Classes I. B. & I. Ca.
81
1. Define ratio, proportion, surd.
2. Write down the product of -9 by a-16; and state why or why not each term in the product
is a perfect square.
3. What are the factors of (i) aa+63; (ii) 27a3-8b3; (iii) 16a1−1; (iv) a2 −10x+16 ;
(v) 9x-32x-16; (vi) ab+be+cd+da.
4. Divide 6æ3-x3y—10x*y2 +31x3y3 — 14x2y2 — 9.xy* + 12y° by 3x2 + 4x3y--5x2y2 + 3y*.
5. Find the H. C. F. of 2x−5x2+5x−3, 2x3−x2-5x+3, 2x3-3x2 + 6x−9, and the L. C. M. of 3(a2—b2), 6(x3—b3), 9(a3—2ab+2ab2 —b3), and 12(a3—3a2b+3al3−l3), expressing it in factors. 6. Solve the equations:--
9 10
+
5
@
У
(i)
(ii)
21 25
У
x2-5xy+4y
-
5418 (y-x).
7x 4
7x + 4
(iii)
1 +
Ba 4
3x + 4
7. Prove that a°
1, and simplify :
→
x V x-1
of
(∞ $)-
−3
1
1
1
8. Simplify
α
-
b
b
C
C
a
a2 + b2 + c2
(b−a) (c—b) (a–c)
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. CV. & II, A.B.
1. What is a quadratic equation? And what do you mean by "cyclic order"? Give examples. 2. Add together a (b+c) b (c-a), b (c+a) e (a-b), and c (a+b)
−
-a (b-c). 3. Subtract a (b−c) − b (c−a) from c (a−b) — a (b+c).
4. Find the square root of—
6x2 + 4x3 + dx2
www
12a + 4.
5. What are the factors of—(i) a3 – b3 ; (ii) a* − 1 ; (iii) x2 + xy – 30y2; (iv) 6a2b + 3abc − 9bc. 6. Find the H. C. F. of 3x2 − x2 + 3x
x2
3x + 1.
7. Solve the equations-
1 and 3x3
3x
4
2x + 3
(i)
6x
ww
4x + 9
(ii) {
21x + 17y 18x - 5ly
(iii) 3x2-7x-6= 0
b + c
173
-
114
8. Simplify
a + b
c + a
+
+
(c- a) (bc)
(a - b) (c - α)
−
(b − c ) ( 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-2x-8, 4x+3y-10x, x-y-6z, 5y+8z+9x, 32−9y-6x.
3. From a-Tab-5b+2 subtract −5a+6ab−3b+4.
4. Multiply 2a-36+4c by 2a-36-4c.
5. Divide 3a-4x3 +4x2+Ex−3 by x2-2x+3.
6. Simplify-
-
4 {3(b − 2α) – 2(c — 3b)} − 4 [a − 4 {2c – 3(b – 2α)}].