# Number - Proportion

a - answer    s - solution    v - video

## Question 1

Write a proportional statement with and without a constant of proportionality for the following

a) $y$ is directly proportional to $x$a s v

b) $m$ is directly proportional to $n$a s v

c) $a$ is directly proportional to the square of $b$a s v

d) $p$ is directly proportional to the cube of $q$a s v

e) $u$ is directly proportional to the root of $v$a s v

f) $g$ is directly proportional to the cube root of $h$a s v

g) $c$ is directly proportional to the $5$th power of $d$a s v

h) $s$ is directly proportional to the $7$th root of $t$a s v

## Question 2

By finding the constant of proportionality form an equation linking the variables

a) $y$ is directly proportional to $x$. When $y=10, x=5$.a s v

b) $a$ is directly proportional to $b$. When $a=20, b=4$.a s v

c) $y$ is directly proportional to the square of $x$. When $y=2, x=1$.a s v

d) $f$ is directly proportional to the square of $g$. When $f=45, g=3$.a s v

e) $y$ is directly proportional to the cube of $x$. When $y=24, x=2$.a s v

f) $m$ is directly proportional to the cube of $n$. When $m=3, n=3$.a s v

g) $y$ is directly proportional to the square of $x$. When $y=2, x=4$.a s v

h) $y$ is directly proportional to the square root of $x$. When $y=10, x=4$.a s v

i) $h$ is directly proportional to the square root of $g$. When $h=5, g=25$.a s v

j) $c$ is directly proportional to the cube root of $d$. When $c=2, d=64$.a s v

k) $w$ is directly proportional to the $5$th root of $z$. When $w=3, z=32$.a s v

## Question 3

By finding the constant of proportionality, answer the following questions

a) $y$ is directly proportional to $x$. When $y=6, x=2$. Find $y$ when $x=10$a s v

b) $y$ is directly proportional to $x$. When $y=2, x=20$. Find $y$ when $x=150$a s v

c) $a$ is directly proportional to $b$. When $a=3, b=8$. Find $b$ when $a=5$a s v

d) $y$ is directly proportional to the square of $x$. When $y=16, x=4$. Find $y$ when $x=9$a s v

e) $r$ is directly proportional to the square of $s$. When $r=15, s=5$. Find $r$ when $s=15$a s v

f) $p$ is directly proportional to the cube of $q$. When $p=9, q=3$. Find $q$ when $p=243$a s v

g) $y$ is directly proportional to the square root $x$. When $y=18, x=36$. Find $y$ when $x=64$a s v

h) $y$ is directly proportional to the cube root $x$. When $y=1, x=27$. Find $y$ when $x=64$a s v

## Question 4

Write a proportional statement with and without a constant of proportionality for the following

a) $y$ is inversely proportional to $x$a s v

b) $P$ is inversely proportional to $Q$a s v

c) $y$ is inversely proportional to the square of $x$a s v

d) $a$ is inversely proportional to the cube of $b$a s v

e) $h$ is inversely proportional to the square root of $g$a s v

f) $E$ is inversely proportional to the cube root of $F$a s v

g) $y$ is inversely proportional to the fourth power of $x$a s v

h) $s$ is inversely proportional to the ninth root of $t$a s v

## Question 5

By finding the constant of proportionality form an equation linking the variables

a) $y$ is inversely proportional to $x$. When $y=\frac{2}{5}, x=5$.a s v

b) $A$ is inversely proportional to $B$. When $A=10, B=\frac12$.a s v

c) $g$ is inversely proportional to the square of $h$. When $g=3, h=2$.a s v

d) $y$ is inversely proportional to the square of $x$. When $y=18, x=\frac13$.a s v

e) $P$ is inversely proportional to the cube of $Q$. When $P=\frac34, Q=2$.a s v

f) $S$ is inversely proportional to the square root of $T$. When $S=5, T=16$.a s v

g) $u$ is inversely proportional to the cube root of $w$. When $u=1, w=27$.a s v

h) $Y$ is inversely proportional to the sixth root of $X$. When $Y=\frac{1}{6}, X=64$.a s v

## Question 6

By finding the constant of proportionality, answer the following questions

a) $y$ is inversely proportional to $x$. When $y=4, x=3$. Find $y$ when $x=4$a s v

b) $C$ is inversely proportional to $D$. When $C=\frac12, D=4$. Find $C$ when $D=7$a s v

c) $y$ is inversely proportional to the square of $x$. When $y=3, x=4$. Find $y$ when $x=2$a s v

d) $a$ is inversely proportional to the cube of $b$. When $a=6, b=1$. Find $a$ when $b=2$a s v

e) $g$ is inversely proportional to the square root of $h$. When $g=4, h=49$. Find $g$ when $h=16$a s v

f) $R$ is inversely proportional to the cube root of $S$. When $R=1, S=8$. Find $R$ when $S=27$a s v

g) $f$ is inversely proportional to the cube of $g$. When $f=\frac12, g=2$. Find $g$ when $f=32$a s v

h) $W$ is inversely proportional to the square root of $X$. When $W=\sqrt8, X=2$. Find $W$ when $X=4$a s v

## Question 7

By forming an equation with a constant of proportionality, answer the following

a) $£5$ can be exchanged for $\$7$. Find how much$£20$can buy in$\.a s v

b) $5$ people can dig $8$ holes in an hour. They all work at the same rate. How many complete holes can $12$ people dig in an hour?a s v

c) The $y$ coordinate on a graph is directly proportional to the square of the $x$ coordinate. The point $(20,2)$ lies on the graph. Find the equation of the graph and hence find the $y$ coordinate when $x=5$.a s v

d) The amount of flour put into a bread mix is directly proportional to the cube root of the volume of the bread, once baked. When I put in $50$g of flour, I get a bread with volume $6859$cm$^3$. How much flour is needed to make a bread with volume $10,000$cm$^3$? Give you answer to the nearest gram.a s v

e) Gravitational force is inversely proportional to the square of distance from the earth. At $6000$km from the centre of the earth (so on the earth surface) a person feels a gravitational force of $500$N (Newtons, which is a measure of force). How much gravitational force do they feel $90,000$km away?a s v