Patterns and Function

Look at the table showing the relationship between the number of triangles and the number of sides. How many sides will 6 triangles have?

A pattern is created by subtracting 5 from the previous number. If the pattern starts at 50, what is the 4th number in the sequence?

A gardener is planting trees in a row. He follows a pattern of adding 3 trees for every new section. Look at the coordinates where trees are placed. What is the value of $y$ when $x$ is 4?

Maya is building a staircase with blocks. Figure 1 uses 1 block, Figure 2 uses 2 blocks, and Figure 3 uses 3 blocks. If the pattern continues, how many blocks will she use for Figure 10?

A pattern of hexagons is made. The 1st shape has 6 sides, the 2nd shape (two hexagons joined) has 11 sides. How many sides does the 3rd shape (three hexagons joined in a line) have?

A pattern uses the rule: 'Multiply by $2$ and add $1$'. If the second number is $7$, what is the first number?

If the pattern of numbers is $1, 4, 7, 10, \dots$, find the 20th number.

A function machine takes an input $x$ and produces an output $y$ using the rule $y = (x \times 3) + 5$. If the output $y$ is $47$, what was the input $x$?

A pattern of dots forms a sequence of shapes. Shape 1 has $3$ dots, Shape 2 has $6$ dots, Shape 3 has $10$ dots, and Shape 4 has $15$ dots. How many dots will be in Shape 7?

A ball is dropped from a height and bounces back to $\frac{1}{2}$ of its previous height each time. If the first bounce reaches $160$ cm, what is the height of the $5$th bounce?

An input-output machine follows the rule 'Subtract 12'. If the output is $30$, what was the input?

Look at the pattern in the table. If the rule is 'Multiply by 4', what is the missing value ($y$) in the output column?

A number machine uses a specific rule to transform an 'Input' number into an 'Output' number. Based on the diagram and the rule 'Add 7', what is the output when the input is $15$?

A machine triples a number and then outputs it. If the input is 9, what is the output?

In this table, the rule connects the number of triangles to the number of sides. How many sides are there if there are $15$ triangles?

A pattern follows a two-step rule: 'Multiply by 2, then add 3'. If the input is $7$, what is the output?

The table below shows a relationship between $x$ and $y$. What is the value of $y$ when $x = 20$?

An online store calculates shipping based on the weight of the package. There is a flat processing fee plus a cost per kilogram. Based on the table, what is the shipping cost ($S$) for a $12$ kg package?

A pattern is made using toothpicks to form hexagons in a row. The table shows the number of hexagons ($H$) and the toothpicks ($T$) needed. How many toothpicks are needed for $6$ hexagons?

A car rental company charges a fixed insurance fee plus a rate per day. The table shows the total cost ($K$) for $d$ days. What is the total cost for a $10$-day rental?

If $y = x + 10$, what is the value of $y$ when $x = 25$?

A geometric pattern shows triangles. Figure 1 has $3$ sides, Figure 2 (two triangles joined) has $5$ sides, Figure 3 has $7$ sides. How many sides will Figure 4 have?

Identify the missing value in this table: Input: 1, 2, 3, 4 Output: 5, 10, 15, ?

A pattern uses the rule: multiply by $2$ and then add $3$. If the input is $4$, what is the output?

An input-output table shows: (3, 7), (4, 9), (5, 11). Which formula describes the relationship?

What is the missing output for an input of $6$ if the rule is $Output = (Input \times 2) - Input$?

A rectangular area is being tiled. The length is always $2$ units more than the width. If the width is $w$, which expression represents the area $A$?

A rectangle's length is always $3$ cm more than twice its width ($w$). If the width is $5$ cm, what is the length ($L$)?

A savings account starts with $50$ dollars. Every week, $15$ dollars are added. After how many weeks ($w$) will the account have $155$ dollars?

A balloon is being inflated. Its diameter ($D$) in cm follows the rule $D = 4t + 2$, where $t$ is the time in seconds. What will be the diameter after $4.5$ seconds?