Question 1: The following variables are each directly proportional. Find the equation linking
the two variables in each case:
| a) y = 10, x = 2 | b) y = 10, x = 5 | c) y = 12, x = 0.5 | d) s = 4,00 t = 20 |
| e) h = 5, s = 15 | f) y = 11, x = 3 | g) y = 13, x = 17 | h) t = 18, x = 72 |
Question 2: the following variables are inversely proportional to each other. Find the equations linking the variables in each case.
| a) y = 6, x = 5 | b) y = 100, x = 0.5 | c) y = 8, x = 16 | d) y = 0.1, x = 0.2 |
| e) f = 0.2, t = 0.1 | f) s = 90, t = 0.1 | g) v = 2.5, w = 0.5 | h) u = 21, w = 21 |
Question 3: In the following questions y is proportional to x 2 . Find the equation linking the two variables in each case
| a) y = 100, x = 5 | b) y = 200, x = 10 | c) y = 100, x = 2 | d) y = 100, x = 8 |
| e) y = 150, x = 9 | f) y = 52, x = 6 | g) y = 4, x = 4 | h) y = 1, x=10 |
Question 4: Sketch the graph that would indicate the following proportions:
| a) y ∝ x | b) y ∝ 1/x (inversely proportional) | c) y ∝ x 2 | d) y ∝ 1 / x2 |
Question 5: The height (h) and weight (w) of a flower are directly proportional. A certain flower has a height
of 20 cm and a weight of 2 grams.
a) Find an equation linking h and w
b) Find the height of a flower that weighs 26 grams
c) Find the weight of a flower that is 45 cm tall
d) Sketch a graph to represent the relationship between the height and the weight of this flower species.
Question 6: The area (A) of a shape is proportional to the square of it's length (l).
When the shape has a length of 6, it has an area of 54.
a) Find the equation linking length and area
b) When the area is 42, what is the length of the shape.
c) Sketch a graph to indicate the relationship between the variables
Question 7: We are told that the nutritional value of a certain piece of veg (N) is inversely proportional
to the length of time it has been boiled (t). We are told that after it has been boiled for 2 minutes, it
has a nutritional value of 15.
a) Find an equation linking these two variables
b) When it has been boiled for 240 seconds, what is its nutritional value
c) Suppose that you want a nutritional value greater than 6. After what time must you remove the veg from
the boiling water.
d) Sketch a graph to represent the relationship between N and t.