Higher Unit 9 Topic Test

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Name:Higher Unit 9 topic testDate:Time: 45 minutesTotal marks available: 41Total marks achieved:Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

QuestionsQ1.(a) (i) Factorisex2 – 12x 27.(ii) Solve the equationx2 – 12x 27 0.(3)(b) Factorisey2 – 100.(1)(Total for Question is 4 marks)Q2.Solve, by factorising, the equation8x2 30x 27 0.(Total for Question is 3 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q3.The expression x2 – 8x 21 can be written in the form (x – a)2 b for all values of x.(a) Find the value of a and the value of b.a .b .(3)The equation of a curve is y f(x) where f(x) x2 – 8x 21The diagram shows part of a sketch of the graph of y f(x).The minimum point of the curve is M.(b) Write down the coordinates of M.(1)(Total for Question is 4 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q4.Solve the simultaneous equations4x y 25x 3y 16x .y .(Total for Question is 3 marks)Q5.Solve the equationsx2 y2 36x 2y 6.(Total for Question is 5 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q6.A cinema sells adult tickets and child tickets.The total cost of 3 adult tickets and 1 child ticket is 30The total cost of 1 adult ticket and 3 child tickets is 22Work out the cost of an adult ticket and the cost of a child ticket.adult ticket .child ticket .(Total for question 4 marks)Q7.Solve 3x2 5x 1 0Give your solutions correct to 3 significant figures.(Total for question 3 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q8.–2 n 3(a) Represent this inequality on the number line.(2)(b) Solve the inequality 8x – 3 6x 4.(2)(Total for Question is 4 marks)Q9.3x 5 16x is an integer.Find the smallest value of x.(Total for Question is 3 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q10.(a) Solve the inequality 5e 3 e 12.(2)(b) On the grid, shade the region defined by the inequality x y 1(2)(Total for Question is 4 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q11.On the grid below, show by shading, the region defined by the inequalitiesx y 6x 1y 2Mark this region with the letter R.(Total for Question is 4 marks)Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Examiner's ReportQ1.It was disappointing to see that less than a quarter of candidates could factorise a three-term quadraticexpression correctly and then solve the associated quadratic equation. However, some managed tofactorise correctly and about the same number were able to give a solution where the 3 and 9 in the factorshad the incorrect signs.A surprising number of candidates did not realise that part (ii) followed on from part (i) and gave a solutioninvolving the quadratic formula. In part (b) only a quarter of candidates were able to correctly factorise aquadratic expression where the terms were the difference of two squares (a popular question to include ona Higher Tier paper).Q2.Factorisation of a quadratic function with non-unitary coefficient of x2 was poor. Many chose to employ theformula to solve the given equation. Any mistake in the use of the formula, which was more often than not,resulted in no marks. A fully correct solution by this method gained just one of the three available marks.Many did make good attempts at factorising but then failed to complete the solution. A common incorrectattempt at factorisation was (4x 9)(2x 3).Q3.This question was poorly answered. It was clear that only a small minority of candidates were wellpractised in the technique of completing the square. Candidates who realised what was required oftenwent on to carry out this technique but then spoiled their responses by writing a 4, b 5. Othercandidates wrote (x 4)2 5 then a 4, b 5. This was clearly incorrect working and could not be awardedthe marks. "8" and "21" were commonly seen incorrect answers. Part (b) was answered correctly by only asmall minority of candidates with many of the more able candidates failing to see the connection betweenthe two parts of the question.Q4.This was a standard simultaneous equation question which was, for some candidates a single step toeliminate one of the variables. Most candidates who had an idea of what to do multiplied the first equationby 3 and added. Those that subtracted were not awarded any marks. Others multiplied the secondequation by 4 and subtracted. Those that added were not awarded any marks. In fact, elimination ratherthan substitution was the overwhelmingly commonly seen approach. Often, the elimination was carried outincorrectly with the difference between 12x and – x being found as 11x, for example. Once again,arithmetical weakness meant that candidates were losing marks. Typical errors included: Getting to 13x 91 and failing to go any further Working out the difference between 64 and 25 and getting 41It was a pleasure to see some candidatesproperly checking their solution.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q5.The algebra required to solve these simultaneous equations was beyond the capabilities of most students,although the majority of students attempted the question. The first step was to perform a substitution intothe first equation. Those who did this were often able to go on to expand their squared bracket, although afrequent error occurred with the squared term. Many students were able to simplify their quadratic equationinto a form to be solved either by factorisation or by the use of the quadratic formula. Many studentsstopped at this point. It was pleasing to see a few go on to solve the quadratic, and to realise that theirvalues for x and y needed to be correctly paired.Q6.Only a minority of students chose to derive a set of simultaneous equations to solve. The majority ofstudents used a trial and improvement approach to the solution, which could only be credited on giving thecorrect answers. Common incorrect answers scoring 0 marks were 7.50 (from 30 4) and 5.50 (from22 4).Q7.The most common error was in using 5 instead of 5 at the front of the formula. Another common error wasin copying the formula but not extending the division line under the –b, or in performing thecalculations in the wrong order. Too many attempted T&I or factorising methods but failed to showsufficient progress to gain any marks.Q8.Part (a) of this question was quite well done though some candidates were unable to use the correctnotation, ie that of empty or solid circles, at each end of the interval. A relatively common error was forcandidates to draw a line from 1 to 3. It would appear that these candidates assumed that the valuesneeded to be integers but then drew a continuous line between the 2 values. Some candidates indicatedthe correct end points of the interval but did not draw a line joining them. In part (b) candidates often foundthe critical value 3.5 or equivalent and so gained one mark. However 3.5 alone or x 3.5 was often writtenon the answer line and examiners could not give this full marks. Poor manipulation of the inequality wasalso commonplace with incorrect simplifications such as 2x 1 seen.Q9.A large number of candidates failed to see the significance of the word ' integer' and so gave a fraction ordecimal as their final answer. Most candidates were able to reach a value of 3.6 or 3.7 by either solving theequation 3x 5 16 or dealing correctly with the inequality. Algebraic methods did not have to be usedand some candidates, aware of the meaning of integer, simply substituted in integer values of x until theinequality became false.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q10.Part (a) was often answered well with students scoring at least one mark. Many treated this as an equalitywhich resulted in e 2.25 for one mark. Many quoted e 2.25 and then simply write 2.25 on the answerline. This was not penalised. Failure to conclude with a value of 2.25 or equivalent was generally a result ofeither poor arithmetic (12 3 anything but 9 was common) or poor algebraic manipulation; many addinge to both sides of the inequality by mistake.In part (b), many students were unable to draw the straight line x y 1. The most common error was todraw the lines x 1 and y 1 and then shade the positive quadrant formed. Many drew the line x y 2.In addition shading was often in error showing confusion with the inequality.Q11.A fully correct solution was not the norm in this question. A great many candidates were unable to draw thethree lines correctly; x 1 and y 2 were often drawn as y 1 and x 2 and often x y 5 or x 6 andy 6 were drawn instead of x y 6. Shading, whether 'in' or 'out', was generally well done but credit wasdependent upon at least two correct lines.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Mark SchemeQ1.Q2.Q3.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q4.Q5.Q6.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q7.Q8.Q9.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Q10.Q11.Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in MathematicsHigher Unit 9 topic test Pearson Education 2015

Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Q3. The expression x 2 – 8 x 21 can be

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