GCSE(9-1) Mathematics J560/04 Paper 4 - Higher Tier

Sep 5, 2026

GCSE(9-1) Mathematics J560/04 Paper 4 (Higher Tier) includes a full set of assessment instructions and information on marks, calculator use, and working methods. The questions cover arithmetic and calorie estimation, geometry including circle area and volume/thickness, functions and algebraic substitutions for vehicle depreciation, and graph sketching for direct proportion and cubic relationships. Additional tasks involve plotting rectangle dimensions with a fixed area and solving ratio and probability problems requiring correct reasoning and clear answers.

LanguageEnglish

CategoryExam

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

INSTRUCTIONS

INFORMATION

Answer all the questions

Questions 1-3

Questions 4-6

Questions 7-8

# GCSE(9-1)MathematicsJ560/04 Paper 4 (Higher Tier) Sample Question Paper Date-Morning/Afternoon Time allowed:1 hour 30 minutes Aouhons You may use: ·A scientific or graphical calculator ·Geometrical instruments ·Tracing paper | First name | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Last name | | | | | | | | | | | | | Centre
number | | | | | | | Candidate
number | | | | | ## INSTRUCTIONS ·Use black ink.You may use an HB pencil for graphs and diagrams. ·Complete the boxes above with your name,centre number and candidate number. ·Answer all the questions. ·Read each question carefully before you start to write your answer. ·Where appropriate,your answers should be supported with working.Marks may begiven for a correct method even if the answer is incorrect. ·Write your answer to each question in the space provided. ·Additional paper may be used if required but you must clearly show your candidatenumber,centre number and question number(s). ·Do not write in the bar codes. ## INFORMATION ·The total mark for this paper is 100. ·The marks for each question are shown in brackets[]. ·Use the π button on your calculator or take π to be 3.142 unless the question saysotherwise. ·This document consists of 20 pages. PhysicsAndMathsTutor.com 2 ## Answer all the questions 1 18 rice cakes weigh a total of 130g.There are 329 calories in 100g of rice cakes. How many calories are there in one rice cake? edlories in Onriu Cak ……23.8……calories [3] 2 A circular table top has radius 70cm. (a)Calculate the area of the table top in cm²,giving your answer as a multiple of π. (a)…4900π…cm²[2] (b)The volume of the table top is 17150πcm³. Calculate the thickness of the table top. (b)………3.5……cm [2] ◎OCR 2014 PhysicsAndMathsTutor.com 3 3 The value of a car £Vis given by V=20000×0.9 where tis the age of the car in complete years. (a)Write down the value of Vwhen t=0. V二20o₀6×0-9°=20000×1 (a)£...20.ooo…[1]=tzopoc (b)What is the value of Vwhen t=3? V=∈2o,o₀0×0-9³61457o二 (b)£.14,.S8………[2] (c)After how many complete years will the car's value drop below £10000? (100007 zo000×0.9 E0.s>0.9c whn t=6→0.⁶=0·S31441>0·S 0.9⁷=04782969∠O·Swhu 5=7· (c)……… …………[2] ◎OCR 2014 PhysicsAndMathsTutor.com 4 4 (a)(i)Sketch a graph on the axes below that shows that y is directly proportional to x. (ii)Sketch a graph on the axes below that shows y=x³. PhysicsAndMathsTutor.com 5 (b)It is possible to draw many rectangles that have area 24cm²Here are two of them. 2cm3cm12cm 8cmNot to scale (i)Plot the dimensions of these two rectangles on the grid below. [1] (ii)Complete the graph to show the relationship between length and width forrectangles with area 24cm².[3] Length (cm) 0 4 8 12 16 20 24 28 Width(cm) PhysicsAndMathsTutor.com 6 5 Kieran,Jermaine and Chris play football. ·Kieran has scored 8 more goals than Chris. ·Jermaine has scored 5 more goals than Kieran. ·Altogether they have scored 72 goals. How many goals did they each score? k+J+c=72 (L+8)+(C+13)+(=723C+13=723c=59 so k=C+8So J=C+13 二17+8三17+13 二2S=3 Kieran..25………Jermaine ...30…………..Chris ..17………… PhysicsAndMathsTutor.com 7 6 Peter makes a large amount of pink paint by mixing red and white paint in the ratio 2:3. Red paint costs £80 per 10 litres.White paint costs £5 per 10 litres. Peter sells his pink paint in 10-litre tins for £60 per tin. Calculate how much profit he makes for each tin he sells. Pcofit→incom-(GstIへcon =56Cost ned:whik ukl S parls ot10 likces 2:3 10/s =2litres pr pat So foc ned paint 2×2ar5=41ikes f…… ……………………-5] so 4/10×580=32 For whk peint 2×3pdt二6likr5So 6/10×ES=t3 TokJ cost→53Z+t3=53S Pcolit→60-∈35 =25 ◎OCR 2014 PhysicsAndMathsTutor.com 8 7 Dan believes he

FAQs

What calculator and equipment are allowed for this paper?

A scientific or graphical calculator is allowed, along with geometrical instruments and tracing paper. An HB pencil may be used for graphs and diagrams.

How are marks awarded on the questions?

Marks are given for correct method even if the final answer is incorrect. The marks for each question are shown in brackets.

What topic areas are included in Paper 4?

The paper includes questions on calorie/rate calculations, circle geometry and volume, algebraic substitution for functions, graph sketching for proportionality and cubic functions, and probability plus function machine problems.

Sep 5, 2026

Upload by Evangeline