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GCSE Mathematics

Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be acceptable where you are asked to calculate. The number of marks is given in brackets at the end of each question or part-question. Lee has a 37 4 inch chest and a 28 inch waist. He is ordering a long coat from equations for maths paper 2 80 years catalogue. What size would you suggest that he orders?

Give a clear reason for your answer. Bill has a 84 cm waist. He is ordering trousers from the catalogue. Which size should he order? Show your working to support your answer. Complete the line in the table below which gives the same information for customers in centimetres. Write all measurements correct to the nearest whole number. X Diagram not drawn to scale.

The above diagram shows three points X, P and Z which lie on a straight line. The bearing of Z from P is Find the bearing of X from P. Mr Lucas received an electricity bill from R. Electricity Company. The bill, with some of the entries removed, is shown. Use the equations for maths paper 2 80 years given on the bill to complete all of the missing entries and calculate the total amount that Mr Lucas has to pay.

The age and sale value of each of 22 cars of one particular make and model are recorded. The results are shown on the following scatter diagram. Sale value in s. Write down the age and sale value of the cheapest car. Another survey of cars is carried. In this survey, sale values of 15 year-old cars are recorded.

Sale value, x. Calculate an estimate for the mean sale value. A garden centre makes compost for planting. The compost is made equations for maths paper 2 80 years mixing peat, fertilizer and grit. Eight buckets of the compost are made using 5 buckets of peat, 2 buckets of fertilizer and 1 bucket of grit. Calculate the cost of buying 10 buckets of compost in the special offer.

The garden centre buys a delivery van at a cost of At the end of two years by how much has the value of the van depreciated? Use the method of trial and improvement to find this solution correct to 1 decimal place. Find the size of the angle marked x. At Pizza 2 Go a Standard Pizza has a thin base with diameter 20 cm and costs 7. A Party Pizza has a thin base with diameter 30 cm. The two types of pizza offer the same value for money and have the same thickness.

Calculate the price for the Party Pizza. Show your working and explain your answer. Diagram not drawn to scale. The diameter of the circle is 40 cm. Find the area of the square. The diagram shows a circle with centre O of radius 68 cm. The straight line PCT is a tangent to the circle.

On the diagram above, mark another angle that is equal to x. State a reason for your answer using your knowledge of circle theorems. Give your answers correct to one decimal place. Two beads are selected at random from a bag containing 6 blue beads and 4 red beads. Find the probability Equations For Maths Paper 1 Letters that at least one red bead is selected.

The results of gathering and measuring the lengths of sticks found in a wood are represented in the histogram. Frequency density. C Diagram not drawn to scale. Find the length of DC. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Paper 2 Maths. Uploaded by Meurig Jenkins. Did you find this document useful? Is this content inappropriate?

Report this Document. Flag for inappropriate content. Download. Related titles. Carousel Previous Carousel Next. Kevin G. Equations for maths paper 2 80 years More variations on the Sierpinski sieve.

Jump to Page. Search inside document. Take as or use the button on your calculator. Examiner only A clothing catalogue gives the following sizing guide. Size Chest size in inches Waist size in inches 34 to 36 27 to 29 37 to 38 30 to 31 39 to 42 32 to 35 XL 43 to 45 36 to 37 All measurements are given to the nearest inch 1 inch cm a Lee has a 37 4 inch chest and a 28 inch waist.

Size To fit chest XL cm to cm To fit waist Examiner only Mr Lucas received an electricity bill from R. Quarterly charge Total charge including V. Previous amount owing Examiner only The age and sale value of each of 22 cars of one particular make and model are recorded.

Sale value in s a 10 12 Age of car in years Write down the age and sale value of the cheapest car. Sale value, x Number of cars X x! Examiner only A garden centre makes compost for planting. Here is a sequence of numbers. What is the first number in the sequence that is less than zero?

