4MA1 Mathematics A: May/June 2024 Paper 1HRHigher Tier Paper 1

Here are six cards.

Five of the cards have a number written on them.

Work out the number that should be written on the last card so that the mean of the six numbers will be 11

[3]

Here is a biased spinner.

The table gives information about the probability that, when the spinner is spun once, it will land on each number.

Alexis is going to spin the spinner 400 times.

Work out an estimate for the number of times the spinner will land on an odd number.

[4]

Norberto sells white loaves of bread and brown loaves of bread.

He sells a total of 200 loaves such that

the number of white loaves sold : the number of brown loaves sold = 3 : 2

Norberto sells the white loaves for £1.50 each. He sells the brown loaves for £1.75 each.

40% of the price of a white loaf is profit. 60% of the price of a brown loaf is profit.

Work out Norberto’s total profit when he sells all 200 loaves.

£ [5]

Show that 2 13  5 14  49[3]

Slavomir invests 5200 euros in a savings account for 4 years. He gets 2.5% per year compound interest.

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

_euros[3]

The diagram shows a solid wooden cylinder.

The cylinder has radius 8 cm and height h cm. The volume of the cylinder is 1208 cm³

(a)Work out the value of h Give your answer correct to the nearest whole number.

h = [2]

The density of the wood is 1.25 g/cm³

(b)Work out the mass of the cylinder. Give your answer in kilograms.

_kilograms[2]

(a)Simplify g⁹ ÷ g²

[1]

(b)Expand 5k² (k³ + 4)

[2]

(c)(i)Factorise x² − 2x − 63

[2]

(ii)Hence, solve x² − 2x − 63 = 0

[1]

(d)Solve the inequality 7  2 y  3y  12

[3]

The diagram shows a trapezium, ABCD

DAB and ADC are right angles.

AD = 15 cm DC = 14 cm

The area of the trapezium is 360 cm²

Work out the perimeter of the trapezium.

cm[6]

Line L is drawn on the grid.

Find an equation for L Give your answer in the form y = mx + c

[3]

Here are the numbers of goals scored by a hockey team in its 11 games this season.

Work out the interquartile range of the numbers of goals.

[2]

A  2⁵  5  7² B  2³  5³  7⁴

(a)Write down the highest common factor (HCF) of 5A and 2B Give your answer as a product of prime factors.

[2]

A  2⁵  5  7² B  2³  5³  7⁴

(b)Work out the value of  AB² Give your answer as a product of prime factors.

[2]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [4]

A, B, C and D are points on a circle, centre O

Angle BCD = 128°

Work out the size of angle OBD Give a reason for each stage of your working.

angle OBD = °[5]

(a)Expand and simplify

[3]

(b)Simplify fully  a b a b

[3]

The diagram shows isosceles triangle EFG

Angle EFG = 130° The area of triangle EFG is 74 cm²

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

_cm[3]

The table gives information about the heights, in metres, of the trees in a park.

10 < h 20

20 < h 35

On the grid, draw a histogram for this information.

[3]

(a)⁴ k¹² = k ⁿ  

Find the value of n

n = [1]

(b)Express 72 − in the form c + d where c and d are integers.

Show your working clearly.

[3]

The diagram shows two similar vases, A and B

The height of vase A is 30 cm The height of vase B is 12 cm

Given that

surface area of vase A ‒ surface area of vase B = 178.5 cm²

find the surface area of vase A

_cm²[4]

A curve C has equation y  x³  8x² 12x  5

Curve C has exactly two stationary points, one at point A and one at point B such that

Find the coordinates of point A Show clear algebraic working.

( , )[5]

(a)Express 2x² 11x  9 in the form a(x − b)² − c where a, b and c are numbers to be found.

[3]

The curve C has equation y  2(x  3)²  11(x  3)  9

The point P is the minimum point on C

(b)Find the coordinates of P

( , )[2]

There are 25 counters in a bag such that

6 counters are blue x counters are orange, where x > 9 the rest of the counters are pink

Maalam takes at random two of the counters from the bag.

The probability that Maalam takes one orange counter and one pink counter is 2275

Calculate the probability that Maalam takes 2 pink counters from the bag. Show clear algebraic working.

[5]

The diagram shows a cuboid ABCDEFGH with horizontal base ADEH

M is the midpoint of the base ADEH and P is the midpoint of the edge CF

Work out the size of angle BMP Give your answer correct to one decimal place.

[6]

Here are the first three terms of an arithmetic sequence.

Find, as an integer, the sum of the first 40 terms of the sequence. Show clear algebraic working.

[4]