4MB1/02R — June 2019 (Edexcel IGCSE Maths): Past Paper

Gis the universal set and A, B and C are three sets where &={multiples A {positiveofintegers 5} less than 13} B= {even numbers} C = {factors of 8} The Venn diagram below can be used to show these sets.

Complete the Venn diagram for the sets 2 A, B and C. é B AC List the elements of the sets

BANC

AUB

(AUBUCY Find

(BUC)

Find

n(B′ ∩ C′)

Solve the inequality 6x + 10 > 2x + 2

Represent your solution on the number line on the next page.

Solve the inequality (4x + 3)(2x — 1) < (6x + 5)(x — 2)

Represent your solution on the same number line.

Write down the set of values for which

both $6x + 10 \geq slant 2x + 2$ and $(4x + 3)(2x - 1) < (6x + 5)(x - 2)$

counters 7 blue whitecounters counters. Priya takes at random 2 counters from the bag.

Complete the probability tree diagram. First counter Second counter orange orange blue 3 fe) white orange blue blue white orange white blue white

Calculate the probability that Priya takes 2 white counters.

Calculate the probability that the counters Priya takes are not of the same colour.

The total amount of money that was spent last March by Marco’s family was $4200 The table below gives information about the amount Marco’s family spent on each of four items last March.

Calculate the percentage of the total amount that was spent on healthcare. The amount spent on travel was divided between Marco’s car, his wife’s car and other transport in the ratios $4 : 3 : 2$

Calculate the amount, in $, that was spent on Marco’s car. The amount last February. that was spent on food last March was 12% more than was spent on food

Calculate the amount, in $, that was spent on food last February. The amount of money of was that money not spent spent on on entertainment last March healthcare, insurance, was food 12.5% and of the total amount travel.

Calculate the amount, in $, that was spent on entertainment. Marco draws a pie chart for the amounts his family spent on all the items last March.

Calculate the size of the angle, in degrees, for insurance. The angle in the pie chart for housing is 114°

The angle in the pie chart for housing is 114°

Calculate the amount, in $, that was spent on housing.

Triangles 4 and B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B. Triangle A is reflected in the y-axis to give triangle C.

On the grid, draw and label triangle C. Triangle D is the image of triangle C under the transformation with matrix M where M(2 0 2«0

On the grid, draw and label triangle D. Triangle D is the image of triangle A under the transformation with matrix N.

Triangle $D$ is the image of triangle $A$ under the transformation with matrix $\mathbf{N}$.

Find the matrix $\mathbf{N}$.

Figure 1 shows a right pentagonal prism, with a horizontal square base $PQRS$ of side 12 cm.

YP = WQ = 5 cm ∠WXY = 140° ∠YPQ = ∠WQP = 90° M is the midpoint of PQ so that XM is an axis of symmetry of the pentagon.

(a) Calculate the size, in degrees to one decimal place, of ∠VMR.

(b) Calculate the length, in cm to one decimal place, of PU.

The equation of a curve is $y = 5 - \frac{x}{2} - x^2$

Complete the table of values for $y = 5 - \frac{x}{2} - x^2$

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

Using x your curve, find an estimate of the maximum value, to one decimal place, of y=5- a x?

xUse your curve to find the range of values of x, to one decimal place, for which 5 - 5 -x?>3

By drawing a suitable straight line on the grid, find estimates, to one decimal place, for the solutions of the equation $3 - x - x^2 = 0$

The functions f and g are defined as fixr3x-5 gixre 2x —3

State the value of x that must be excluded from any domain of g.

Find gf(4) The function h is defined as h:ixre x where x # 3 x_

Solve fh(x) = 7

Express the inverse function h™! in the form ht! : x +>...

Solve the equation $g(x) + h(x) = 1$

Show your working clearly.

Give your solutions in the form $a \pm \sqrt{b}$ where $a$ and $b$ are integers.

Figure 2 shows a solid right square-based pyramid with height 20 cm. The volume of the pyramid is 960 cm³ The pyramid is standing with its square base on a horizontal table.

The pyramid is divided into a smaller right square-based pyramid of height 10 cm and a frustum of the pyramid, as shown in Figure 3, by a horizontal cut.

Calculate the volume, in cm³, of the smaller pyramid.

Calculate the total surface area, in cm² to 3 significant figures, of the frustum of the pyramid.

A particle, P, is moving along a straight line through the fixed point O. The displacement, s metres, of P from O at time t seconds is given by

s = t³ − 7t² − 5t + 121 (t ⩾ 0)

Find the displacement, in metres, of P from O when P is instantaneously at rest.

Figure 4 shows triangle OAB in which $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$

P is the point on AB such that AP : PB = 2 : 1 Q is the point on OP such that OQ : QP = 1 : 3 R is the point on OB such that RQA is a straight line.

Calculate, in its simplest form, the ratio OR : RB