Frequency density 10 0 a 20 40 60 80 Length of stick in cm Use the histogram to complete the grouped frequency table. Length, l cm 0! Documents Similar To Paper 2 Maths.

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College of Copenhagen sight scientist Niels Secher's investigate reveals which chosen rowers have been high as well as have gaunta stronger you will have a support a aloft.

It is suggested that an analogous distribution of heating and cooling may be instrumental in maintaining the general circulation of the atmosphere. Lorenz's abstract begins:- The variations of five-day mean sea-level pressure, averaged about selected latitude circles in the northern hemisphere, and the variations of differences between five-day mean pressures at selected pairs of latitudes are examined statistically. The first sentences of the abstract read:- An approximate differential equation is presented, relating the change in speed of the zonal westerly winds to the contemporary zonal wind-speed and the meridional flow of absolute angular momentum.

This equation is tested statistically by means of values of the momentum flow and the zonal wind-speed, computed with the aid of the geostrophic-wind approximation, from pressure and height data extracted from analyzed northern-hemisphere maps.

Lorenz spent his whole career at the Massachusetts Institute of Technology, being appointed assistant professor in , then promoted to associate professor before becoming Professor of Meteorology in He served as Head of Department from to , retiring in when he was made professor emeritus.

It was a simple event in which led Lorenz to results which brought him worldwide fame. He was using a computer to investigate models of the atmosphere which he had devised involving twelve differential equations. Having obtained results from running his program, he decided that he would like to carry the calculations further. Rather than start the whole program again for although he was using an up-to-date computer, it was painfully slow by later standards , he started the program in the middle of the calculation inputting the data as calculated by the machine at that middle point.

After going away for a cup of coffee, he came back to see how the computer was getting on with the calculations. He was surprised to see that the computer had found significantly different answers over the range that it had calculated before. At first he thought it must be a hardware problem, since the software should come up with the same answer every time when given the same input data.

Eventually he discovered that the data he had input to begin the second run had not been printed out to the same number of decimal places as the machine had stored, so the initial data was slightly different for the second run differing in the fourth decimal place. He then set about trying to understand how a tiny change in the initial data could have such a major effect on the calculations.

Lorenz had discovered chaos. Lorenz was not the first person to discover chaos. Now that Lorenz understood the significance of his discovery he wrote it up in the paper Deterministic Nonperiodic Flow and it appeared in the Journal of the Atmospheric Sciences in The abstract begins:- Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow.

Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.

However, it has gone on to become one of the most quoted papers of all time. The set of equations and the attractors described by this set of equations are now called the 'Lorenz equations' and 'Lorenz attractors', respectively.

It would be fair to say that Lorenz began a scientific revolution with this paper which he and many others developed over the following years. By encapsulating the essence of chaos theory in the title of his talk, Lorenz succeeded in capturing the public's imagination and the term "butterfly effect" was soon the popular term for chaos.

Another account of aperiodic behaviour in ordinary differential equations, and difference equations, in which Lorenz describes how he arrived, starting from the description of convection in meteorology, at the Lorenz equations is contained in his paper On the prevalence of aperiodicity in simple systems delivered at the Biennial Seminar of the Canadian Mathematical Congress in Calgary, Canada, in In he published Attractor sets and quasigeostrophic equilibrium :- The primary purpose of this study is to find out what the attractor set looks like for some simple atmospheric model.

Later papers include: A very narrow spectral band which investigates the spectral properties of the Lorenz system ; The local structure of a chaotic attractor in four dimensions ; Lyapunov numbers and the local structure of attractors ; On the existence of a slow manifold ; Atmospheric models as dynamical systems ; Computational chaos - a prelude to computational instability ; and The slow manifold - what is it?

He used this series of three lectures as a basis for his famous text The essence of chaos Andrew Fowler writes in a review:- This is an excellent book, providing a popular exposition of the science of chaos by an undisputed international authority. Simplify and Solve Equations 2.

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