1.1

a and b
are directly proportional to each other because their graph is a straight line and the

Δb

gradient of
the line is constant, so that the rate —— remains constant.

Δa

1.2

a and b are
directly proportional to each other because their graph is a straight line (See 1.1).

1.3

a and b are
directly proportional to each other because their graph is a straight line (See 1.1).

1.4

a and b are
inversely proportional to each other because the product, ab, is a constant.

1.5

a and b are
inversely proportional to each other because their product, ab, is a constant.

1.6

The relationship
between a and b is unknown – probably it is a quadratic or cube relationship.

1.7

It is a
quadratic relationship – a is equal to cb² where c is a positive constant.

1.8

It is a
quadratic relationship – a is equal to cb² where c is a negative constant.

1.9

The relationship
between a and b is unknown – probably it is a quadratic or cube relationship.

1.10

a and b are
directly proportional to each other because their graph is a straight line (See 1.1).

1.11

a and b are
directly proportional to each other because their graph is a straight line (See 1.1).

m has a
negative value.

1.12

a and b are
directly proportional to each other because their graph is a straight line (See 1.1).

cost

2.1

Yes. The
rate ————————— remains constant and it
has a value of 4.

number of articles

2.2

The graph
will be a straight line because the rate is costant – the variables are directly

proportional to each other.

2.3

See
the accompanying graph.

2.4

Yes, the shape
is as predicted.

2.5.1

cost of 4 articles = 16 (P)

2.5.2

number of
articles = 6,5 (Q)

2.6

No. A fraction
of an article is not made.

men

3.1

No. The rate
———— does not remain constant. The relationship
is that men and hours

hours

are inversely
proportional to each other because their product , men X hours, is a constant.

3.2

The graph will
be a hyperbola because men and hours

are inversely proportional and their

product is a constant.

3.3

See the
accompanying graph.

3.4

Yes.

3.5.1

9,6 hours.
Yes, it is a suitable answer because one can

work for a fraction of an hour.

3.5.2

2,4 men.
No, it is not a suitable answer because a fraction of a man does not exist.

3.6

48 hours, the
time that 1 man will take to complete the task. Seeing that a fraction of a man

does not
exist, it is the longest time.

3.7

Not
propable. There will be 192 men necessary to complete the task and they will probably

be in one another's way. It is not a suitable solution.

b

4.1

Yes. The
rate —— remains constant. The value is approximately 3 for every set of values.

a

4.2

The value
of b is equal to three times the

value of a.

In symbols:
b = 3a

4.3

The graph
will be a straight line because a and b

are directly
proportional to each other.

4.4

See the
accompanying graph.

4.5.1

b = 18

4.5.2

a = 3,5

4.6

b = 18
and a = 3,5. The values correspond well.

b

5.1

No. The rate
—— does not remain constant. The product, ab, is constant and therefore

a

a and b are inversely proportional to each other.

5.2

a and b
are inversely proportional to each other.

In symbols: ab = 16

5.3

The graph
is a hyperbola.

5.4

See the
accompanying graph.

5.5.1

b = 3,2 (P)

5.5.2

a = 1,6 (Q)

5.6

a = 1,6
and b = 3,2

b

6.1

No. The
rate —— is not constant. Furthermore, the product, ab, is not constant

a

and therefore a and b are not inversely proportional to each other. b is equal to a²

The relationship
between a and b is thus a quadratic relationship.

6.2

b is
equal to the square of a [or a squared].

In
symbols: b = a².

6.3

The graph
will be a parabola in the first quadrant.

6.4

See
the accompanying graph.

6.5.1

b = 2,25 (P)

6.5.2

a = 3 (Q)

6.6

a = 3 and
b = 2,25. Values correspond well.

7.1

Length and breadth are inversely proportional to each other because the product,

length X breadth, remains constant.

In symbols : lb = 36 . . . where l = length and b = breadth

7.2

The graph
will be a rectangular hyperbola in the first quadrant because length and breadth

are inversely proportional to each other and both are positive.

7.3

Length | 1 | 2 | 4 | 6 | 9 | 12 | 18 | 36 |

Breadth | 36 | 18 | 9 | 6 | 4 | 3 | 2 | 1 |

7.2

See the
accompanying graph.

7.3.1

b = 12 (P)

7.3.2

l = 1,8

7.4

R is the
point (6 ; 6)

7.5

At point R
the x- and the y-coordinates

are equal, so that length = breadth.

7.6

Length
of the sides of the square is 6 m.

Length = breadth, see 7.5 above.

7.7

Length
of wire netting = perimeter of the square

= 4 x 6 m = 24 m

7.8

Perimeter of
coop is 24,4 m and the area = 36 m².

Thus, 2(l + b)
= 24,4 . . . (1) and lb = 36 . . . (2)

From (1) : l = 12,2 — b

Put into (2):
(12,2 — b)b = 36 so that b² —12,2b + 36 = 0

Thus b = 5 or b = 7,2 . . . solved by using the formula

Thus, breadth = 5 m and length = 7,2 m ** OR ** breadth = 7,2 m and length = 5 m