Algebra

Factorize the trinomial $x^2 + 13x + 42$.

Expand and simplify $(x - 6)(x - 2)$.

Factorize $16x^2 - 25$.

Expand the expression $4(x + y - 2)$.

Expand and simplify $(x + y - z)(x + y + z)$.

Factorize $10x^2 - 19x + 6$.

Factorize $x^2 + x - 30$.

Expand and simplify $(x-1)(x+1)(x^2+1)(x^4+1)$.

Factorize $2x^2 - 7x + 3$.

Factorize $(x-y)^3 + (y-z)^3 + (z-x)^3$ completely.

Solve the inequality $3x + 1 \leq 10$.

Solve for $x$: $\frac{x}{-4} = 2$

What is the value of $x$ in the equation $9x = 0$?

Solve for $x$: $2x + 8 = 2$

Solve for $x$: $2x + \frac{1}{2} = \frac{3}{4}$.

Solve the inequality: $4 - 3x \leq 19$.

Solve for $x$: $5x - 2(x-4) = 20$.

Solve for $x$: $\frac{3}{4}x - \frac{1}{2} = \frac{2}{3}x + \frac{5}{6}$

Solve the inequality: $5(1 - x) < 3(x - 11)$

Determine the solution for $x$: $\frac{x-a}{b} = \frac{x-b}{a}$ where $a \neq b$.

What is the solution to $2x + 2y = 10$ and $x - y = 1$?

Solve the system: $3x + y = 7$ and $x - y = 1$.

If the sum of two variables is $13$ and their difference is $1$, find the variables.

Given $y = 2x + 4$ and $x + y = 10$, find the point of intersection.

Determine the solution $(x, y)$ to the following system of linear equations:

$x + 3(y - 1) = 6$ $2(x + 1) - y = 6$

Find the values of $x$ and $y$: $11x - 2y = 20$ and $4x + 3y = 21$.

Solve simultaneously: $7x + 3y = 27$ and $5x - y = 1$.

Solve for $x, y$: $\frac{x}{a+b} + \frac{y}{a-b} = 2$ and $ax - by = a^2 + b^2$.

Find the value of $m$ if the lines $y=3x+1$, $y=x+3$, and $y=mx+4$ are concurrent.

A tank is filled in 12 hours by two pipes A and B. If pipe A is used for 4 hours and pipe B for 9 hours, only half of the tank is filled. How many hours does B take alone?

Evaluate $f(1)$ for the function $f(x) = (x + 1)^3$.

What is the $x$-intercept of the function $f(x) = 10 - 2x$?

Find the $y$-intercept of the quadratic function $g(x) = 2x^2 + 5x$.

The domain of $f(x) = \frac{1}{x}$ is all real numbers except for which value?

The function $f(x) = x^2 - 8x + 12$ is defined for the domain $1 \leq x \leq 6$. Determine the range of $f$.

If $f(x) = 10 - 2x$ and the domain is $x \in \{0, 1, 2, 3\}$, what is the largest value in the range?

A mapping is given by $y^2 = x$. Why is this NOT a function of $x$?

Find the $y$-intercept of the inverse of $f(x) = 2x+5$.

If $f(x) = \frac{x+2}{2x-1}$, what is the value of $x$ for which the function is undefined?

Solve $f(x) = 2$ for $f(x) = |2x-6| - 4$.

Which point lies on the graph of $y = x^2 - 1$?

In the standard form of a quadratic $y = ax^2 + bx + c$, the value of $c$ represents the:

Find the $y$-intercept of $y = x^2 + 3x$.

What is the vertex of the function $y = -x^2$?

The parabola $y = x^2 + bx + c$ passes through the point $(0, -5)$. What is the value of $c$?

Which of the following points lies on the line $y = 3x - 2$?

The graph of $y = (x + 4)^2 - 1$ is a translation of $y = x^2$ by:

Determine the value of $m$ such that the line $y = mx$ bisects the area of the triangle with vertices $(0,0), (4,0), (0,4)$.

The quadratic $y = ax^2 + bx + c$ has roots $1$ and $5$. If the graph passes through $(2, -6)$, what is the value of $a$?

What is the equation of the line that passes through the vertex of $y = x^2 - 4x + 9$ and the origin?

Solve for $x$: $2x - 10 = 0$.

Find $x$ if $x^2 = 1$.

Solve the system: $x + y = 8$ and $x - y = 8$.

Solve for $x$: $14 = 2x + 4$.

Solve for $x$: $\frac{3}{x - 1} = 2$.

A rectangle's length is 3 cm more than its width. If the area is 40 cm$^2$, what is the width?

Solve the equation $5x^2 - 13x - 6 = 0$ by factoring.

Solve the simultaneous equations $x^2 + y^2 = 20$ and $y = 2x$.

Solve the equation $x^2 + 10x + 13 = 0$ by completing the square.

Find the values of $k$ for which the line $y = x + k$ intersects the circle $x^2 + y^2 = 8$ at exactly one point.

Solve for $x$ in $y = 3(x - 2)$.

Rearrange $p = \frac{w}{a}$ to make $w$ the subject.

Make $y$ the subject of $x = 12 - y$.

If $T = 20 + 5h$, make $h$ the subject.

Make $x$ the subject of $y = \frac{1}{x^2 + 1}$, where $x > 0$.

The formula for linear expansion is $L = L_0(1 + \alpha \Delta T)$. Make $\alpha$ the subject.

In the arithmetic sequence formula $T = a + (n - 1)d$, make $n$ the subject.

Make $v$ the subject of $a = \frac{v-u}{t}$.

Rearrange $y = \frac{5}{x+a} - b$ for $x$.

Make $w$ the subject of $P = 2l + 2w$.

What is the image of $-1$ under the mapping $f(x) = 5x + 5$?

Which of these values is in the range of $f(x) = 2x$ for domain $\{1, 2, 3\}$?

If $f(x) = x^2 - x$, find $f(2)$.

The image of $x$ under a mapping $f$ is often written as:

For the mapping $f(x) = c$, where $c$ is a constant, if $f(5) = 12$, find $f(-100)$.

If $f(x) = 3x$ and $g(x) = x + 2$, find the value of $f(g(4))$.

Solve for $x$ if $h(x) = 4x - 8$ and $h(x) = 0$.

If $g(x) = 2x - 3$ and $(f \circ g)(x) = 4x^2 - 12x + 11$, find $f(x)$.

The range of $f(x) = \sqrt{x^2 + 9}$ is:

If $f(x) = 3x - 2$ and $g(x) = \frac{x+2}{3}$, find $(f \circ g)(100)$.

Solve for $x$: $0.5x = 10$.

If $3x = 21$, find the value of $x + 5$.

Simplify the expression $3(x + y) - 2x$.

Solve the equation $x - 7 = -7$.

If $x \diamond y = x^2 - 2y$, calculate the value of $5 \diamond 3$.

The perimeter of a square is $4x + 12$. What is the length of one side?

Which of the following describes the algorithm to find the inverse of the function $f(x) = 5x - 2$?

In an arithmetic sequence, the first term $a_1 = 7$ and the 10th term $a_{10} = 52$. Find the common difference $d$.

If $3^x = m$, express $3^{x+2} - 3^{x-1}$ in terms of $m$.

Find the arithmetic mean of the three expressions: $2x - 3$, $x + 4$, and $3x + 5$.

If line $A$ has gradient $m = -\frac{1}{6}$ and line $B$ is parallel to $A$, what is the gradient of $B$?

Which gradient is perpendicular to a gradient of $1.25$?