NI
408
8. If the square described on one of the sides of a triangle be equal to the sum of the squares described
on the other two sides, the angle contained by these two sides is a right angle.
9. Two circles intersect: prove that, by joining the centres with one another, and with the points of
intersection, two equal triangles are thus formed.
10. Prove that if the bisectors of the angles at the base of an isosceles triangle meet within the triangls
they are equal to one another,
Class III. 4.
1. Define a straight line, a scalene triangle, a circle, a square.
Where dhee?
2. From a given point to draw a straight line equal to a given straight line.
3. Enunciate Proposition 4 of Book 1.
4. If two angles of a triangle be equal, the sides also which are opposite to the equal angles shall be
equal to one another.
5. If two triangles have the three sides of the one equal to the three sides of the other each to each
they shall be equal in all respects. (Proposition 8.)
6. To draw a straight line perpendicular to a given straight line of unlimited length from a given
point without it.
7. Any two sides of a triangle are together greater than the third side.
8. Two circles intersect: prove that if their centres be joined with one another and with the points of
intersection two equal triangles are thus formed.
I very much doubt that of. & indussable is it presupposes know.
Classes II. Ca. & III. B.
1. Define--a straight line, a scalenc triangle, a circle.
ledge of chorde re
2. From a given point to draw a straight line equal to a given straight live.
3. Enunciate Proposition 4 of Book 1,
II 2.
4. If two angles of a triangle be equal, the sides also which are opposite to the equal angles shall be
equal to one another.
5. To bisect a given rectilineal angle.
6. From the centres A and B describe two circles at a distance equal to half AB.
How would you show that the two circles are equal?
ALGEBRA. Class I. 4.
&e ir a catch
7 misprint?
1. Define a progression, duplicate ratio, inverse variation.
2. Write down the factors of—(1) a' —b1; (ii) œa ~b2; (iii) ao + b3 ; (iv) 4a′+ 1; (v) 20x2 - 43x-12; ;
(vi) x' + x1y* + y'.
3. Find the continued product of
4. Divide a+b+c2 - 3abc by a+b+c.
(i) (a−b) (a+b) (a−b) (a2+b2) (a*+b1). (ii) (a+b+c) (a+b−c) (a−b+c) (a−b−c).
5. Solve the equations :-
(1)
@+3
3x + 1
2x
-9
a-3
(ii)
æ–1 2-2
æ– 6
23
2-4
+
+
it 7
4
x-5
(iv)
26-a-b
(iii) 2x + 9a 350.
J x2 + xy + y2=39
} ( x − y)2 =-27
6. Simplify (first arranging in cyclic order):---
(a-e) (c-b)'
7. Write down the Arithmetical, Geometrical and Harmonic means between
they are in geometric progression.
8. Find the sum of
2a-b-c
e+a-20
―
-
(a−b) (a-c)
(b−c) (b−a)
+
+ +
p
aud 9:
and show that
Babe-ba
+
...to 15 terms. .........to 4 terms. .........to 4 terms.
9. Solve the quadratic az2 + bæ + c == 0); and if a and ẞ are the roots show that a3 + μ3=
10. 4 spends half as much again as B who sures one third of his income. B spends £200 less than
A, who saves three times as much as B. Find their incones.
Classes I. B. & 1. Ca.
1. Define ratio, proportion, surd.
Write down the product of a2-9 by z2-16; and state why or why not each term in the product
is a perfect square.
s. What are the factors of (i) a+b); (ii) 27æ3 ~8b3 ; (iii) 16α-1; (iv) æ3 −10x + 16;
(v) 9æ31−32x−16; (vi) ab+be+cd + dà.
4. Divide Ga:"--x′′y— 10x*y* + 31x®y3—14x2y* — 9ey* + 12y° by 3x2 + 4x3y—5x*y3 +3y^.
Find the H. C. F. of 2xa—5x2+5x−3, 2x3-x2 -5x+3, 2x3-3x2+62-9, and the L. C. M. of Ca{ a2~b2), 6(a3—b3), 9(a3~2ab+2ab3—¿3), and 12(a3-3a2b+3ab2-b3), expressing it in factors. 6. Solve the equations :----
9 10
+
ส
2
y
(i)
21 25
2
Z
y
(ii)
(iii)
7x 3.x
7. Prove that ar°
1, and simplify:-
8. Simplify
-5xy+4y2:
4
1 +
54
7x+4
3x + 1
18 (y-x).
x / x-i
÷
1
+
+
b € c-a
of (atze (2)-
a2 + }o + c (b− a) (c—b) (a−c)
7
9. A man walked 60 miles at a certain pace: when he had gone twice as many miles as the number
of minutes in which he went one mile, he found he would be 6 hrs. 40 min. more on his journey. Find the pace at which he walked.
Classes I. Cb. & II. A.B.
1. What is a quadratic equation ? And what do you mean by "cyclic order "?
2. Add together a (b+c) − b (c−a), b (c+a)
3. Subtract a (b-c) b (e-a) from e (a−b)
4. Find the square root of→
6. What are the factors of--(1) a
6. Find the H. C. F. of Ba
7. Solve the equations-
8. Simplify
a + b
(c − a) (b − c )
+
-
x2 + 3x 1 and 3x3
Give examples.
c (a−b), and c (a+b) - a (b−c). a (b+c),
6x+4x2 b3; (ii) a1
+ 9x2
12x + 4.
1; (iii) x2 + xy
30y'; (iv) 6a2b + 3abe – 9bc2.
J
x2 - 3x + 1.
2x + 3
4x + 9
173
114
32 - 4
(i) 6x 5
(ii)
218 + 17y
|18v - 51y =
(iii) 3x2 - 7æ - 6 − 0
+
e+ a
6+ e (a - b) (ť − a) (b − e) ( a − b )
9. Two different numbers are represented By the same two digits: the larger number is 21 times as great as its units figure: the difference between the two numbers is 12 less than the smaller number. What are they?
Classes II. Ca. & III. A.B.
1. What is a negative quantity? And what are simultaneous equations ?
2. Add together 3x-2y-5z, 4y-2æ-82, 4x+3y−10x, x-y−6z, 5y+8z+9æ, 3z−9y-6x.
3. From a-Tab-56+2 subtract -5a+6ab ~3b+4.
4. Multiply 2a-36+4c by 2a-36-4c.
5. Divide Ba1-4a3+4x2+8x−3 by x2-2x+3.
6. Simplify--
4 (3(b − 2a) ~ 2( c − 36)} − 4 (m − 1 (2e − 3(b – 2a)]].
No comments yet.
Private notes are available after approval.