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Edexcel IGCSE Math B Number and Algebra Question Bank

Build confidence across Number, Sets, Algebra, Functions and Matrices by practising calculations, symbolic methods, graphs and transformations.

Syllabus
First assessment 2018
Course
Math B 4MB1

Covered syllabus points

1 Number2 Sets3 Algebra4 Functions5 Matrices

Number and algebra question 1

[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.

Question (a)

(a)

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

[ 2 ]

Question (b)

(b)

Factorise x2+8x−20x^2+8x-20.

[ 2 ]

Question (c)

(c)

Hence write down the range of values of x for which the area of the rectangle is greater than 20 m220\text{ m}^2.

[ 1 ]

Number and algebra question 2

[Maximum number: 1]
Figure for Question Number and algebra question 2 — Edexcel IGCSE Math B

Ahmed and Hani play a game with 20 numbered balls.
The 20 balls are numbered from 1 to 20.
The balls are put in a bag.
Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag.
If the number is a multiple of 5, Ahmed wins.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 3.
If Hani does not win, Ahmed takes a ball, replaces it, and wins if the number is a multiple of 6.
If Ahmed does not win, Hani takes a ball, replaces it, and wins if the number is a multiple of 4.
If Hani does not win, the game stops and the result is a draw.

Write down all the multiples of 3 lying between 1 and 20.

Number and algebra question 3

[Maximum number: 4]

15E={1,2,3,4,5,6,7,8,9}15 \mathscr{E}=\{1,2,3,4,5,6,7,8,9\}A={2,4,6,8}A=\{2,4,6,8\}B={1,3,5,7,9}B=\{1,3,5,7,9\}C={2,3,5,7}C=\{2,3,5,7\}

Question (a)

(a)

List the elements of the set

[ 3 ]

Question (i)

(i)

B∪CB \cup C

[ 1 ]

Question (ii)

(ii)

A′∩CA^{\prime} \cap C

[ 1 ]

Question (iii)

(iii)

(A∩B)′(A \cap B)^{\prime}
(3)

[ 1 ]

Question (b)

(b)

Explain why A∩B∩C=∅A \cap B \cap C=\varnothing

[ 1 ]

Number and algebra question 4

[Maximum number: 13]
Figure for Question Number and algebra question 4 — Edexcel IGCSE Math B
Figure for Question Number and algebra question 4 — 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 cm3V\,\mathrm{cm}^3.

Question (a)

(a)

Find, to 3 significant figures, the value of x such that dVdx=0\frac{dV}{dx}=0.

Solutions of ax2+bx+c=0 are x=−b±b2−4ac2a.\text{Solutions of } ax^2+bx+c=0 \text{ are } x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.

[ 4 ]

Question (b)

(b)

Complete the following table of values for V=4x3−60x2+200xV=4x^3-60x^2+200x.

Table for Question (b) — Edexcel IGCSE Math B
[ 2 ]

Question (c)

(c)
Figure for Question (c) — Edexcel IGCSE Math B

On the grid opposite, plot the points from your completed table and, using your answer to part (b), join them to form a smooth curve.

[ 2 ]

Question (d)

(d)

By drawing on the grid a tangent to the curve, find an estimate of the gradient of the curve at the point where x=1.5.

[ 2 ]

Question (e)

(e)

Starting with a square of side 15 cm and removing a square with sides of length x cm from each corner, a second box without a lid is formed by folding as in part (a).
The volume of this box is B cm3B\,\mathrm{cm}^3, where
B=4x3−60x2+225x.B=4x^3-60x^2+225x.
Given that B=200, find, by drawing a suitable straight line on the grid, estimates, to one decimal place, of the possible values of x.

[ 3 ]
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