4MA1 Mathematics A: January 2023 Paper 2HHigher Tier Paper 2

Show that 3 57 ÷ 1 58 = 2 27[3]

Change a speed of 90 kilometres per hour to a speed in metres per second. Show your working clearly.

_m/s[3]

ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {even numbers} A ∩ B = {12, 16, 20} (A ∪ B)ʹ = {17, 19}

Complete the Venn diagram for the sets ℰ, A and B

[3]

The diagram shows rectangle ABCD

Work out the perimeter of the rectangle. Show your working clearly.

_cm[4]

The weight of a cake is 2.75 kg, correct to 2 decimal places.

(a)Write down the lower bound of the weight of the cake.

_kg[1]

(b)Write down the upper bound of the weight of the cake.

_kg[1]

Penny has worked out 81 .3 × 59 .21.9₂ on her calculator.

Her answer is 13 332.299 17

Penny’s answer is not sensible.

(c)By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible. Show your working clearly.[2]

The points A and B are on a coordinate grid.

The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant.

The midpoint of AB has coordinates (k, 15) where k is a constant.

Find the value of j and the value of k

j =

k = [3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

Matteo is going to invest 5000 Swiss francs for two years.

He can invest his money in Bank G or in Bank H.

The total amount of interest Matteo would receive at the end of two years from Bank G is more than the amount of interest Matteo would receive at the end of two years from Bank H.

How much more?

_Swissfrancs[4]

(a)Write down the value of (m + 2)⁰ where m is a positive integer.

[1]

(b)Simplify (3a² b⁴)³

[2]

(c)Factorise fully 14x² y⁴+ 21x³ y²

[2]

The diagram shows a straight line drawn on a grid.

(d)Write down an equation of the line.

[2]

The diagram shows an isosceles triangle, with base length 24 cm.

The perimeter of the triangle is 54 cm.

Work out the area of the triangle.

_cm²[5]

Here are six graphs.

Complete the table below with the letter of the graph that could represent each given equation. Write your answers on the dotted lines.

[3]

The cumulative frequency graph gives information about the time, in minutes, each of 60 people took to shop in a market.

60

50

40

(a)Use the graph to find an estimate for the median time people took to shop in the market.

_minutes[1]

(b)Use the graph to find an estimate for the number of people who took longer than 55 minutes to shop in the market.

[2]

(c)Use the graph to complete the frequency table to give information about the time, in minutes, each of the 60 people took to shop in the market.

[2]

Solve x + 34 − 7 − x5 = 4.3

Show clear algebraic working.

x = [3]

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

EBF is the tangent to the circle at B

(a)(i)Work out the size of angle DCB

[1]

(ii)Give a reason for your answer to (a)(i)

[1]

(b)Work out the size of angle ADO

[3]

Here is a list giving the numbers of runs scored last week by the eleven members of cricket team A.

The interquartile range of the numbers of runs scored last week by the eleven members of cricket team B was 42

Using a suitable calculation, write down one comparison between the numbers of runs scored by the members of cricket team A and the members of cricket team B. Show your working clearly.

[3]

Use algebra to show that 0.43 8 = 217495[2]

Given that 8 m + 49m − 9m = k m where k is an integer and m is a prime number,

(a)work out the value of k

k = [1]

(b)Show that 5 −1 − 182 can be written in the form a + b 2

where a and b are integers. Show each stage of your working clearly.[3]

The table gives information about the weights, in kg, of the parcels that Pedro delivers on Monday.

0 < w  2 12

2 < w  3 7

3 < w  6 15

6 < w  9 12

9 < w  14 9

(a)On the grid, draw a histogram for this information.

8

6

[3]

One of the parcels that Pedro delivered on Monday is chosen at random.

(b)Using the information in the table, find an estimate for the probability that this parcel weighs more than 7 kg.

[2]

A and B are two similar vases.

The vases are such that

Calculate the volume of vase B

_cm³[4]

Solve the simultaneous equations

Show clear algebraic working.

[5]

Given that the surface area of a sphere is 49π cm²

find the volume of the sphere. Give your answer correct to the nearest integer.

_cm³[3]

Solve the inequality 6x²+ 37x  35 Show clear algebraic working.

[3]

The diagram shows a solid prism ABCDEFGHIJ

The prism is such that each cross section is a pentagon where

Given that AG = BH = EF = DJ = CI = 12 cm

calculate the angle that AJ makes with the base ABHG of the prism. Give your answer correct to 3 significant figures.

[5]

The graph of y = a sin x° + b is drawn on the grid.

Find the value of a and the value of b

a =

b = [2]

The function f is such that f(x) = 3x²– 12x + 7 where x  2

Express the inverse function f^–1 in the form f^–1(x) = …

f ^–1(x) = [4]

Find the values of n such that

Show clear algebraic working.

[5]