Algebra

Rearrange $2x = y$ to make $x$ the subject.

If $z = 2(x + y)$, find the value of $z$ when $x = 3$ and $y = 5$.

Write an expression for 'half of $p$'.

Simplify the expression $k + k + k + m + m$.

Rearrange $y = \frac{k}{x}$ to make $x$ the subject.

Factorize $x^2 - 9x + 20$.

Expand the expression $(2x + 1)(2x - 1)$.

Rearrange $y = \frac{x^2 + 5}{3}$ to make $x$ the subject.

Make $k$ the subject of $T = 2\pi\sqrt{\frac{m}{k}}$.

If $x = a + \frac{1}{b + c}$, express $c$ in terms of $x, a,$ and $b$.

Simplify the expression: $2(x + 4) - x$

Factorise completely: $6m^2 - 2m$

Expand the expression: $5(2a - 3b)$

Simplify the expression using index laws: $\frac{x^6}{x^2}$

Factorise completely the following expression: $12x^2 + 7x - 10$

Factorise completely: $4x^2 - 100$

Expand and simplify: $3(x-4) - 2(2x-5)$

Factorise the expression $(x^2 - 2x)^2 - 11(x^2 - 2x) + 24$ completely.

Factorize the expression $1 - 16x^4$ completely.

Simplify the complex fraction: $\frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{x^2} - \frac{1}{y^2}}$.

Find $x$ if $\frac{3x}{2} = 9$.

Solve $x(x + 1) = 0$.

Solve the equation $x^2 = 4$.

Solve $2(x - 3) = 10$.

Solve the quadratic equation $x^2 - 4x - 12 = 0$.

Find $x$ if $15 - 2(x - 3) = 5$.

Solve $5x^2 - 13x - 6 = 0$.

Solve the equation $x = \sqrt{x+6}$.

If $x^2 - 5x + k = 0$ and one root is double the other, find $k$.

Find the vertex of the parabola $y = -3x^2 + 12x - 10$.

Solve for $x$ and $y$: $y = x + 4$ and $2x + y = 10$.

If $2x + 2y = 10$ and $x = 3$, find $y$.

Find $x$ and $y$ such that $x - y = 7$ and $x + y = 13$.

Solve the system: $x + y = 18$ and $x = 2y$.

Solve the simultaneous equations: $2x + 3y = 6$ and $3x + 2y = 9$.

The sum of two numbers is 20 and their product is 96. Find the numbers.

Find the solutions for $y = x^2 - 9$ and $y = 2x - 1$.

Solve the following equations: $2x^2 + y^2 = 17$ and $x + y = 1$.

Solve the system: $y = \frac{5}{x} - 2$ and $y = x + 2$.

Determine the coordinates: $x^2 + y^2 = 41$ and $x + y = 9$.

Solve the inequality: $x - 5 > -2x + 4$.

Solve the inequality: $3(x + 4) \geq 18$.

Find the solution to: $4x \leq 2x + 10$.

Solve the inequality: $12 - x > 15$.

Solve for $x$: $4(x - 1) \geq 6x + 8$.

Solve the inequality: $\frac{x}{5} + 1 > \frac{x}{2} - 2$.

Find the range of $k$ given that $-1 < 5 - 2k \leq 9$.

Solve the inequality: $5(x+2) - 3(x-1) \leq 2x + 13$.

The region bounded by $x \geq 0, y \geq 0,$ and $3x + 4y \leq 12$ is a triangle. What is its area?

If $x$ is an integer, find the number of solutions to $3 < 2x - 1 < 12$.

What is the next term in the arithmetic sequence: $-15, -10, -5, 0, \dots$?

Find the common ratio ($r$) for: $2, -2, 2, -2, \dots$

What is the $n^{\text{th}}$ term formula for the sequence: $2, 4, 6, 8, \dots$?

Identify the next term in: $64, 32, 16, 8, \dots$

An arithmetic sequence has $u_1 = 7$ and $u_{10} = 43$. Find the sum of these first $10$ terms.

