4MB1/01R — June 2023 (Edexcel IGCSE Maths): Past Paper

Find the Lowest Common Multiple (LCM) of 12, 14 and 15 Show your working clearly.

Without using your calculator and showing each stage of your working, calculate 1 7 1 × 5 12 Give your answer as a fraction in its simplest form.

Simplify 5x2 + 3x2

Simplify 2y2 × 3y3

The shape above is made from four squares. Two of the squares are shaded.

Draw, on the shape above, all the lines of symmetry of the shape. The shape above is made from four identical equilateral triangles. Three of the triangles are half shaded.

Write down the order of rotational symmetry of the shape.

Here are the first 5 terms of a sequence 3 10 17 24 31

Write down the next 2 terms of the sequence , The 15th term of the sequence is 101

Find the 12th term of the sequence.

Factorise x² – 5x – 14

Here are ten numbers 3 5 8 5 2 7 9 11 5 10

Write down the mode.

Find the median.

A regular polygon has 24 sides. Calculate the size, in degrees, of each interior angle of the regular polygon.

…………… °

Make g the subject of T = g

Given that y = 5x4 + x² (3x + 1) dy find dx dy = ……………dx

Given that y = 5x4 + x² (3x + 1) dy find dx dy = dx

ABC is an arc of a circle centre O Angle AOC is 120° Sector OABC has an area of 48π cm² Find, in terms of π, the length of the perimeter of OABC cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C, O · Figure values: 120°.

Solve 6 4 Show clear algebraic working. x = ……………Solve 6 4 Show clear algebraic working. x =

For the two non-zero, non-parallel vectors a and b 5 (3a – b) – p (a + 2b) = qb where p and q are scalars. Find the value of p and the value of q p = q =

A factory makes bottles. Of all the bottles the factory made on Monday 7% are made by machine A 12% are made by machine B Let y be the total number of bottles that the factory made on Monday.

Write down an expression, in terms of y, for the number of bottles that machine A made on Monday. On Monday machine B made 60 more bottles than machine A

Find the value of y y =

Solve the simultaneous equations 20x + 7y = 4 2x – 2y = –5 Show clear algebraic working. x = y =

16 208 students travelled to school by bus, which is 10.4% of the students in the school. 510 students walk to school. The remaining students travel to school by car. Calculate the percentage of students who travel to school by car

…………… %

A model of a train is made to a scale of 1 : 48 The engine of the train has a length of 16.1 m

Calculate, in cm to 3 significant figures, the length of the engine of the model cm The volume of a carriage on the model is 995

…………… cm³

Calculate, in m³ to 3 significant figures, the volume of this carriage on the train

…………… m³

The diagram shows triangle ABC A B C The point P is inside the triangle ABC such that P is the same distance from AB and BC P is 10 cm from the point C Using ruler and compasses only and showing all your construction lines, find and label the point P

In a class of 30 students 15 have a black pen (B) 16 have a pencil (P) 3 have no black pen and no pencil x have a black pen and a pencil

Use the information above to complete the Venn diagram, giving answers in terms of x where necessary. E B P x

Find the value of x x =

One of these 30 students is chosen at random. Write down the probability that this student has a black pen but does not have a pencil.

cm The diagram shows a solid shape made by fixing a solid right circular cone of diameter 20 cm to the circular face of a solid hemisphere of diameter 20 cm. The centre of the base of the cone coincides with the centre of the circular face of the hemisphere. The overall height of the shape is h cm. Given that for this shape volume of cone : volume of hemisphere = 3 : 4 find the value of h h =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

E F Diagram NOT accurately drawn 3 cm C D G H 4 cm A 12 cm B The diagram shows the cuboid ABCDEFGH AB = 12 cm BG = 4 cm FG = 3 cm

Show that AF = 13 cm

Find, in degrees to one decimal place, the size of angle GAF ° ∠GAF =

Given that (x + k) is a factor of x³ + 4x2 –20x + k where k is a non-zero constant, find the possible values of k k =

B Diagram NOT accurately drawn 19.5 cm O N E A C 8 cm D A, B, C and D are points on a circle with centre O and radius 19.5 cm AEC and BNED are chords of the circle. ∠BEC = ∠BNO = 90° BD = 36 cm ED = 8 cm

Show that ON = 7.5 cm

Calculate the length, in cm to 3 significant figures, of AC AC = cm

The table shows the number of children in each of the families from a town.

$k$ is an unknown integer. The mean number of children in a family = 2.0 to 2 significant figures. Find the range of possible values of $k$

3 1 5 1 2 1 A B C 5 2 5 4 5 3

Show that C is the inverse of A AB = D

Find D D

Show that BA = D

Using part (a) and part (b), show that BC = CB

P Q Diagram NOT accurately drawn T R S P, Q, S and R are points on a circle. T is the point where PS intersects QR PQ is parallel to RS

Prove that PT = QT Give a reason for each stage of your working. The area of triangle PQT = 1 cm² and the area of triangle RST = 4

…………… cm²

Find the area of quadrilateral PQSR

…………… cm²