E Summer Proportion Inverse “The light that burns twice as bright burns half as long – and you have burned so very, very brightly, Roy.” BLADE RUNNER Two quantities are in inverse proportion if, when one quantity gets multiplied by any factor, then the other quantity gets divided by the same factor. For example if one quantity is doubled then the other quantity is halved. We say that y ∝ 1x .
Questions 1. The variables x and y vary in inverse proportion. Copy and complete the following table. 8 15
x y
24
11 40 13
260 3 120 39, 18 13 , 5, 11
2. The variables x and y vary in inverse proportion. Copy and complete the following table. 5 16
x y
1 35
625 4 15
2500 3
16 , 2800, 12 300, 125 125
3. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
11 7 18 13
22 91
198 1001
99 455
10, 9, 11
4. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
14 19 12 23
21 873
168 7429
28 1321 6984 , 7926 , 17 437 437
5. The variables p and q vary in inverse proportion. Copy and complete the following table. p q
x y
xy 3
1
1 81
81x 2 y2
1 9
1 , 81x y, 9x y 3, x y, 81x y
6. A and B are positive. A is inversely proportional to B. When A = 48, B = 147. Find the value A = 84 of A when A = B. 7. The variables x and y vary in inverse proportion. Copy and complete the following table.
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x y
1 b2 a
b 1 a
a2
1
b 2 , b 2 , b 2, b a a3 a
8. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
p q
7 q q2
p2
q 7 pq
7q 2
7q
pq 2, p , 7, 2 p
9. The variables p and q vary in inverse proportion. Copy and complete the following table. x2 − 1 x+1
p q
(x + 1) 2 x(x + 1) 2 x−1 , x − 1 x
10. The variables M and t vary in inverse proportion. Copy and complete the following table. M t
x2 y 2
x y x
x y y2 2 x , x2
11. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
n 5n2 + 5n
n 2 +n 2n+4
5n
10n3 + 10n2
n (n + 1), 10n (n + 2), 12
12. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
r 4r + 8
3r + 6 12r 2 + 24 r (r +2) 3(r 2 +2)
13. The variables v and w vary in inverse proportion. Copy and complete the following table. v w
x−y 7q
x 2 − y2
7qx 3 − 7qy2 x
x−y 7q
1 7q, x+y , x (x+y)
14. The variables p and q vary in inverse proportion. Copy and complete the following table. p
3πx
q
15πx + 2
3π x
9π 2 (5x 2 +1) 5x+1
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5x + 1
15. The variables L and M vary in inverse proportion. Copy and complete the following table. L M
y2 − 1
xy − x y+1
x
16. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
3
n3
n 3n2
3n 2
3
3, n 2
17. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
2a bc
b+c
ab c
2 a+b+c
a−b c
2abc , 2c 2, 2abc 2 , abc (a + b + c ) b+c a−b
18. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
n m
m n+1
n 2 +n m
nm2 1 , m2 n (n + 1), m n+1
19. The variables P and Q vary in inverse proportion. Copy and complete the following table. P Q
x y
2x + 4
2xy x+4
x 2 y + 2xy
xy y x+2 xy x+4 1 2(x+2) , x (x + 2), 2 , x+2 , 1
20. The variables r and s vary in inverse proportion. Copy and complete the following table. r s
2xy − 4x − 3y + 6
7y − 14 14x − 21 49
21. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
π 2 − 36 12
12π + 72 π−6
22. The variables x and y vary in inverse proportion. Copy and complete the following table. 3
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x
√
y
1 a2 −2 b
a
b2
b4
23. The variables x and y vary in inverse proportion. Copy and complete the following table. x
√ ( 3 a) 2
y
a√3 b
1
b2
1
a b
24. The variables P and Q vary in inverse proportion. Copy and complete the following table. P Q
3x + 9 5x + 1
5x 2 + 16x + 3
3
25. The variables x and y vary in inverse proportion. Copy and complete the following table. r2 − r r −1
x y
r2 − 1 r (r −1) r +1
26. The variables p and q vary in inverse proportion. Copy and complete the following table. √
p q
√ 3 x 5 + 6x 2 + 9 x 3 2x 2
x2 2(x + 3) 2
27. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
a2 − b2 (a − b) −1
2a2 + 4ab + 2b2 (a + b) −1 1 (a + b) 2 , 2(a+b)
28. The variables p and q vary in inverse proportion. Copy and complete the following table. p q
x3 + x x2 − 1
x6 − x2
x x 4 − 1, x1
29. The variables x and y vary in inverse proportion. Copy and complete the following table. x y
r2
r4 − r2 r2 + 1 r4 − 1
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