Step support programme assignment 12. May 13, 2018 · maths.

Step support programme assignment 12. The lengths of the sides BC , CA and AB are a, b and c, respectively. Our free online STEP Support Programme provides a structured course of assignments to help university applicants develop their advanced mathematical problem- If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you start year 13. Warm-up STEP Support Programme Assignment 19 1 The picture below shows a circle of radius r with centre O and a right-angled triangle OBT . This STEP 2 module consists of 4 STEP questions, some topic notes and useful formulae, a "hints" sheet and a "solutions" booklet. 7K subscribers 8 STEP Support Programme Assignment 5 Warm-up 1 (i) BC, CA and AB re a, b and c, respectively. About this assignment The assignment is published as a pdf file below. haveno prime factors in common with N). The warm up for this assignment derives the small angle approximations for $\sin \theta$, $\cos \theta$ and $\tan \theta$ (which hold when $\theta$ is in radians). Here t is called a `dummy variable': it doesn't matter what letter you use because it will disappear when you do the integral and evaluate the result at t = x and t = a. The STEP question 3 In this question a and b are distinct, non-zero real numbers, and c is a real number. You should explain your reasoning clearly. Apr 12, 2022 · STEP Support Programme Assignment 14 (2010 STEP 2 Q2) Millennium Mathematics Project - maths. ac. 5K views • 2 years ago Cambridge STEP Support Programme The Cambridge STEP Support Programme (that's a mouthful) is a Cambridge-run initiative to help university applicants develop their advanced mathematical problem solving skills and prepare for the STEP examinations. The assignment is published as a pdf file below. Okay, done a little bit of Permalink Submitted by Heirio on Tue, 09/12/2017 - 19:32 (v) In how many distinct ways can you arrange the letters in MISSISSIPPI? The STEP question (2005 STEP I Q1) 3 47231 is a ve-digit number whose digits sum to 4 + 7 + 2 + 3 + 1 = 17 . Note that the y-intercept of y = x4 6x2 The STEP question 3 In this question a and b are distinct, non-zero real numbers, and c is a real number. Let A, B and P be points on the circumference of a circle with centre O, such that O lies inside the triangle ABP . (i) Show that there are 15 ve-digit numbers whose digits sum to 43. 6K subscribers 55 Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. This document provides an assignment on functions and calculus concepts. Jun 28, 2017 · In an exam I would then either re-write it the correct way around or put something like "each of these steps can be reversed" or something similar! The final part uses c2 = 1 −(a + b a − b)2 c 2 = 1 − (a + b a − b) 2 to show that 0 <c2 ≤ 1 0 <c 2 ≤ 1. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. If possible, get a friend or a teacher to help you check your answers for flaws, missing cases, or gaps in your arguments. Check your The STEP question n + qn2 + rn r= 1 are numbers. org, on behalf of the Faculty of Mathematics. (i) By considering the areas of the triangle OBT , the sector OBA and the triangle OBA, show that: (ii) The function defined in this question is called the Euler totient function. The STEP Support Programme is an excellent resource, particularly if you’re starting in Year 12. The provide a structured introduction to solving STEP If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you start year 13. There are a few different approaches you can take for each part. Find an expression for F(x) in terms of x. Further reading You can find further explanations of proof by induction, and more questions to try, in this NRICH Advanced problem solving module. Factorising out some common factors helps with the arithmetic: Assignment 8 is now published and ready. When n = 1 (the `base case') we have 111 41 = 7, so the result is true when n = 1. Previous assignments can be found here, but you can do this one without having done the others first. The STEP Support programme is designed to help university applicants develop their advanced problem-solving skills and prepare for sitting STEP Mathematics examinations. Nov 14, 2011 · If you can, start working on the STEP Support Programme foundation modules in year 12. e. The "hints and partial solutions" for all the assignments have been updated (and now include some answers). Submitted by Heirio on Tue, 09/05/2017 - 20:29 Forums: General discussion The STEP Support Programme is developed by the University of Cambridge's Millennium Mathematics Project - maths. Often, you can sketch the curve without using all this in ormation (though it is good to have it all). Do some STEP 1 questions for the first few weeks if STEP 2 and 3 questions seem scary (but don't dwell too long on them). Points of in ection can be stationary (if = 0 as well) or dx non-stationary. STEP Support - Assignment 12 This module includes proving divisibility of some expressions, probability and a puzzle which on first reading seems to be unsolvable. The inequality (∗) is called the AM-GM inequality: AM stands for Arithmetic Mean (the left hand side of (∗)) and GM stands for Geometric Mean (the right hand side of (∗)). STEP Support Programme Assignment 23 Warm-up ion of functions (a function of a function). Find an expression for F(x) in terms of x Oct 31, 2022 · STEP Support Programme Foundation Assignment 4 R2Drew2 12. The Warm Down to Assignment 1 (The Bell Ringers) is now on Assignment 12. 