4MA1 Mathematics A: May/June 2023 Paper 2HRHigher Tier Paper 2

P = m²– 4c

(a)Work out the value of P when m = –5 and c = 3

P = [2]

(b)Expand and simplify (x + 5)(x – 7)

[2]

Sandeep wants to buy some packets of pens and some boxes of pencils for his stationery shop.

Each packet of pens contains 9 pens. Each box of pencils contains 12 pencils.

Each packet of pens costs £7.60 Each box of pencils costs £4.80

Sandeep can only buy full packets of pens and full boxes of pencils. He wants to buy exactly the same number of pens as pencils.

Work out the minimum amount Sandeep needs to pay.

£ [4]

Anjali travels on the Eurostar train from Paris to Amsterdam.

The distance the train travels between Paris and Amsterdam is 515 km. The time taken by the train to travel between Paris and Amsterdam is 3 hours 18 minutes.

Work out the average speed of the train. Give your answer in km/h correct to the nearest whole number.

km/h[3]

Here are the first four terms of an arithmetic sequence.

Find an expression, in terms of n, for the nth term of the sequence.

[2]

A field is in the shape of a trapezium.

The field is sold for a price of $49 650

Given that 1 hectare = 10 000 m²

work out the average price of the field per hectare.

$ [4]

In his previous job, Pierre was paid 400 euros in total for working a 5-day week.

In his new job, Pierre is paid 14 euros per hour. In his new job, Pierre works for 7 hours each day for a 5-day week.

(a)Work out the percentage increase in the amount that Pierre is paid for a 5-day week.

%[4]

Marie changes her job.

Her salary decreases by 6% Her new salary is 23 030 euros.

(b)Work out Marie’s salary before she changes her job.

_euros[3]

(a)Simplify (4^–2)⁰

[1]

3^–14 × 3⁸= 3^m

(b)Find the value of m

m = [1]

(a)Solve 9 – 4x > 17

[2]

(b)Write down the three inequalities that represent the shaded region R

[3]

The diagram shows a rectangular sheet of metal ABCD

BD = 50 cm and angle BDC = 32°

Nasser joins side AD to side BC to form a cylinder.

BC is the height of the cylinder. DC is the circumference of the cross section of the cylinder.

Work out the volume, in cm³, of the cylinder. Give your answer correct to 3 significant figures.

_cm³[6]

Gemara works as a taxi driver. Last week, he recorded the following information about the distances he drove.

For the 5 days from Monday to Friday, the mean number of kilometres he drove was 104 For the 7 days from Monday to Sunday, the mean number of kilometres he drove was 127

On Saturday, Gemara drove 132 kilometres.

Work out the number of kilometres he drove on Sunday.

_kilometres

[3]

Express m25 in the form kc where a, b and c are integers to be found.

[2]

Here are six graphs.

Write down the letter of the graph of

(a)y =

[1]

(b)y = x – 3 + 3x²– x³

[1]

(c)y = –

[1]

Feruzi invests 80 000 Kenyan shillings (KES) He invests the money for 3 years at x% compound interest each year.

At the end of 3 years, the total interest he receives is 6151.25 KES

Work out the value of x

x = [3]

Akari played a computer game eleven times. Here are her scores.

(a)Find the interquartile range of her scores.

[3]

Machi played the same computer game eleven times.

The interquartile range for Machi’s scores was 9

(b)Who had the more consistent scores, Akari or Machi? Give a reason for your answer.

[1]

Osvaldo has a biased coin. He spins the coin three times.

The probability that the coin lands on a head three times is 2764

Work out the probability that the coin will land on a tail three times.

[3]

Show that can be written in the form a + a where a is an integer.

Show your working clearly.[3]

Make x the subject of y =³ 6 + 5xx + 4

[4]

A, B, C and D are points on a circle.

ABP and DCP are straight lines.

Work out the length of DC

_cm[3]

30 adults booked to stay in a hotel.

19 adults booked breakfast 15 adults booked dinner

Some adults booked breakfast and dinner.

Meihui chooses at random two of the 30 adults.

Work out the probability that these two adults each booked breakfast and dinner.

[4]

A, B and C are points on a circle.

B

MN is the tangent to the circle at C

AB = CB

Angle BCN = 78°

Find the size of angle ABC

[2]

Work out the coordinates of the points of intersection of

Show clear algebraic working.

( , )

( , )[5]

Here is a cuboid ABCDEFGH

(a)Work out the length of BE Give your answer correct to 3 significant figures.

_cm[2]

Here is a cuboid PQRSTUVW

PR = 42 cm

The size of the angle between PU and the plane PQRS is 30°

M is the midpoint of PR

(b)Work out the size of angle UMR Give your answer correct to 3 significant figures.

[3]

Here are the first three terms of an arithmetic sequence.

The sum of the first n terms of the sequence is –1914

Work out the value of n Show your working clearly.

n = [5]

The surface area of sphere A is nine times the surface area of sphere B The difference between the volume of sphere A and the volume of sphere B is 117π cm³

Find the radius of the smaller sphere. Show your working clearly.

_cm[5]

The straight line with equation y – 2x = 7 is the perpendicular bisector of the line AB where A is the point with coordinates ( j, 7) and B is the point with coordinates (6, k)

Find the coordinates of the midpoint of the line AB Show clear algebraic working.

( , )[6]

Here is a sketch of the curve with equation y = a cos bx° + c where –90  x  450

Find the value of a, the value of b and the value of c

a =

b =

c = [3]