Updated 4/3/2017 - typo errors corrected on page 1 of solutions, part b. Updated 8/3/2017 - extra exercise added to question 1) b); solution on page 1a.<br /> <br /> This worksheet has two problems involving circles centred on the origin. The first problem requires the equation of a tangent line to be deduced. The second problem requires a set of simultaneous equations to be set up to find the x and y co-ordinates where the line cuts the circle. When combined these form a quadratic equation. The equation will not factorise, so completing the square method or the Quadratic Formula must be used to solve it. DOCX and PDF worksheets supplied along with 3-page written solution in JPG format.

Updated 27/1/18. Resource now split into 3 files to improve its usability: Exercises, Examples and Answers sheets. The Exercise worksheet comprises three main exercise sections (Basic, Intermediate and Advanced) with a number of problems in each for students to attempt. Diagrams are provided throughout. The Examples sheet follows the same pattern of Basic, Intermediate and Advanced problems.<br /> <br /> On the Exercises sheet, the Basic Exercises section consists of 5 simple triangle problems i.e. finding angles and sides with different triangle sizes and orientations to test spatial awareness skills. The Intermediate Exercises section consists of 7 exercises that require perimeters and areas to be found, but using trigonometry first to find the required sides. The Advanced Exercises section includes practical applications of trigonometry consisting of 7 problems with a mix of a composite triangles and other shapes. Some problems require just angles and sides to be found while others also require perimeters and areas to be found. The more advanced problems also draw on knowledge of mid-points, similar triangles, area of a trapezium, properties of a hexagon, symmetry, corresponding angles and so on. <br /> <br /> The Examples sheet includes the SOH CAH TOA mnemonic, the related trigonmetric equations, guidance on how to recognise the opposite, adjacent and hypotenuse sides, along with accepted conventions for labeling sides and angles with letters. <br /> <br /> A separate, comprehensive answer sheet is provided. It does not give model answers for every problem but does include calculated interim values for the more complex problems so that solutions can be more easily followed. Rounding of final answers are specified to either 3 significant figures or 2 decimal places. For interim calculations it is recommended that teachers instruct students to round to 3 decimal places to preserve the accuracy of their final answers.<br /> <br /> Word DOCX and PDF formats provided. The drawing objects in the diagrams are grouped as one entity so you need to ungroup them if you want to change the position or orientation of individual objects. If you just want to change the value of a text box, for example, Word will allow you to edit it by just clicking on the text box and entering the new value.<br /> <br /> Intuitive Resources is the name I use for selling my resources. This is all my own work. All feedback welcome. I have carefully checked and double-checked the worksheet and answers for errors but will promptly correct any notified to me. If you have bought the resource and notify me of any mathematical/arithmetical errors at kevin_alderson@yahoo.co.uk then I will send you the corrected version free of charge. I promise to use your email for this purpose only. l will not send you marketing emails or share your email address with any other party.<br /> Kevin Alderson

This is an exam-style question in which a factorised equation is given for Celsius in terms of Fahrenheit. It's aimed at students capable of achieving grade 4 upwards. They will need to expand the equation to work out both the gradient and Celsius intercept of the equation, use the equation to find points on the graph and then plot it accordingly. They are then required to take readings from the graph, both in Celsius and Fahrenheit, and then check these with the same results using the equation. To find the Fahrenheit result they will need to rearrange the equation so that Fahrenheit is the subject.<br /> <br /> Fully worked answers are provided. The graph can be constructed and plotted on ordinary graph paper but if you would prefer to use a graph with pre-printed axes then a software-generated JPG file has been provided. Two of the points required to plot the graph come out to whole numbers so it should not be too difficult for students to plot it with reasonable accuracy. The software-plotted graph was originally created using GRAPH, a freely available open-source program. TES does not support upload of GRAPH data files but if you would like a copy of it showing the plotted graph then please email me at kevin_alderson@yahoo.co.uk. Please be assured that I will only use it for this purpose. I will not share your email with anyone else, nor will I use it for promotion of my resources or any other reason.

Worksheet consists of four longer, exam-style exercises based on real-life applications, covering force, mass and acceleration (two exercises: one about force exerted by a factory drop-hammer, the other about the acceleration and mass of racing cars), manufacturing costs (one exercise: about unit costs and areas of carpet rolls made in a factory) and density, mass and volume (one exercise: finding densities and volumes of two new types of plastics developed in a laboratory). All exercises require simultaneous equations to be constructed by interpretation of the problem. The first exercise leads to a linear equation, the rest to quadratic equations that must be solved by either completing the square or using the Quadratic Formula. A short introduction is given for each set of exercises to give students some insight into the concepts on which they are based. The questions are challenging but are also sort of 'formulaic' in that once you know how to do one the rest become much easier. If you want to work through an example first with your students then check out my free resource entitled &quot;GCSE Higher exam-style quadratic problem&quot;, which includes a fully-worked model answer. The latter is a density, mass and volume problem very similar to the one in this resource except that the numbers used are different, thus giving totally different results. <br /> <br /> DOCX and PDF worksheets supplied along with fully-worked model answers in JPEG format.

