x y x y 15 y is directly proportional to x. a Draw the graph of y against x.

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1 3 8.1 Direct proportion 1 x y B a Draw the graph of y against x. y x b Write down a rule for y in terms of x.... c Explain why y is directly proportional to x x y 15 y is directly proportional to x. a Complete the table and draw the graph of y against x. y x b Write down a rule for y in terms of x.... c Explain why y is directly proportional to x is directly proportional to B. B = B a Complete the table. b Find when B = c Find B when =

2 3 8.2 Further direct proportion 1 P is directly proportional to Q. P = 4Q. a Find P when Q = b Find Q when P = V is directly proportional to t. V t = 2 3 a Find V when t = b Find t when V = d is directly proportional to h. d = 0.4h. a Find h when d = b Find d when h = r 4 is directly proportional to r. = 7 4 a Find r when = b Find when r = Write down a formula using constant k for each of these statements. a s t... b x y... c 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 = c Find x when y = 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 = c Find p when q = 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 = c Find v when w =

3 3 8.3 Writing statements of proportionality and formulae 1 Write down the inverse (reciprocal) of each of the following numbers. a 4... b 7... c 9... d e f g h i x... j x 2... D 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 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

4 3 8.4 Problems involving square and cubic proportionality 1 y is directly proportional to the square of x. y = 18 when x = 3. b y when x = 4 c x when y = y is directly proportional to the square of x. y = 48 when x = 4. b y when x = 1 2 c x when y = 4 3 y is directly proportional to the square of x. y = 12 when x = 4. 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. b y when x = 3 c x when y = 8 269

5 3 8.4 Problems involving square and cubic proportionality 5 y is directly proportional to the cube of x. y = 32 when x = 4. 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. b y when x = 4 c x when y = B

6 3 8.5 Problems involving inverse proportion 1 y is inversely proportional to x. y = 8 when x = 5.. b y when x = 10 c x when y = 2 d y when x is y is inversely proportional to the square root of x. y = 2 when x = 4. b y when x = 9 c x when y = 1 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 3 8.5 Problems involving inverse proportion 4 y is inversely proportional to the square of x. y = 4 when x = 5. b y when x = 2 c x when y = 1 5 y is inversely proportional to x. y = 6 when x = 8. 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. b y when x = 3 c x when y = B