Patterns and Algebra

What is the rule for: $1, 11, 21, 31, \dots$?

Which of these is the next term: $2, 4, 8, 16, \dots$?

Find the $4$th term in the sequence where the rule is 'start at $100$ and subtract $25$'.

What is the rule for this geometric sequence: $4, 16, 64, \dots$?

If the rule for a sequence is $3n + 10$, at what position $n$ is the term value equal to $40$?

Find the $3^{rd}$ term of the sequence defined by the rule $n^2 + n$.

Identify the $n^{th}$ term rule for: $11, 22, 33, 44, \dots$.

The $n^{th}$ term of a sequence is $T_n = 12n + 1$. What is the difference between $T_{n+1}$ and $T_n$?

What is the $50^{th}$ term of the sequence $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \dots$?

A sequence is defined by $T_1 = 1$ and $T_{n} = T_{n-1} + n^2$. What is the $4^{th}$ term?

If $a = 2$ and $b = 3$, what is $ab + 5$?

Identify the coefficient in the term $\frac{2}{3}x$.

What is the value of $g \div 1$ for any value of $g$?

Which phrase is represented by $3n + 2$?

Simplify the expression $15y \div 3$.

A rectangle has a length of $x + 2$ and a width of $x - 1$. Which expression represents the perimeter?

For the pattern $4, 8, 12, 16, \dots$, which expression represents the $n^{th}$ term?

What is the value of $n$ if the $n^{th}$ term of the sequence $2, 9, 16, 23, \dots$ is 142?

Simplify the following by factorising: $8x + 12y$.

If the expression $ax + 7$ equals 31 when $x = 3$, what is the value of $a$?

Simplify the expression: $8 + 5k - 3$.

Simplify the following: $d + d + d + 10$.

What is the simplified form of $12p - 3p + 4q$?

Simplify the expression: $9y + 6 - 4y - 3$.

Simplify the expression: $9p - 2(p + 3)$.

Simplify the following: $2(a + b + c) - a$.

Combine the terms: $x + 2y + 3x - y$.

Simplify: $-(4a - 3b) + 2(a - 2b)$

Simplify: $4(3 - x) - 3(4 - x)$

An isosceles triangle has two sides of length $3x - 1$ and a base of length $x + 4$. What is the perimeter in simplest form?

Solve: $(9 - 4) \times 5$.

What is $7 + 7 \times 7$?

Find the result of $16 \div 4 - 3$.

Evaluate: $2 + 3 \times 10$.

Determine the result: $24 \div (2 \times 3) + 3^2$.

Calculate $7 + (3^2 - 4) \times 5$.

What is the value of $[(12 + 18) \div 5] \times 2$?

Calculate: $[ (15 - 5)^2 \div 20 ] \times 3 + 1$

Evaluate the expression: $5^2 - \{ [ (12-4) \times 2 ] - 10 \}$

Determine the value: $\frac{ 4 \times (2^3 + 7) }{ 10 \div 2 }$

Solve for $q$ in the equation $q - 1 = 99$.

Find $x$ in $x + 0.5 = 1$.

Solve for $w$ in the equation $\frac{w}{2} = 25$.

What is the value of $h$ in $15h = 45$?

Solve the equation for $q$: $q - \frac{1}{4} = \frac{1}{2}$.

Find $n$: $n + 18 = 18$.

Solve for $m$: $m - 0.75 = 0.25$.

Solve the equation: $x - \frac{3}{4} = -1 \frac{1}{2}$.

Find $w$ if $\frac{w}{0.01} = 100$.

Solve for $d$: $d + (-5.5) = -12$.

In which quadrant is the point $(-4, -4)$ located?

Which of these points is located in Quadrant I?

Which point is $3$ units to the left of the y-axis and $2$ units above the x-axis?

If you reflect the point $(-3, -3)$ across the x-axis, what are the new coordinates?

Find the area of a triangle with vertices at $(-2, 0), (4, 0),$ and $(1, 5)$.

Three vertices of a rectangle are $(2, 3), (-2, 3),$ and $(-2, -3)$. What are the coordinates of the fourth vertex?

If you are at point $(-2, -2)$ and move to $(2, 2)$, what is the total change in the $x$-coordinate?

A circle is centered at $(2, 2)$ and passes through $(2, 5)$. What is the circumference of the circle in terms of $\\pi$?

The coordinates $(1, 2), (2, 4), (3, 6), (4, 8)$ follow a linear pattern. What is the $y$-coordinate when $x = -5$?

If point $P$ has coordinates $(x, y)$ such that $xy > 0$, in which quadrant(s) could $P$ be located?

Starting at the origin, if you move $2$ units East and $2$ units South, where are you? (Using negative numbers for South)

How many cardinal directions are there on a basic compass rose?

What is the $y$-coordinate of the origin?

If you are at $(4, 4)$ and want to move to $(1, 4)$, which direction do you go?

On a grid, a point moves in a pattern: $(1, 1) \rightarrow (3, 2) \rightarrow (5, 3) \rightarrow (7, 4)$. What is the rule for the $x$-coordinate?

What is the result of a $135^{\circ}$ anti-clockwise turn from East?

If the point $(2, 2)$ is the center of a circle with a radius of $3$ units, which of these points lies on the circle directly to the North?

A rectangle has vertices $A(1, 2), B(4, 2), C(4, 5),$ and $D(1, 5)$. If the rectangle is translated $2$ units left and $3$ units down, what is the new coordinate of the center of the rectangle?

A hiker is at $( -2, -2 )$. To get to a waterfall, they must go $3$ units North and $4$ units East. What is the compass direction from the hiker's start to the waterfall?

What is the reflection of the point $(a, b)$ across the line $y = x$?