4MA1 Mathematics A: May/June 2024 Paper 2HHigher Tier Paper 2

Here are eight numbers written in order of size

where h, j and k are integers.

The median of the eight numbers is 10

The mode of the eight numbers is 18

The range of the eight numbers is 13

Work out the value of h, the value of j and the value of k

h =

j =

k = [3]

(a)On the grid, draw the straight line with equation

(i)y = 2

(ii)x = 6

(iii)y = x + 1

Label each line with its equation.

[3]

(b)Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R[1]

A plane takes 9 hours 36 minutes to fly from New Delhi to Perth.

The plane flies at an average speed of 820 km/h.

Work out the total distance the plane flies.

_km[3]

Show that 2 47 × 3 19 = 8[3]

The diagram shows triangle ABC

Work out the value of x Give your answer correct to one decimal place.

x = [3]

Change a speed of w metres per second to a speed in kilometres per hour. Give your answer in terms of w in its simplest form.

_{kilometresperhour}[3]

The diagram shows a 6-sided shape ABCDEF

The perpendicular height of the shape is h cm CD is parallel to AF

The area of the shape is 390 cm²

Work out the value of h

h = [4]

Ishir plants 600 bulbs in a garden. He plants tulip bulbs, crocus bulbs and daffodil bulbs so that

number of tulip bulbs : number of crocus bulbs : number of daffodil bulbs = 9 : 4 : 2

45% of the tulip bulbs are for yellow flowers.

58 of the crocus bulbs are for yellow flowers.

All of the daffodil bulbs are for yellow flowers.

Work out the number of bulbs that are for yellow flowers.

[5]

Giovanni invests 4500 koruna in a savings account for 4 years. He gets 2.4% per year compound interest.

Work out how much money Giovanni will have in the savings account at the end of 4 years. Give your answer correct to the nearest koruna.

_koruna[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

(i)Factorise x²+ 9x – 22

[2]

(ii)Hence, solve x²+ 9x – 22 = 0

[1]

Ali uses a fitness tracker to count the number of steps he walks each day for 7 days.

For the first 4 days, his mean number of steps is 11 800 For the next 3 days, his mean number of steps is 13 207

Work out his mean number of steps for the 7 days.

[3]

The table gives information about the distances, in km, that 70 teachers travel to school.

(a)Complete the cumulative frequency table.

[1]

(b)On the grid opposite, draw a cumulative frequency graph for your table.[2]

70

60

50

40

(c)Use your graph to find an estimate for the interquartile range of the distances.

_km[2]

(d)Use your graph to find an estimate for the number of teachers who travel more than 46 km.

[2]

(a)Show that 3y(2y + 5)(y + 7) can be written in the form ay³+ by²+ cy where a, b and c are integers.[3]

(b)Solve 2x + 35 + 6x − 54 = 163100

Show clear algebraic working.

x = [4]

(a)Make g the subject of e = 7g + 511 + 2g

[4]

(b)Solve the inequality 3y²+ 4y – 32 > 0 Show your working clearly.

[3]

60 art students were asked if they would like to attend workshops for knitting (K), for photography (P) or for embroidery (E)

Of these students

9 chose knitting, photography and embroidery 17 chose knitting and photography 16 chose photography and embroidery 20 chose knitting and embroidery 28 chose photography 39 chose embroidery 2 chose none of the workshops

(a)Using this information, complete the Venn diagram to show the numbers of students in each subset.

E

[3]

One of the students is chosen at random.

Given that this student chose photography,

(b)find the probability that this student also chose knitting.

[2]

(c)Find n(P ∩ K¢)

[1]

(d)Find n([P ∪ E] ∩ K)

[1]

Q is directly proportional to the square root of d

Q = 4.5 when d = 324

Find a formula for Q in terms of d

[3]

The straight line P has equation 5y + 2x = 7

Find the gradient of a straight line that is perpendicular to P

c[2]

G =

c = 8 correct to the nearest whole number f = 6.62 correct to 2 decimal places h = 1.2 correct to 1 decimal place

Work out the lower bound for the value of G Give your answer correct to 3 decimal places. Show your working clearly.

[3]

Given that k = x – y and x = 14 y

5k a  by²

x + 2 c  dy

[3]

The diagram shows a square ABCD and a circle.

The sides of the square are tangents to the circle.

The total area of the shaded regions is 80 cm²

Work out the length of AC Give your answer correct to 3 significant figures.

_cm[5]

The straight line L has equation x + y = 5

The curve C has equation 2x²+ 3y²= 210

Find the coordinates of the points where L and C intersect. Show clear algebraic working.

( , ) ( , )

[5]

Simplify_4x9

Give your answer in the form 5^w where w is an expression in terms of x Show each stage of your working clearly.

[3]

The diagram shows a quadrilateral OACB in which

(a)Find AC in terms of a and b Give your answer in its simplest form.

AC = [2]

The point P lies on AC such that AP : PC = 3 : 2

The point Q is such that OPQ and BCQ are straight lines.

(b)Using a vector method, find OQ in terms of a and b Give your answer in its simplest form. Show your working clearly.

OQ = [4]

The diagram shows a sketch of the graph of y = 2sin(x + 60)°

(i)Find the coordinates of the point A

( , )[1]

(ii)Find the coordinates of the point B

( , )[1]