4MA1 Mathematics A: Oct/Nov 2025 Paper 2HHigher Tier Paper 2

The point P has coordinates (3, 4) The point Q has coordinates (9, 16)

M is the midpoint of the line PQ

Find the coordinates of M

( , )[2]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

A box contains only

and some yellow bricks

720 of the bricks are yellow bricks.

Each brick weighs 35 grams.

Work out the total weight of the yellow bricks.

_grams[4]

Here are three similar quadrilaterals.

Work out the length of JK

_cm[3]

Otis sells ice creams.

On Friday, Otis sells 75 ice creams. On Saturday, Otis sells 87 ice creams.

(a)Work out the percentage increase in the number of ice creams Otis sells from Friday to Saturday.

%[3]

Claudia buys an ice cream machine for 960 Swiss francs.

The value of the ice cream machine depreciates by 20% each year.

(b)Work out the value of the ice cream machine at the end of 3 years.

_Swissfrancs[3]

A large circle with centre O contains 3 identical small circles. Each circle touches two other circles.

A, O and B are the centres of the small circles. AOB is a straight line.

The circumference of the large circle is 160 cm

Work out the area of one small circle. Give your answer correct to 3 significant figures.

_cm²[5]

(i)Factorise x²+ 2x – 48

[2]

(ii)Hence, solve x²+ 2x – 48 = 0

[1]

(a)Write 5.76 × 10⁴ as an ordinary number.

[1]

(b)Work out 3  104  10₂

Give your answer in standard form.

[2]

Mark has three bags, bag A, bag B and bag C

Bag A contains 120 counters. The probability of taking at random a red counter from bag A is 0.45

Bag B contains 80 counters. The probability of taking at random a red counter from bag B is 0.3

Bag C is empty.

Mark puts all the counters from bag A and bag B into bag C

Mark takes at random a counter from bag C

Work out the probability that he takes a red counter.

[3]

(a)On the number line, represent the inequality w < 1

[1]

The region R, shown shaded in the diagram, is bounded by three straight lines.

(b)Write down the three inequalities that define the region R

[3]

The diagram shows a right-angled triangle ABC

C

Area of triangle ABC = 240 cm²

Work out the perimeter of triangle ABC

_cm[4]

(a)Complete the table of values for y = 1 2 x + 4x

[1]

(b)Draw the graph of y = 1 2 x + 4x for 0.5  x  6

[2]

(c)By drawing a suitable line on the grid, find estimates for the solutions of

the equation x + 4x = 6

Give your answers correct to one decimal place.

[2]

(a)Simplify fully  125x₁₅ 

[2]

Given that 4ⁿ = 464_p

(b)Express n in terms of m and p

n = [2]

The cumulative frequency graph shows information about the heights of 40 plants that Greta has grown.

(a)Use the graph to find an estimate for the median height.

_cm[1]

(b)Use the graph to find an estimate for the interquartile range of the heights.

_cm[2]

Plants with a height greater than 40 cm are premium plants. Greta sells all the premium plants for 30 euros each.

(c)Work out the total amount of money Greta receives for the premium plants.

_euros[2]

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

Angle DAB = 48°

(a)(i)Work out the size of the obtuse angle DOB

[1]

(ii)Give a reason for your answer.

[1]

(b)(i)Work out the size of angle BCD

[1]

(ii)Give a reason for your answer.

[1]

Use algebra to show that 0.378 = 2566[2]

T is inversely proportional to m

T = 15 when m = 36

Find a formula for T in terms of m

[3]

Bianca asked 40 students which of the languages Latin (L), Greek (G) and Sanskrit (S) they study.

The Venn diagram gives some information about her results. It shows the number of students in each subset.

One of these students is selected at random. Work out the probability that this student studies Latin or Sanskrit.

[3]

The functions f and g are such that

(a)Find g(3)

[1]

(b)Find gf(x) Give your answer in its simplest form.

gf(x) = [2]

Here is a quadratic equation.

The solutions of this equation are given by x = 4  210

Find the value of a and the value of c Show your working clearly.

a =

c = [3]

The histogram shows information about the times, in minutes, that some trains arrived late at a station one day.

20 of these trains arrived between 10 minutes late and 15 minutes late.

No trains arrived more than 60 minutes late.

Work out an estimate for the number of these trains that arrived at least 25 minutes late.

[3]

Curve C has equation y = x³– 16x + 7

At two points on C, the gradient is 11 The tangents to C at these two points have equations of the form y = ax + b

Work out the two possible values of b Show clear algebraic working.

[6]

Shape P is similar to shape Q

The table shows some information about shape P and shape Q

Surface area (cm²) Volume (cm³)

Work out the volume of shape Q

_cm³

[3]

D =

n = 10.3 correct to 1 decimal place p = 7.24 correct to 2 decimal places q = 4.39 correct to 2 decimal places

By considering bounds, work out the value of D to a suitable degree of accuracy. Show your working clearly.

[5]

The first term of an arithmetic series is 10 The 20th term of the series is 86

The sum of the first N terms of the series is 5194

Work out the value of N Show your working clearly.

N = [5]

A solid cone is joined to a solid hemisphere to make the solid shown below.

The cone is made from copper. The density of copper is 9 g/cm³

The hemisphere is made from a different metal.

The total mass of the solid is 4752π grams The total volume of the solid is 504π cm³

Work out the density of the hemisphere. Show your working clearly.

_g/cm³[6]