1

a Draw the graph of y against x.

b Write down a rule for y in terms of x. ...............................................................................................................................................

c Explain why y is directly proportional to x. ......................................................................................................................................

2

y is directly proportional to x.

a Complete the table and draw the graph of y against x.

b Write down a rule for y in terms of x. ...............................................................................................................................................

c Explain why y is directly proportional to x. .....................................................................................................................................

3 A is directly proportional to B.

A B= 52

a Complete the table.

b Find A when B = 60. ..................................................................

c Find B when A = 60. ..................................................................

�3 8.1 Direct proportion

263

00 5 10 15 20

10

20

30

40

y

x

00 10 20 30 40

10

20

30

40

y

x

x 2 3 5 10 12

y 6 9 15 30 36

x 8 10 12 16 20

y 15

A 2 6 10 12 20

B

Guided practice worksheet

B

Questions are targeted at the grades indicated

1 P is directly proportional to Q. P = 4Q.

a Find P when Q = 2.5 ....................................................... b Find Q when P = 13 .........................................................

.................................................................................................... .....................................................................................................

2 V is directly proportional to t. V t= 23

a Find V when t = 12 .......................................................... b Find t when V = 13 ...........................................................

.................................................................................................... ....................................................................................................

.................................................................................................... .....................................................................................................

3 d is directly proportional to h. d = 0.4h.

a Find h when d = 2.5 ......................................................... b Find d when h = 13 ...........................................................

..................................................................................................... .....................................................................................................

4 A is directly proportional to r. A r= 74

a Find r when A = 2.5 .......................................................... b Find A when r = 13 ..........................................................

..................................................................................................... .....................................................................................................

..................................................................................................... .....................................................................................................

5 Write down a formula using constant k for each of these statements.

a s ∝ t .................................................................. b x ∝ y ..................................................................

c A ∝ B .................................................................. d p ∝ q ..................................................................

e T ∝ V .................................................................. f w ∝ s ..................................................................

6 y is directly proportional to x. When x = 3, y = 12

a Write down a formula for y in terms of x. ..................................................................

b Find y when x = 3.5 ................................................................................................................

c Find x when y = 28 ..................................................................................................................

7 q is directly proportional to p. When p = 8, q = 20

a Write down a formula for q in terms of p. ..................................................................

b Find q when p = 13 ................................................................................................................

c Find p when q = 25 .................................................................................................................

8 w is directly proportional to v. When v = 12, w = 4

a Write down a formula for w in terms of v. ................................................................

b Find w when v = 21 ...............................................................................................................

c Find v when w = 5 ...................................................................................................................

�3 8.2 Further direct proportion

265

Guided practice worksheet Questions are targeted at the grades indicated

A

1 Write down the inverse (reciprocal) of each of the following numbers.

a 4 ...................................... b 7 ...................................... c 9 ...................................... d 14 ......................................

e 25 ...................................... f 0.7 ...................................... g 1

3 ...................................... h 0.3 ......................................

i x ...................................... j x2 ......................................

2 Write the following statements as algebraic expressions:

a the square of d ............................................................. b the cube of x .............................................................

c the square root of y ............................................................. d the cube root of f ............................................................

e the square of c ............................................................. f the square root of h .............................................................

g the cube of m ............................................................. h the cube root of p ............................................................

i the square of q ............................................................. j the cube of n ............................................................

3 For each of the following:

i write down a statement of proportionality using the symbol ∝ii write down a formula using the constant k

a s is proportional to the square of t i ............................................................... ii ...............................................................

b x is proportional to the cube root of y i ............................................................... ii ...............................................................

c A is proportional to the square root of B i .............................................................. ii ..............................................................

d p is proportional to the square of q i ............................................................... ii ...............................................................

e T is proportional to the cube of v i ............................................................... ii ...............................................................

f w is proportional to the square root of z i .............................................................. ii ..............................................................

g d is proportional to the square root of e i ............................................................... ii ...............................................................

h f is proportional to the cube of g i ............................................................... ii ..............................................................

�3 8.3 Writing statements of proportionality and formulae

267

Guided practice worksheet Questions are targeted at the grades indicated

D

A

�3 8.4 Problems involving square and cubic proportionality

269A

1 y is directly proportional to the square of x. y = 18 when x = 3.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 4 c x when y = 12

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

2 y is directly proportional to the square of x. y = 48 when x = 4.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 12 c x when y = 4

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

3 y is directly proportional to the square of x. y = 12 when x = 4.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 12 c x when y = 48

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

4 y is directly proportional to the cube of x. y = 64 when x = 2.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 3 c x when y = 8

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

Guided practice worksheet Questions are targeted at the grades indicated

A

�3 8.4 Problems involving square and cubic proportionality

269B

Guided practice worksheet

5 y is directly proportional to the cube of x. y = 32 when x = 4.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 6 c x when y = 4

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

6 y is directly proportional to the cube of x. y = 3 when x = 2.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 4 c x when y = 81

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

A

�3 8.5 Problems involving inverse proportion

271A

1 y is inversely proportional to x. y = 8 when x = 5.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

......................................................................................................................................................................................................................................

b y when x = 10 c x when y = 2

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

d y when x is –4

...............................................................

...............................................................

...............................................................

2 y is inversely proportional to the square root of x. y = 2 when x = 4.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 9 c x when y = 1

............................................................... ..............................................................

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3 p is inversely proportional to v. p = 15 when v = 20.

Find a a formula for p in terms of v .......................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b p when v = 30 c v when p = 7.5

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Guided practice worksheet Questions are targeted at the grades indicated

A

�3 8.5 Problems involving inverse proportion

271B

4 y is inversely proportional to the square of x. y = 4 when x = 5.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 2 c x when y = 1

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

5 y is inversely proportional to x. y = 6 when x = 8.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 12 c x when y = 4

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

6 y is inversely proportional to the cube of x. y = 7 when x = 6.

Find a a formula for y in terms of x .........................................................................................................................................................

.....................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................

b y when x = 3 c x when y = 189

............................................................... ..............................................................

............................................................... ...............................................................

............................................................... ...............................................................

Guided practice worksheet

A