After each week, the number of apples on an apple tree increase according to the figures:
Complete the table of values below:
| Week | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Number of apples |
Amy is building a brick shed and starts on one of the side walls. Her progress is shown in the figure:
Complete the table of values below:
| Hours | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Number of layers |
The height of a candle is measured at 15-minute intervals and is shown in the figure:
Complete the table of values below:
| \text{Time (minutes)} | 15 | 30 | 45 | 60 |
|---|---|---|---|---|
| \text{Height (cm)} |
Complete the table of values for the figures in the given pattern:
| \text{Step} \\ \text{number} \left( x \right) | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| \text{Number of} \\ \text{squares} \left( y \right) |
Each of the patterns below was created in steps using matchsticks.
Complete the following table of values for each of the given patterns:
| Step number | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| Number of matchsticks |
For each of the following equations, complete the given table of values:
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
| x | - 1 | 1 | 4 | 5 |
|---|---|---|---|---|
| y |
| x | - 10 | - 5 | 0 | 5 |
|---|---|---|---|---|
| y |
| p | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| q |
| r | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| s |
| u | -2 | 0 | 2 | 4 | 10 |
|---|---|---|---|---|---|
| v |
For each of the following equations, complete the given table of values:
| x | - 2 | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
| x | - 2 | - 1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| y |
| x | - 2 | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
| x | - 4 | - 2 | - 1 | 1 | 2 | 4 |
|---|---|---|---|---|---|---|
| y |
| T | - 4 | - 2 | - 1 | 1 | 2 | 4 |
|---|---|---|---|---|---|---|
| D |
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y |
Consider the equation W = 4 \sqrt{d}.
Complete the given table of values. Round your answers to two decimal places where necessary.
| d | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| W |
The cost of a taxi ride C, in dollars, is given by C = 2.50 t + 3 where t is the duration of the trip in minutes.
Calculate the cost of the following:
A 6-minute trip.
A 7-minute trip.
Complete the table of values:
| \text{Time in minutes }(t) | 6 | 7 | 8 | 9 | 11 | 16 |
|---|---|---|---|---|---|---|
| \text{Cost in dollars }(C) |
The formula for the surface area A of a cube with side length L is given by \\ A = 6 L^{2}.
Complete the given table of values showing the surface areas of cubes of various side lengths.
| L | 4 | 6 | 8 | 13 | 16 |
|---|---|---|---|---|---|
| A |
There are 20 \text{ L} of water in a rainwater tank. It rains for a period of 24 hours and during this time, the tank fills up at a rate of 8 \text{ L/h}. Complete the table of values:
| \text{Number of hours passed }(x) | 0 | 4 | 6 | 7 | 9 | 11 | 12 |
|---|---|---|---|---|---|---|---|
| \text{Amount of water in tank }(y) |
A racing car starts the race with 140 \text{ L} of fuel. From there, it uses fuel at a rate of 2 \text{ L} per minute. Complete the table of values:
| \text{Number of minutes passed } \left(x\right) | 0 | 5 | 10 | 15 | 20 | 70 |
|---|---|---|---|---|---|---|
| \text{Amount of fuel left } \left(y\right) |
If \$5000 was invested at 6\% per annum, compounding annually, then the balance after n years would be given by: B = 5000 \times \left(1.06\right)^{n}.
\text{}\\Complete the table of values to show the balance after n years.
| n | 1 | 2 | 3 | 5 | 10 |
|---|---|---|---|---|---|
| B |
Vanessa is making a sequence of shapes out of tiles. She creates a table comparing the sequence number of a shape to the number of tiles needed to make it:
| \text{Sequence} \\ \text{number } \left(n\right) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{Number of} \\ \text{tiles } \left(T\right) | 3 | 5 | 7 |
How many new tiles are added at each step?
Find how many tiles Vanessa will need to make the next three shapes in the sequence by completing the table of values.
An equation to represent the relationship between a shape's sequence number and the number of tiles needed can be written in the form T=s+(n-1)d, where s is the starting number of tiles and d is the number of new tiles added each step.
Find how many tiles Vanessa will need to make the 20th shape in the sequence.
Triangular numbers count the number of objects that make up an equilateral triangle. The first three triangular numbers are shown below:
Complete the table, showing the first 6 triangular numbers:
| n | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| S | 1 | 3 | 6 |
The number of spots needed to represent the nth triangular number is given by the formula S = \dfrac{n \left(n + 1\right)}{2}. Find the number of spots needed to represent the 10th triangular number.
James is making snowflakes out of hexagonal tiles:
He creates a table comparing the width of a snowflake to the number of tiles needed to make it:
| \text{Width } \left(W\right) | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
|---|---|---|---|---|---|---|---|
| \text{Number of tiles } \left(T\right) | 1 | 7 | 13 | 19 |
How many new tiles are added at each step?
Find how many tiles James will need to make the next three snowflakes in the sequence by completing the table of values.
Which of the following equations represents the relationship between a snowflake's width and the number of tiles needed?
Hence, find the number of tiles required if the width of the snowflake is 21.
A population of rabbits are counted in an area, and it is found that the population is doubling each month. The population counts at the end of each of the first three months are shown below:
Complete the table, showing the population at the end of each of the first 5 months:
| n | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| P |
If the population continues to grow in this manner, the population at the end of the nth month would be given by P = 2^{n}. Find the population at the end of 1 year.