This worksheet is aimed at students capable of attaining levels 6, 7, 8 or 9 of the new maths specification. This is a high-quality resource but priced low to encourage sales. I'm not bothered so much about the money, I just want people to use it and evaluate it. Worksheet consists of three longer, challenging exam-style exercises based on practical applications, using formulae for cylinders and spheres. The last sheet lists the formulae students will need to use. Diagrams are used to illustrate all three exercises. Each exercise has multiple parts. The 1st exercise requires additional skills with ratios; the 2nd requires skills in both simultaneous and quadratic equations (this is hinted at in the question by saying 'Using an algebraic method..'); and the 3rd requires skill in creating an equation that links the volumes of a cylinder and a hemisphere. In the latter, calculation of the surface area of the machine part (see cover image) is more complex than normal, though entirely logical. This is a Level 8 or 9 type of exercise, but is not too difficult as long as a methodical approach is taken. This exercise also includes using density and volume to calculate a mass of zinc needed to galvanise a production run of the machine part. There are also various measurement conversions required such as converting cubic millimetres to cubic centimetres and litres, and grams to kilograms.<br /> <br /> DOCX and PDF worksheets supplied along with 9 pages of fully-worked model answers in JPEG format.

This worksheet has three longer exercises similar to the types of questions found on typical specimen 2017 Higher maths papers.<br /> <br /> DOCX and PDF worksheets supplied along with 2-page solution in JPEG format.

This is a longer, exam-style problem that requires the densities of two very different types of plastics to be found. It involves interpreting a description to form two simultaneous equations. The equations are based on the formula for density i.e. mass divided by volume. When combined these form a quadratic equation that must be rearranged to the form ax^2 + bx + c = 0 to solve it. The equation will not factorise, so completing the square method or the Quadratic Formula must be used. When both densities are found, there is a further requirement to express the ratio of the higher density plastic to the lower density plastic.<br /> <br /> DOCX and PDF worksheets supplied along with 2-page solution in JPEG format.

I've used this worksheet for revision with my Higher-streamed GCSE students aged 13 <br /> to 15. The exercises start from an easy level but get progressively harder and test skills in basic (i.e. one bracket) factorisation, making the first term in bracket positive, grouping &quot;two and two&quot;, difference of two squares, and simplifying expressions by expansion, grouping like terms, re-factorising and cancelling. Does not include any quadratic factorising.<br /> <br /> Created using MS Word 2007. Feel free to edit. PDF also supplied. REVIEWS WELCOME.<br /> <br />

Updated 16/3/2017 - part-question (e) added.<br /> <br /> This worksheet involves two concentric circles centred on the origin, with 3 straight lines tangent to the inner circle and cutting the outer circle. No quadratic equations are needed for this problem, rather it tests students' understanding of straight line properties, perpendiculars, surds, circle equations and circle formula. Marks have been assigned for each part-question. This is an original worksheet - it's not copied from an exam paper. DOCX and PDF worksheets supplied along with 1-page written solution in JPG format.

Includes tips on rearranging equations, worked examples, exercises and answers. I've used it for revision with my Higher-streamed GCSE students aged 13 to 15. The exercises start from an easy level but get progressively harder. There are some references to formula such as the Cosine Rule and an equation of motion. Feel free to edit the Word version to suit.<br /> <br /> Version 2 update includes more tips and exercises than the first version. There are now 12 exercises instead of 7. <br /> <br /> REVIEWS WELCOME. Answers were checked before publishing but I will correct any errors if notified to me.<br /> <br /> Created using LibreOffice Writer and Math and saved in MS Word and PDF formats. Please note that the equations only display correctly in the .docx format for Word files. Saving the file in the older .doc format causes the font size to shrink and the equations to move upwards and out of line with the accompanying text.

Version 2 includes more questions on length conversions as these were distinctly lacking. I have also added more conversion questions between imperial and metric and an extra currency question. <br /> <br /> I've used this worksheet for revision with my Higher-streamed GCSE students aged 13 to 15. Consists of diverse problems on Imperial, Metric and currency conversions, including area and volume conversions. Standard Form answers are required where appropriate. The longer 'wordy' questions relate to population density and international trade. There is a deliberate logic error in the wording of Q4. See if your students can spot it!<br /> <br /> Created using MS Word 2007. Feel free to edit. PDF also supplied. REVIEWS WELCOME.<br /> <br />

Includes a diverse range of rearranging problems. I've used it for revision with my Higher-streamed GCSE students aged 15. Some questions also require substitution of a value to solve for an unknown. All answers included.<br /> <br /> Created using MS Word 2007. PDF also supplied.

Includes worked examples, exercises and answers. I've used it for revision with my Higher-streamed GCSE students aged 13 to 15. The exercises start from an easy level but get progressively harder. Also includes a couple of exercises requiring substitution of values to solve for an unknown.<br /> <br /> Created using MS Word 2007. Feel free to edit. PDF also supplied. Answers were checked before publishing but I will correct any errors that I've missed, if notified to me.

Includes a diverse range of rearranging problems. I've used it for revision with my Higher-streamed GCSE students aged 15. Some questions also require substitution of a value to solve for an unknown. All answers included.<br /> <br /> DOCX and PDF files supplied.

I created this worksheet for BTEC Level 3 engineering students but it will also be useful for A Level students and possibly GCSE Higher students. Answers supplied on same page as exercises, because I found it better for the students to check each question as they go along because subsequent questions in Exercise 2 depend on previous answers.<br /> <br /> Worksheet created using MS Word 2007. PDF also supplied.

<p>This exercise is suitable for students capable of grade 5 upwards. It tests various aspects of maths such as bisecting a chord with a perpendicular from the circle centre, right-angled trigonometry, finding a sector angle and a segment area, and the area of a triangle.</p> <p>Worksheets supplied as Word and PDF. Answer sheet supplied as JPG .</p>