9K subscribers Subscribed STEP Support Programme Assignment 23 Warm-up ion of functions (a function of a function). The programme consists of online modules for individual additional study, along with hints and full solutions. The warm up for this assignment involves some algebraic manipulation. Only one of these is a solution of the original equation. p 3 11 In the rst case you should end up with y = . I read the hints where they told us to use the first equation given which involves c^2. 6K subscribers Subscribed A printable 12 step worksheet packet to assist in working the 12 steps in 12 step programs. They offer various assignments to ease you into the STEP style and can be a valuable resource. The warm up for this assignment introduces the definitions of convex and concave graphs, and also discusses points of inflection. There are 25 Foundation modules, and the intention is that you work through them in order. Working through solution to 1999 STEP 1 Question 6 - STEP Support Programme Assignment 2 Millennium Mathematics Project - maths. org/step STEP Support Programme Assignment 5 Warm-up 1 (i) The triangle ABC has a right-angle at C . This is an extremely powerful STEP Support Programme Foundation Assignment 25 (1994 STEP 1 Q8) V2 Millennium Mathematics Project - maths. You don't need a particularly fancy argument here. Question: Prove that 11n 4n is divisible by 7 for integers n > 1. STEP Support Programme Assignment 13 Warm-up dy You probably already know that for a graph with gradient : dx dy General remark: to show that A > B, it is often easiest to show (equivalently) that A−B > 0. The function de ned in this question is called the Euler totient function. You will find it helpful to complete the "STEP 2 Calculus" module first. Please see here for more detailed advice on how to use the STEP Support Programme. 9K subscribers Subscribe The simplest way to show that x = 15 is a root is to set x = 15 in the equation and check that this gives 0. org/step STEP Support Programme Assignment 1 Warm-up 1 (i) Simplify p 50 + p 18. Let F(x) = f g(x) . Hints, support and self evaluation The “Hints and partial solutions for Assignment 25” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers. STEP Support Programme Assignment 10 Warm-up 1 (i) In the triangle below, BP is perpendicular to AC. About this assignment Many STEP 2 questions will expect you to be fluent with A-Level Calculus techniques, even if they do not look like "Calculus questions" at first glance. f(2) = 2 Thus f(2) f(6) = 2 6= f(12) = 1, and f(6) = 6 If p is prime, then f(p) = p(1 1 p) = p 1. Apr 20, 2022 · STEP Support Programme Assignment 15 (2006 STEP 2 Question 1) Millennium Mathematics Project - maths. (c) University of Cambridge. Apr 27, 2022 · STEP Support Programme Assignment 16 (2015 STEP 1 Q2) Millennium Mathematics Project - maths. Do not worry if the STEP questions seem very difficult. You will need to use the fact that a a and b b are distinct and non-zero. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2024 Google LLC However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). Mar 31, 2022 · STEP Support Programme Assignment 12 (2011 Step 1 Q12) Millennium Mathematics Project - maths. . Feb 14, 2024 · The STEP support programme has put together a STEP specification mapping document which shows how the syllabus from old STEP papers from 2018 and earlier relates to the new syllabus. Sep 14, 2017 · Okay, done a little bit of Permalink Submitted by Heirio on Tue, 09/12/2017 - 19:32 Worked Solution to 2011 STEP 1 Question 12 In the video below, Claire runs through a possible solution to 2011 STEP 1 Question 12. The only letters you should not use are x and a, because they have been used as limits. org 11. If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you start year 13. Hence n(n + 1)(n + 2) is divisible by 3. STEP Support Programme Hints and Partial Solutions for Assignment 1 (b) 4 x2 + = 12 x2 x4 12x2 + 4 = 0 p STEP Support - Assignment 5 This STEP Support module involves some trigonometry and a question about a tetrahedron (and a question about socks!). Email us: step@maths. Finally, there is a warm-down exercise. The value of f(N) is exactly equal to the number of integers less than or equal to N that are coprime to N (i. There are non-stationary points of in ection at (1; 4) distinct roots of y = x4 6x2 + 9, which are the two minimum turning points. 