometrical axioms. 10. The angles at the base of an isosceles triangle are equal to one another, and if the equal sides be produced the angles upon the other side of the base shall be equal. 11. If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. 12. Define similar segments of circles. On the same straight line, and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. 13. Draw a circle, the circumference of which passes through any three given points. 14. From a given circle cut off a segment containing an angle equal to given rectilineal angle. 15. If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. 16. If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is to the plane in which they are. 2. Resolve 16.-81y into three factors, and (x2+5x)2 + 10(x2 + 5x) + 24 into four factors. 3. Find the H.C.F. of x + 1 and 12 + 203. Reduce to its lowest terms: 4. Simplify (+1)+( 1 − 1 = √) 5. Find the square root of 1+ √x 9x1 — 12ax3 +2 (2a + 3b) ax2 — 4a2bx + a2b2. 6. When are (i) a" + b′′, (ii) a" — b" divisible by (i) a+b, (ii) a — b? 8. Explain the phrase, "a varies as b." If z varies as (x+a) (y+b) and is equal to (a + b)3 when x=b and y=a, show that z=4 (a + b) y = 2a + b. when x = a +26 and |