Edexcel IGCSE Math B 3 Algebra Questions

The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.

Diagrams NOT accurately drawn.

Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4.
The volume of the box is $V\,\mathrm{cm}^3$.

Complete the following table of values for $V=4x^3-60x^2+200x$.

$$\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.$$
The determinant of matrix $\mathbf A$ is equal to the determinant of matrix $\mathbf B$.

The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.

Find an expression in terms of x for the perimeter, in metres, of the rectangle.
Simplify your answer.

The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.

Factorise $x^2+8x-20$.

$$\mathbf A=\begin{pmatrix}2k^2&k-9\\-3k&k+1\end{pmatrix}, \qquad \mathbf B=\begin{pmatrix}1&-5\\3&k\end{pmatrix}.$$
The determinant of matrix $\mathbf A$ is equal to the determinant of matrix $\mathbf B$.

Given that $f(k)=2k^3+5k^2-28k-15$, use the factor theorem to show that (k+5) is a factor of f(k).

Given that (x-3) is a factor of $5 x^{3}+2 x^{2}+k x+36$ where k is a constant,

Given that, for all values of x,
$$5x^3+2x^2-63x+36=(x-3)(ax^2+bx+c),$$
where a, b and c are constants,
find the value of a, the value of b and the value of c.

Simplify fully
$$\frac{20x^4+26x^3-6x^2}{5x^2-x}.$$

Here are the functions f, g and h.
$$\begin{aligned}f:x&\mapsto 2x-5,\quad x>1,\\g:x&\mapsto 7-\frac{8x}{2x+1},\\h:x&\mapsto 2x^2+4x-5,\quad x>-1.\end{aligned}$$

Information about the function f is shown in Figure 3.
Given that f is the mapping $\mathrm{f}: x \mapsto a x^{3}+b$ where a and b are constants,

Hence find the value of a and the value of b.

Figure 2 shows two shapes A and B.
All the lengths are in metres.

The corners of shape A are all right angles.
The area of shape A is $400 \mathrm{~m}^{2}$
Shape B is triangle PQR.
The perimeter of shape A is equal to the perimeter of shape B.

Find the value of x and the value of y.
Show clear algebraic working.

The nth term of a sequence is $u_{n}$ where $u_{n}=25-2 n$

Find the greatest value of n for which $u_n > n$.

The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.

Hence write down the range of values of x for which the area of the rectangle is greater than $20\text{ m}^2$.

The nth term of a sequence is $u_{n}$ where $u_{n}=25-2 n$

Find $u_{1}$