Edexcel IGCSE Math B 3 algebra

Use this Algebra hub to move from expanding and factorising into equations, inequalities, simultaneous equations and algebraic graph work.

Covered syllabus points

3.A Basic algebra processes 3.B Formulae 3.C Factorisation 3.D Factor theorem 3.E Algebraic division 3.F Algebraic fractions 3.G Equations 3.H Linear simultaneous equations 3.I Linear and quadratic simultaneous equations 3.J Linear inequalities 3.K Quadratic inequalities 3.L Sequences

[Maximum number: 5]

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

(a)

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

[ 2 ]

(b)

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

[ 2 ]

(c)

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

[ 1 ]

From part (b):
$x^{2}+8x-20=(x+10)(x-2)$
For the rectangle area to be greater than $20\text{ m}^{2}$ :
$x^{2}+8x>20$
so
$x^{2}+8x-20>0$
Final answer:
x>2

Marking notes:
Follow through their part (b) where the factorised form has only one positive critical value and only one region is given. Condone $x\ge2$ .

[Maximum number: 2]

Figure for Question 3 Algebra question 2 — Edexcel IGCSE Math B

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 $V=4x^3-60x^2+200x$ .

Table for Question 3 Algebra question 2 — Edexcel IGCSE Math B

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Covered syllabus points

3 Algebra question 1

Question (a)

Question (b)

Question (c)

3 Algebra question 2