4MB1/01R — June 2018 (Edexcel IGCSE Maths): Past Paper

Without using a calculator and showing all your working, calculate 7 3 2 ×1 8 5 Give your answer as a mixed number in its simplest form.

Each interior angle of a regular polygon is 168° Calculate the number of sides of the polygon.

The number of people living in Delhi is 1.7 × 10⁷ The land area of Delhi is 1.5 × 10³ square kilometres. Calculate the average number of people per square kilometre living in Delhi. Give your answer in standard form to 2 significant figures.

Given that y = 3 − x⁵ x dy find dx dy = ……………dx

Given that y = 3 − x⁵ x dy find dx dy = dx

Without using your calculator, and showing all your working, express 12/(3 − √5) in the form a + b√5 where a and b are integers.

In the diagram, ABC is parallel to DEF. BEG is a straight line and ΔEFG is isosceles with EF = EG and ∠EGF = 63° Find the size, in degrees, of ∠ABE. ° ∠ABE =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C, D, F, E, G · Figure values: 63°.

Solve the simultaneous equations 4x − y = 4 2 x + y = −10 Show clear algebraic working. x = y =

When a biased coin is thrown once, the probability that it lands Heads is 0.6 The coin is thrown 4 times. Find the probability that the coin lands Heads exactly 3 times.

Solve = 2x − 3 Show clear algebraic working. x = ……………Solve = 2x − 3 Show clear algebraic working. x =

X = 2a + b X = 19.4 to 1 decimal place. a = 2.4 to 1 decimal place. Calculate the upper bound for the value of b. Show your working clearly.

Make x the subject of = c − x³ 3 x = ……………Make x the subject of = c − x³ 3 x =

Given that 6 × $5^{3k+4}$ = 750 find the exact value of k. k = ……………Given that 6 × $5^{3k+4}$ = 750 find the exact value of k. k =

The diagram shows triangle ACD and triangle ABE. The point B is on AC and the point E is on AD such that BE is parallel to CD. CD = 9.6 cm Area of triangle ABE = 27 cm² Area of trapezium BCDE = 21 cm² Calculate the length, in cm, of BE cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, E, C, D · Figure values: 9.6.

y O 1 2 3 4 5 6 7 x

y=2

x + y = 5

y = 2x + 1

On the grid, show by shading, the region defined by the inequalities y . 2 and x + y - 5 and y - 2x + 1 Label the region R.

Barry and Carlos share $120 in the ratio 3 : 2 Barry gives of his share to Mary. Carlos gives 35% of his share to Mary. Express the total amount that Barry and Carlos give to Mary as a fraction of the $120 Give your answer in its simplest form.

Simplify 2w4y3 q 3wy5

Simplify (27a c ) 6 3 3

and B are points on the circumference of a circle, centre O. CBD is the tangent to the circle at B. CAO is a straight line. ∠ABC = 38° Giving your reasons, find the size, in degrees, of ∠ACB. ° ∠ACB =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: O, D, A, B, C, A · Figure values: 38°.

OA = and OB = −2⎠ ⎝ 6⎠ →

Find AB as a column vector. ⎛ ⎞ → AB = →

Calculate the modulus of AB

Write (3 x + 2) ÷ − as a single fraction in its simplest form. ⎝ 5 ⎠ x+3 Show clear algebraic working.

The diagram shows a trapezium OACB in which → → → OA = a, AC = 3b, OB = 5b The point P lies on OC such that OP : PC = 5 : 1 D is the point such that OBD is a straight line and APD is a straight line. Prove that OB : OD = 1 : 3

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

The diagram shows a right prism of length 9 cm. A cross section of the prism is a trapezium in which the parallel sides are of length 18 cm and 10 cm and the distance between these parallel sides is 15 cm. Calculate the total surface area, in cm², of the prism cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Figure values: 18, 10, 9, 15.

T varies inversely as the square of y. T = 0.32 when y = 5

Find a formula for T in terms of y.

Find the positive value of y when T = 200

Write x² + 10x – 7 in the form (x + p)² + q

Hence solve the equation x² + 10x – 7 = 0 Give your answer in the form a ± b where a and b are integers. Show your working clearly.

(x + 2) is a factor of x³ – 3x2 + ax + 12 where a is a constant.

Show that a = – 4

Factorise completely x³ – 3x2 – 4x + 12

A box of toy bricks contains only red bricks, blue bricks, green bricks, yellow bricks and orange bricks. A brick is taken at random from the box. The table gives information about the probabilities that the brick is red or is blue or is green or is yellow or is orange.

Calculate the value of x. x = There are 39 blue bricks in the box.

Find the number of yellow bricks in the box. Alvaro draws a pie chart to show information about the number of bricks of each colour.

Calculate the size of the angle, in degrees, of the sector for red bricks.

…………… °

A = $\begin{pmatrix} 4 & 3 \\ -2 & 1 \end{pmatrix}$ B = $\begin{pmatrix} 2 & -3 \\ 1 & 4 \end{pmatrix}$ C = $\begin{pmatrix} 5 & 2 \end{pmatrix}$ Find

3A + 2B

AB

CB

In the diagram, ABDFE is a circle, centre O and radius 6 cm. ABC and EDC are straight lines. The arc EFD is of length π cm. Calculate the length, in cm to 3 significant figures, of DC cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, O, C, D, E, F · Figure values: 7, 9, 6.