6K subscribers Subscribed In the video below, Jake runs through a possible solution to 1999 STEP 1 Question 4. The STEP question of say (and you can do this algebraically or by using a geometrical argument). 6K subscribers Subscribed For example, the equation x + 1 = 3 has just one solution (x = 2), but if your rst step had (rather bizarrely) been to square both sides to get (x + 1)2 = 9 you would nd two solutions (x = 2 and x = 4). NB: the Faculty of Mathematics provides a free online STEP Support programme to help you develop your advanced problem-solving skills, from the summer of Y12 onwards, and prepare for STEP - see below for more details. You can then write the equation of the circle as (x a)2 + y2 = r2 and use the distance n you must ensure that there are no gaps in y 6 1 =) 6 q 4 3. maths. May 25, 2022 · STEP Support Programme Foundation Assignment 23 (2009 STEP 1 Q8) Millennium Mathematics Project - maths. what happens as x ! 1 or y ! 1). The modules also contain "topic notes" which consists of useful formulae you should be aware of, together with some general hints and advice. Find About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2025 Google LLC About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2025 Google LLC The Indian mathematician Brahmagupta (597–668 AD) was the first to obtain the formula for solving quadratic equations. Express cos and sin in terms of a STEP Support Programme Assignment 20 (1st Q) (1996 STEP 2 Question 3) First page« First Previous page‹ Previous Page 1 Current page 2 Page 3 Next pageNext › Last pageLast » The STEP question (2012 STEP I Q2) 3 (i) dy d2y pt is at (0; 9) and there dx p dx2 are turning points at ( 3; 0) an (0; 9). What sort of triangle is AP O? Feb 23, 2022 · STEP Support Programme Assignment 7 (2002 STEP 1 Question 5) - video worked solution Millennium Mathematics Project - maths. It introduces AS Maths concepts through STEP-style questions, helping you build a strong foundation before progressing to more advanced problems. The STEP question (1996 STEP II Q3) 3 To show that F2 = 1 etc. Show from rst principles, using the de nition of di erentiation as given in Assignment 20 question 1(i), that d(ax) = Kax dx and that d(a x) = dx This is very typical of STEP: the question involves a function (or process or notation) that is | or may be | unfamiliar to you but which is de ned carefully in the question; then you are asked to use the function for progressively more di cult tasks. 6K subscribers Subscribed The STEP question 3 The given by F0 = 0, F1 = 1, F2 = 1 and F3 = 2. STEP Support Programme Assignment 8 Warm-up 1 By considering (x y)2, prove that x2 + y2 > 2xy and hence show that, if a and b are non-negative numbers, then a + b p Submitted by Heirio on Tue, 09/05/2017 - 20:29 Forums: General discussion However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). Angle CAB is . The following shows an example of how to prove a conjecture by induction. The warm up for this assignment involves manipulating surds and simplifying them. Try it out | maybe starting with f(12) and f(20) and you'll begin to see how it works. For f(12), the numbers less than or equal to 12 that are coprime to 12 are 1,5,7 STEP Support Programme Assignment 18 Warm-up totes (i. have no prime factors in common with N). org/step STEP Support Programme Assignment 9 Warm-up 1 (i) The isosceles triangle 4ABC has AB = BC. May 12, 2022 · STEP Support Programme Assignment 21 (1991 STEP 1 Q4) Millennium Mathematics Project - maths. n(n + 1) is the product of two consecutive integers, so one of them is divisible by 2. If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2025 Google LLC The STEP question (2005 STEP I Q6) 3 (i) It may be easier to use AP 2 = 4BP 2 which gives: (5 x)2 + (16 y)2 = 4 ( 4 May 4, 2022 · STEP Support Programme Foundation Assignment 17 (2003 STEP 1 Q1) Millennium Mathematics Project - maths. Most of the questions are taken from old STEP 1 papers, with some STEP 2 questions appearing in later modules. If you have any questions about the assignments, or STEP in general, or feedback about our resources you can email us at step@maths. This is the STEP question which appears in Assignment 21. 