3 8.1 Direct proportion 1 x 2 3 5 10 12 y 6 9 15 30 36 B a Draw the graph of y against x. y 40 30 20 10 0 0 5 10 15 20 x b Write down a rule for y in terms of x.... c Explain why y is directly proportional to x.... 2 x 8 10 12 16 20 y 15 y is directly proportional to x. a Complete the table and draw the graph of y against x. y 40 30 20 10 0 0 10 20 30 40 x b Write down a rule for y in terms of x.... c Explain why y is directly proportional to x.... 3 is directly proportional to B. B = 5 2 2 6 10 12 20 B a Complete the table. b Find when B = 60.... c Find B when = 60.... 263
3 8.2 Further direct proportion 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 = 2 3 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...... r 4 is directly proportional to r. = 7 4 a Find r when = 2.5... b Find when r = 13......... 5 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 = 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... 265
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 1 4... e 2 5... f 0.7... g 1 3... h 0.3... 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... 267
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 = 1 2 2 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
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 = 81 269B
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 4......... 2 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 = 7.5 271
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 = 189 271B