GCSE MATHEMATICS H Unit 2: Number and Algebra (Higher) Report on the Examination. Specification 4360 November Version: 1.

Transcription

1 GCSE MATHEMATICS 43602H Unit 2: Number and Algebra (Higher) Report on the Examination Specification 4360 November 2014 Version: 1.0

2 Further copies of this Report are available from aqa.org.uk Copyright 2014 AQA and its licensors. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even for internal use within the centre.

3 General Students found the paper accessible. Working was generally presented clearly and working was clearly shown in most cases. Arithmetic errors caused problems for students who had otherwise engaged with a question: some students could not correctly carry out multiplication, division and subtraction often after quite complex understanding had been achieved. Topics that were well done included: percentage reduction price comparisons with fractions and percentages sequence pattern expanding brackets and simplifying. Topics which students found difficult included: expression for nth term of a linear sequence proportion problem solving solving and showing an inequality on a number line factorising and solving a quadratic changing the subject of a formula multiplying with standard form algebraic fractions completing the square. Question 1 This question provided an excellent starter for many students. The majority were able to correctly work with the linked calculations. Question 2 This question was well answered. The majority of students correctly calculated 10% and then scaled up to 30% before subtracting from the initial amount to calculate the sale price. Some students gave an incorrect money notation answer of 2.80p. Question 3 This question was a good discriminator. The majority knew how to solve the problem and were able to work out 5%, but some students were unable to correctly calculate one fifth of 70 and made mistakes with multiplication. Question 4 Part (a) was well answered. Part (b) was not well answered with a common incorrect answer of n + 4 shown. There were a significant number of non-attempts. 3 of 6

4 Question 5 This question was a good discriminator, with the majority scoring marks. The majority did not use an algebraic approach. Most of those who were successful subtracted 30 from 110 and then halved their difference to find Ann s amount first. A common misconception was to divide 110 by 2 and then add 30 for an incorrect value of 85 for Tom. Question 6 This question was a good discriminator. Common errors were not multiplying the second term in the bracket to achieve 6x + 5 or not changing the sign on the final term when expanding the second bracket with multiplication by 2 to achieve 2x 8. Some students did not simplify their four terms correctly. Question 7 Both parts of this question were not well answered. In part (a) many students did not solve using the inequality symbol throughout. In part (b) the majority of students did not know how to show an inequality on a number line. Question 8 This question was a good discriminator. A common approach by many students was to convert their fractions to percentages by scaling their numerator and denominator to 100 or a Some students needlessly showed proportions for both boys and girls and this approach often caused confusion. Question 9 In part (a) many identified the correct factors of 24 but made errors with the signs in the brackets or did not choose the correct factor pair to add to 10. There were a significant number of nonattempts in part (b) even after a correct answer to part (a). A common misconception was to show the same signs for the solution as shown in their brackets and many did not know how to solve a quadratic after factorising. Question 10 This question was a good discriminator. Some students correctly converted the mixed numbers to improper fractions, but poor arithmetic skills caused errors. Other students changed the mixed numbers to decimals and used a build-up approach to find the total distance. Question 11 This question was not well answered. Some did not understand how to show division by 3 as an 4 12 algebraic fraction with a denominator of 3. A common misconception was y = x. Some 3 students incorrectly adopted a flow chart approach to correctly find the inverse operations and y gave the answer as 4x = 12 by not using the flow chart in reverse. 3 4 of 6

5 Question 12 Both parts were attempted by the large majority, but many students showed very poor knowledge of the equation of a line and most were unable to find the y-intercept or gradient from the equation of the straight line. Question 13 The majority of students did not answer the question well. A common misconception was to multiply and apply index laws to the powers of 10 but leave a final answer of , without converting into standard form. Where students converted standard form into numbers before multiplying, incorrect place value manipulation and poor arithmetic caused incorrect solutions. Some left their answer as whilst others did not correctly convert into standard form. Question 14 This question was a good discriminator. Many failed to recognise this question involved simultaneous equations and did not attempt to set up equations to solve in the conventional manner. The large majority of students who were successful simply added to find the price of 5 fish and 5 portions of chips and then divided by 5. There were many attempts to subtract to find the price of 1 fish and 3 portions of chips which often did not lead to success. Some poor arithmetic was seen after a correct method had been used. Question 15 There were a significant number of non-attempts and the question was not well answered. Many students did not know how to achieve a correct common denominator of x(x 2) and of those who found the denominator, many failed to correctly find the numerator with a common misconception 4x 3x 4x 3x 2 4x 3x 6 of or failing to correctly expand the bracket leading to or. x 2 2x x 2 2x x 2 2x Question 16 Many students were unable to correctly manipulate surds. After successfully finding many incorrectly showed giving an incorrect final answer of 25 2 or leading to then and There were a significant number of non-attempts. Question 17 This question was a good discriminator. Errors in expanding brackets ranged from missing square indices of the first x and last y term, missing an x or y from the two middle terms, incorrect multiplication of numbers and also incorrect signs on both the third and fourth terms. The majority of students were able to correctly simplify by collecting their four terms. Question 18 There were a significant number of non-attempts. Those students who were successful used a method to find half of 8x to correctly identify a = 4, but did not then know how to go on to find the correct value of b. Common misconceptions were ( x + 4) and (x + 4) of 6

6 Question 19 This question was a good discriminator. Most students were able to substitute correctly into the formula. Those who had further success worked with a common denominator of 1.8 and then went on to achieve = or =. R 1.8 R 18 Question 20 This question was not well answered and there was a large number of non-attempts. Some 3 students did not know that 64 = 4. Others were not able to correctly evaluate = 4 and did not recognise a negative power as the reciprocal. 4 and 2 1 were common incorrect answers Question 21 The large majority of students did not answer this question well. Working with powers of 2 and 3 was a common approach rather than equating and applying index laws. Some students worked out 2 5 p 5 = 32 by listing powers of 2 but were unable to proceed further than 9 = 3 Some p students were able to achieve 9 = 243 by listing powers of 3 but did not have the knowledge to find p as a fractional power. Mark Ranges and Award of Grades Grade boundaries and cumulative percentage grades are available on the Results Statistics page of the AQA Website. Converting Marks into UMS marks Convert raw marks into Uniform Mark Scale (UMS) marks by using the link below. UMS conversion calculator 6 of 6