6K subscribers Subscribed However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). STEP Support Programme Assignment 12 Warm-up this question, n denotes a positive integ (i) Show that n(n + 1) is divisible by 2. We have f(12) = 4 from above. It defines two new functions, C(x) and S(x), and asks students to show various properties of these functions, including: 1) C(x) - S(x) = 1, C(x)C(y) + S(x)S(y) = C(x+y), and C(x)S(y) + S(x)C(y) = S(x+y). The STEP Support Programme consists of three types of module: The Foundation modules provide an introduction to problem solving through carefully selected STEP 1 and 2 questions. Each STEP 3 module consists of STEP questions, some topic notes and useful formulae, a "hints" sheet and a "solutions" booklet. STEP Support - Assignment 12 This STEP support module includes proving divisibility of some expressions, probability and a logic puzzle. n(n+1)(n+2) is the product of three consecutive integers, so one of them is a multiple of 3. Dec 27, 2016 · Assignment 1 Submitted by Edogowa Conan on Tue, 12/27/2016 - 14:21 Hi, I'm stuck on the last part of the step question where they ask you to show that c^2 is between 1 and 0, but one of the equations they gave us shows that c^2 is negative. If you already know the chain rule, please forget it for the = 2x3 + 1 and f(x) = x2. The STEP 2 modules are designed to be started near the beginning of Year 13. Since algebra (the use of letters in equations) did not exist at that time, he had to write his discovery in words: To the absolute number multiplied by four times the coefficient of the square, add the square of the coefficient of the middle term; the square root of the Hi, I found this one tricky Permalink Submitted by FletchOnMaths on Sat, 07/22/2017 - 20:17 STEP Support Programme Assignment 25 Warm-up concerned with integration by substituti e trying to integrate f(x), without success. 2Note the use of a di erent letter for the variable in the rst integral. STEP 3 Coordinate Geometry (including Polar Coordinates) This module contains STEP questions on coordinate geometry and polar coordinates. Each assignment has a “Hints and partial solutions A simple counterexample (remember the simpler the better!) would be f(12) 6= f(2) f(6). Each of these STEP 2 modules consists of a selection of STEP questions, together with hints and solutions. The Warm Down to Assignment 2 (Holditch Theorem is now on Assignment 1. The STEP Support programme is a programme of resources for students taking STEP. Try it out — maybe starting with f (12) and f (20) and you’llbegin to see how it works. By setting n = 1, 0, 1 and 2, obtain four equations that must be satis ed by STEP Support - Assignment 22 This STEP support module derives some more differentiation results and asks you to sketch some graphs. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). This module introduces you to STEP questions which involve Curve Sketching. This is the STEP question which appears in Assignment 12. 7K subscribers Subscribed STEP 2 Complex Numbers Complex numbers are a new addition to the 2019 STEP specification for papers 2. Hence 1The di erence of two cubes identity from Assignment 14 will be useful. The STEP question No calculators or spreadsheets for this question please! 3 The sequence of real numbers u1, u2, u3, : : : is de ned by ; = 2 u1 and un+1 = k A lot of these assignments only require GCSE or AS knowledge (though they will ask you to use it in unusual ways!), and the first 10 to 15 Assignments are aimed at year 12 students. You may nd it helpful to use letters for the sizes of some of the angles; for example, you might want to write `Let \AP O = x'. At the point of in ection = 0; in addition, the sign of the second derivative must dx2 dy be di erent on either of the point. If p and q are distinct primes, then f(pq) = pq(1 2 = 2 3 (p ) = p)(1 1 1 1)(q 1) = f(p)f(q). Oct 10, 2016 · Assignment 8 is now published and ready. The STEP question (2013 STEP I Q1) 3 Substitutions work quite nicely for all three equations. It consists of for individual additional study, along with hints and full solutions. Hints, support and self evaluation The “Hints and partial solutions for Assignment 20” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers. Please let us know if you find a mistake! STEP Support Foundation modules These Foundation modules are designed to develop your problem solving skills and provide an introduction to solving STEP (and STEP-like) problems. 3K subscribers Subscribed 12 432 views 2 years ago If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you start year 13. So we replace x with some function g(u Further reading This NRICH advanced problem solving module offers some hints for solving STEP integration and some more questions for you to try. Warm-up 1 This question is about the product rule for di erentiating a product of two functions. STEP questions are challenging, so don't worry if you get stuck. cam. Our STEP Support Programme is designed to help university applicants develop their advanced problem-solving skills and prepare for sitting STEP Mathematics examinations. (ii) Express (3 + 2 p 5)3 in the form a+ b p 5 where a and b are integers. The value of f (N) isexactly equal to the number of integers less than or equal to N that are coprime to N (i. May 13, 2018 · maths. you should write something like: F2 = F1 + F0 = 1 + 0 = 1 : You should also obtain F5 = 5, F6 = 8 and F7 = 13. Introduction to STEP preparation page Introduction to advanced problem solving Read all about our Advanced Problem Solving resources Eve Pound, currently a Part III (4th year) Mathematics student at Murray Edwards College, University of Cambridge, works through the solution to the STEP question featured in Assignment 1 of the STEP Support Programme Foundation Assignment 1 R2Drew2 11. 