Pattern and Function

A student is creating a pattern using square tiles. The first pattern has 1 tile, the second has 4 tiles, and the third has 9 tiles. Following this geometric pattern, how many tiles will be in the $5^{th}$ pattern?

A geometric sequence starts $5, 10, 20, \dots$. What is the $5$th term?

In the function graph $y = x + 2$, what is the value of $y$ when $x = 3$?

A pattern is formed by adding rows of dots. How many dots will be in the 5th triangle?

A pattern starts with $200$ and decreases by half each time. What is the $5$th term?

Which of the following coordinates would lie on the line for the rule: $y = 2x + 1$?

A tile pattern is shown. Each step adds a border of tiles around the previous shape. How many tiles are in Step $3$?

A sequence of shapes is made from small equilateral triangles. Figure 1 is $1$ triangle. Figure 2 is made of $4$ triangles forming a larger triangle. Figure 3 is made of $9$ triangles forming an even larger triangle. If the side length of the large triangle in Figure $n$ is $n$ units, how many small triangles are needed for Figure $8$?

A toy train track is laid out in a pattern. The first section uses $4$ curved pieces and $2$ straight pieces. Each additional section adds $2$ curved pieces and $3$ straight pieces. How many total pieces of track are used for a train line consisting of $6$ sections?

A pattern of squares is built. Figure 1 is a $1 \times 1$ square. Figure 2 is a $2 \times 2$ square with a $1 \times 1$ hole in the middle. Figure 3 is a $3 \times 3$ square with a $2 \times 2$ hole. Figure 4 is a $4 \times 4$ square with a $3 \times 3$ hole. How many small $1 \times 1$ tiles are used to build Figure 10?

Which expression represents 'double a number $k$ and then add $7$'?

If the pattern continues, how many circles will be in the 5th figure?

A rectangle's length is always twice its width. If $w$ is the width, what is the formula for the area $A$?

Which of the following describes the rule for the sequence: $5, 9, 13, 17, ...$?

If a square's side length $s$ increases by $1$ unit, how much does the perimeter $P$ increase?

Which of these graphs represents the rule $y = x + 3$?

A geometric sequence doubles each time: $3, 6, 12, 24, ...$ What is the 6th term?

A cooling fan rotates such that the number of rotations $R$ is proportional to the time $t$ in seconds. If the fan makes 120 rotations in 4 seconds, which equation expresses the relationship between $R$ and $t$?

A sequence of patterns is made using toothpicks to form a chain of hexagons. One hexagon takes 6 toothpicks. Two hexagons share one side and take 11 toothpicks. Three hexagons take 16 toothpicks. What is the rule for $n$ hexagons?

The area of a square $A$ is related to its side length $s$. If you increase the side length by 1 unit, the new area follows a pattern. If the original side is $s$, what is the rule for the area $A$ of the square?

If $a = 4$ and $b = 5$, what is the value of $2a + b$?

What is the value of $m$ if $m + 15 = 40$?

A car travels at a speed of $v$ km/h. The distance $d$ it covers in $3$ hours is given by $d = 3v$. If $v = 60$, find $d$.

A pattern is made of circles. Term 1 has $2$ circles, Term 2 has $4$, Term 3 has $6$. How many circles are in Term $n$?

A pattern is made using equal-sized square tiles. The first three stages of the pattern are shown. If $n$ represents the stage number and $T$ represents the total number of tiles, which equation correctly describes the relationship between the stage number and the number of tiles?

The sum of three consecutive integers is $33$. If the middle integer is $x$, the equation is $(x-1) + x + (x+1) = 33$. Find $x$.

If $x = 4$, which of these expressions has the largest value?

An isosceles triangle has two equal sides of length $x$ and a third side of 10 cm. If the perimeter is 36 cm, what is the length of one of the equal sides?

The sum of three consecutive whole numbers is 54. If the smallest number is $n$, the equation is $n + (n+1) + (n+2) = 54$. What is the middle number?

A circle has a radius of $r + 2$ cm. If the diameter of the circle is 18 cm, what is the value of $r$?

A sequence follows the rule $y = 3x - 1$. If $x=2$, what is $y$?

The total cost $C$ of buying $n$ notebooks at $2$ dollars each is shown. What is the cost of $8$ notebooks?

A car travels at a constant speed of $60$ km/h. How many kilometers ($d$) does it travel in $t$ hours?

Which of these points lies on the line representing the function $y = x + 5$?

The graph shows the relationship between the number of tickets sold ($x$) and the total cost in dollars ($y$). Based on the linear pattern shown, which coordinate pair $(x, y)$ represents the cost for 8 tickets?

A student tracks the growth of a plant over several weeks. The height of the plant follows a specific rule based on the week number. The table below shows the relationship:

Which equation describes the relationship between the Week ($x$) and the Height ($y$), and what will be the height of the plant in Week 10?

Which of the following points does NOT lie on the line $y = 2x + 1$?

A rectangular area is being fenced. One side is fixed against a wall. The total fence length $L$ for a width $w$ and a length that is twice the width is $L = 4w$. If the width $w$ is 8 meters, what is the total length of the fence needed?

Look at the function machine diagram. If the input $x$ is 5 and the output is 21, and the input 10 results in 41, what is the rule the machine is using?

An online store calculates shipping cost $S$ based on the weight $w$ of the package. The rule is $S = 3w + 10$. If the shipping cost is $40, what was the weight of the package?