Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

(a(i))[1]

Factorise $4x^3-10xy$ completely.

(a(ii))[1]

Factorise $9a^2-b^2$ completely.

(b)[2]

Solve $\frac{7}{3-2m}=4$ for $m$.

(c(i))[2]

A right-angled triangle has a height of $h\text{ cm}$ and a base that is $7\text{ cm}$ longer than the height. Its hypotenuse is $23\text{ cm}$. Show that $h$ satisfies $h^2+7h-240=0$.

(c(ii))[1]

Write an expression for the area of the triangle in terms of $h$.

(c(iii))[1]

Hence state the triangle’s exact area.

(c(iv))[3]

Solve $h^2+7h-240=0$, and give your answers correct to $1$ decimal place.

(c(v))[1]

Calculate the perimeter of the triangle.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: So the factorised form is $2x(2x^2-5y)$.

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