If $u_n = 3n - 5$, calculate the sum of the first $20$ terms of this arithmetic sequence.

The sum to infinity of a geometric sequence is $10$ and the first term is $2$. Find the common ratio $r$.

Find the $10^{th}$ term of the sequence $u_n$ defined by the second differences being constant at $2$, with $u_1=2$ and $u_2=3$.

If $x, 2x+2,$ and $3x+3$ are consecutive terms of a geometric progression, find the common ratio $r$.

The arithmetic mean of two positive numbers is $10$ and their geometric mean is $8$. Find the two numbers.

Simplify $\frac{x+1}{5} \div \frac{x+1}{10}$.

Work out $\frac{p}{4} \times \frac{8}{p}$ and give the simplest form.

Simplify $\frac{10}{n} - \frac{5}{n}$.

Simplify $\frac{9x^2}{3x}$.

Simplify fully: $\frac{x^2-4x+4}{x^2-2x}$

Express $\frac{x+3}{x} - \frac{x}{x+3}$ as a single fraction in its simplest form.

Simplify the expression: $\frac{a^2-b^2}{a^2-2ab+b^2}$

Express the following as a single fraction in its simplest form: $\frac{x}{x-3} - \frac{18}{x^2-9} - 1$

Simplify: $\frac{1}{x^2-3x+2} + \frac{1}{x^2-x}$

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

The diagram shows a mapping for the function $f(x)$. Based on the mapping, find the value of $f(2)$.

The graph of the function $f(x) = x + 2$ is shown. If $g(x) = 3x$, find the value of the composite function $gf(1)$.

Based on the mapping diagram, what is the domain of the function?

Given the function $f(x) = 5 - x$, which point lies on the line shown in the diagram?

Given the functions $f(x) = 2x + 1$ and $g(x) = x^2$, the diagram displays the graph of $g(x)$. Calculate the value of the composite function $fg(3)$.

The functions $f$ and $g$ are defined as $f(x) = x^2$ and $g(x) = x - 3$. The diagram shows the graph of $y = f(x)$. Find the expression for the composite function $fg(x)$.

From the graph of $f(x) = \sin(x)$ (where $x$ is in radians), what is the value of $f(\pi)$?

A water tank is being filled. The volume $V$ (in liters) at height $h$ (in cm) is $V(h) = 0.1h^2$. The height $h$ increases over time $t$ (in minutes) as $h(t) = 5t + 2$. At what time $t$ will the volume be $90$ liters?

Given $f(x) = 3x + 1$ and $g(x) = x^2 - 2$, solve the equation $g(f(x)) = 23$ for positive $x$.

An investor's profit $P$ is $P(s) = 4s - 200$, where $s$ is the number of shares. The number of shares bought depends on the price $x$ by $s(x) = \frac{1000}{x}$. If the price per share is $x = 5$, what is the profit?

1. Introduction to Algebra: practice question 1 for Algebra?

1. Introduction to Algebra: practice question 2 for Algebra?

1. Introduction to Algebra: practice question 3 for Algebra?

1. Introduction to Algebra: practice question 4 for Algebra?

1. Introduction to Algebra: practice question 5 for Algebra?

1. Introduction to Algebra: practice question 6 for Algebra?

1. Introduction to Algebra: practice question 7 for Algebra?

1. Introduction to Algebra: practice question 8 for Algebra?

1. Introduction to Algebra: practice question 9 for Algebra?

1. Introduction to Algebra: practice question 10 for Algebra?

1. Algebraic Indices: practice question 1 for Algebra?

1. Algebraic Indices: practice question 2 for Algebra?

1. Algebraic Indices: practice question 3 for Algebra?

1. Algebraic Indices: practice question 4 for Algebra?

1. Algebraic Indices: practice question 5 for Algebra?

1. Algebraic Indices: practice question 6 for Algebra?

1. Algebraic Indices: practice question 7 for Algebra?