Algebra

Simplify: $y^2 \times y^2 \times y^2$.

Expand: $4(p + q + r)$.

Factorize: $14 + 7n$.

Simplify: $2a + 3a - a$.

Simplify the algebraic fraction: $\frac{a^2b + ab^2}{ab}$.

Rearrange $P = 2l + 2w$ to make $w$ the subject.

Factorize the trinomial: $x^2 + x - 20$.

Factorize $m^4 - 16n^4$ completely.

Simplify the fraction $\frac{12x^2 + 7x - 10}{4x + 5}$.

Factorize the expression $ax + ay - x - y$ completely.

Calculate $x$ in the equation: $\frac{x}{10} = 6$

Solve the linear equation: $2n + 7 = 17$

Solve for $x$: $x - 4 = 18$

Solve for $k$: $6k = 60$

Find the value of $x$: $\frac{x}{4} + \frac{x}{3} = \frac{7}{6}$

Solve the equation: $4(x + 3) - 2x = x + 18$

Find $x$: $\frac{3}{5}x + 2 = 11$

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

Solve the equation: $4x - [2x - (x - 3)] = 15$

Solve for $y$: $0.4(2y - 3) + 0.5y = 2.5(y - 2)$

Solve the inequality: $2x + 3 < 13$

Find the solution to $y - 1.2 \ge 0.8$.

Solve the inequality: $10x \le 50$

Solve for $x$: $\frac{x}{3} + 4 > 5$

Solve the inequality: $5x - 7 > 8x + 2$.

Find the solution to $-1 \leq 2x + 3 < 11$.

Solve for $x$: $3x + 5 \leq 2(x + 4)$.

Solve the compound inequality: $2x + 1 < 3x - 5 \leq 2x + 12$.

Solve for $x$: $2(3x - 5) \geq 7x - (2x + 1)$.

How many integers $x$ satisfy the inequality $-3 < \frac{2x - 5}{3} \leq 1$?

Find the 9th term of the sequence with $n$-th term formula $n + 9$.

What is the next term in the sequence: $2, 5, 8, 11, \dots$?

What is the common difference in the sequence $3, 1, -1, -3, \dots$?

Calculate the 6th term of the sequence $4n$.

In the sequence where $u_n = 4n + 6$, which term is equal to $30$?

Which expression represents the $n$-th term of the sequence $21, 18, 15, 12, \dots$?

Determine the 10th term ($u_{10}$) for the sequence $u_n = n(n - 1)$.

For the sequence $u_n = \frac{n}{n+1} - \frac{n-1}{n}$, find the 10th term.

Identify the $n$-th term for the sequence: $2, 6, 12, 20, 30, \dots$

A sequence follows the rule $u_n = n^3 - n^2$. What is the difference between the 4th and 3rd terms?

The diagram shows a straight line. By looking at the rise and run between the marked points, determine the gradient ($m$) of the line.

What is the gradient of the horizontal line shown in the diagram?

In the equation $y = mx + c$, which letter represents the gradient of the line?

Which of the following is the $y$-intercept of the line shown in the graph?

Find the equation of the straight line shown in the diagram, which passes through the origin $(0, 0)$ and the point $(4, 2)$.

A line has a gradient of $-\frac{1}{2}$ and passes through the point $(0, 5)$. What is the $x$-coordinate where this line crosses the $x$-axis?

The diagram shows the graph of the line $y = mx + 4$. Given that the line passes through the point $(3, 1)$, calculate the value of the gradient $m$.

A rental car service charges a base fee plus a rate per kilometer driven. The total cost $y$ for driving $x$ kilometers is given by the line shown. If the cost for 100 km is $80 and the cost for 250 km is$170, what is the base fee (the y-intercept)?

An architect is designing a roof with a constant slope. In a coordinate system where the base of the roof starts at $(2, 5)$, the roofline follows the equation $y = mx + c$. If the roof reaches a height of $y = 11$ when $x = 14$, determine the equation of the roofline.

The conversion between temperature in degrees Celsius ($C$) and degrees Fahrenheit ($F$) is a linear relationship. The graph of this relationship passes through $(0, 32)$, the freezing point of water, and $(100, 212)$, the boiling point of water. What is the gradient $m$ and the y-intercept $c$ for the equation $F = mC + c$?

Solve the system: (y = x - 3) and (x + y = 7).

If (x + y = 22) and (x - y = 2), what is the value of (x)?

Solve: (x + y = 1) and (x - y = 1).

Solve: (4x + y = 10) and (y = 2).

Solve the system: $x + y = 15$ $2x - y = 0$

Find $x$ and $y$: $4x - y = 5$ $2x + y = 7$

Solve: $2x + y = 8$ $x + y = 5$

If $x + y = 10$ and $x - y = 4$, find the value of $x^2 - y^2$.

Solve the equations: $0.1x + 0.2y = 0.8$ and $0.4x - 0.3y = 1$.

Find $x$ and $y$ if $\frac{x+1}{y+1} = \frac{2}{3}$ and $\frac{x-1}{y-1} = \frac{1}{2}$.