Question Bank

Achieved

Expand and simplify the expression: $(x - 2)(x + 3)(x + 1)$.

Achieved

The area of a rectangle is $2x^2 + 2x - 12$. If its width is $x+3$, find an expression for its length.

Achieved

Solve the following linear equation for $x$:

$3(x-2) = \frac{1}{2}x + 4$
Achieved

Factorise the following quadratic expression:

$3x^2 + 5x - 2$
Achieved

Factorise the following quadratic expression:

$4x^2 + 4x - 15$
Achieved

Expand and fully simplify the following expression:

$(2x-3)(x+4) - 2x(x+1)$
Achieved

Expand and fully simplify the following expression:

$3(y-2)(y+1) - (y-3)^2$
Achieved

Expand and fully simplify the following expression in terms of $a$ and $b$:

$(a+2b)(a-2b) + (a+b)^2$
Merit

The equation $my^2 + 2n^2 = 5p^2 - 3qy^2$ relates five variables. Give the equation for $y$ in terms of $m, n, p,$ and $q$.

Merit

If $a(x-b) = c(x+d)$, give the equation for $x$ in terms of $a, b, c,$ and $d$.

Merit

If $m - k = \frac{\sqrt{a(n^2+b)}}{c}$, give the equation for $n$ in terms of $a, b, c, k,$ and $m$.

Merit

The surface area of a cone is given by $A = \pi r(r + \sqrt{h^2+r^2})$. Give the equation for the height $h$, in terms of $A, r,$ and $\pi$.

Merit

If $k = 5\sqrt[3]{\frac{x^2+a}{b}}$, give the equation for $x$ in terms of $a, b,$ and $k$.

Merit

What same number must be added to the top (numerator) and bottom (denominator) of the fraction $\frac{81}{148}$ to make it equal to $\frac{2}{3}$?

You must form an equation to represent this situation and then solve your equation.