8K subscribers Subscribed STEP Support Foundation modules These Foundation modules are designed to develop your problem solving skills and provide an introduction to solving STEP (and STEP-like) problems. 6K subscribers Subscribed STEP Support - Assignment 17 This STEP support module includes some work with summations, and an introduction to Modular Arithmetic. STEP Support Programme Assignment 7 Warm-up 1 (i) 1 Sketch (on di erent axes) the graphs of y = x + and y = x However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). You may nd it useful to think about nsformations (translations 1 After finishing the preparation part for assignment 12, I found there may be some difference between CIE statistics and STEP statistics, just the question (iv): (b) and (c) in preparation STEP Support Programme Foundation Assignment 2 R2Drew2 11. uk. 1K subscribers Subscribed 12 536 views 2 years ago Assignment 13 point of in ection is a point at which the graph changes from being concave to being convex or d2y vice versa. The diagram below shows the di erence between a stationary and a non About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2025 Google LLC The assignment is published as a pdf file below. These STEP 2 modules assume that you have already begun to develop your problem-solving skills and approach to STEP questions by working on the Foundation modules. 2) Finding the derivatives of C(x) and S(x), and that C(x) satisfies the differential equation d2C(x)/dx2 = K2C( If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we strongly advise that you start working on these assignments in year 12, or in the summer before you start year 13. Foundation assignment changes Submitted by cg213 on Thu, 12/14/2017 - 13:00 Hi all, We have made a couple of changes to the Warm Downs in Foundation Assignments 1, 2 and 12. Free download available in PDF, ODT, DOCX, XLSX and RTF. They also introduce mathematical ideas which you may not have been taught at school, and show how some of the formulae commonly used in A-levels are derived. STEP Support - Assignment 23 This STEP support module introduces the chain rule and asks some questions about coordinate geometry. Full solutions are available to guide you if you get stuck. This module introduces you to the complex number topics included in the STEP 2 specification. Thus the inequality (∗) says that for two non-negative numbers, AM is not less than GM. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2025 Google LLC For this question, you need a *good* diagram | nice and big. The general term is given by Fn = a n + b n ; where a, b, ( ) (i) Show that Proof by induction is part of the STEP I speci cation, even though it only appears on Further Mathematics speci cations. Hence n(n + 1) is divisible by 2. For f (12), the numbers less than or equal to 12 that are coprime to 12are STEP Support - Assignment 18 This STEP support module includes some curve sketching, equation solving and an introduction to fractal. The programme is developed by the and . 7K subscribers Subscribed STEP Support Programme Assignment 24 (1998 STEP 2 Q 4) This content is blocked because Video cookies have not been accepted. These assignments are designed to help you to develop the skills you need, so that by the time you sit the STEP exam you will feel well-prepared. STEP Support Programme Assignment 12 Warm-up this question, n denotes a positive i STEP Support Programme Assignment 2 Warm-up 1 (i) 1)2, giving your answer in factorised form. The answers to the last part can be expressed surprisingly neatly! STEP Support Programme Foundation Assignment 1 R2Drew2 • 2. STEP questions are difficult, they are supposed to be and you should expect to get stuck. The STEP question 3 Sketch the curve f(x) = x3 + Ax2 + B rst in the case A > 0 and B > 0, and then in the case A < 0 and B > 0: Show that the equation x3 + ax2 + b = 0; where a and b are real, will have three distinct real roots if Apr 2, 2019 · Working through solution to 2004 STEP 1 Question 2 - STEP Support Programme Assignment 3 Millennium Mathematics Project - maths. Oct 30, 2022 · STEP Foundation Support Programme Assignment 3 R2Drew2 12. The resources are free and open to everyone. 7K subscribers Subscribed STEP Support Programme Assignment 9 (1993 STEP 1 Question 7) - video solution Millennium Mathematics Project - maths. Then you should note that as 2 The second part needs you to cancel out all the common factors and appreciate which ones are left | the rst part should act as a guide. Step Support Programme Assignment 5 (2006 STEP 1 Question 8) - video solution This content is blocked because Video cookies have not been accepted. A line is drawn connecting B to the midpoint M of AC. zwvf lihaov ppp cweurpx ftpyrkf ppetf pryo tyzd drl vcf