Mathematics. Foundation. Set E Paper 2 (Calculator)

Transcription

1 Mark scheme Ch 1 Mathematics oundation Set E Paper 2 (Calculator) 80 marks 1 expression 1 Award 1 mark for correct answer. Students often find the distinction between these terms difficult Award 1 mark for correct answer. Some students may forget to calculate the total number of balls for the denominator. 1 Award 1 mark for correct answer. Some students may reason that there are three options, both heads, both tails, one head and tail, and so choose, not realising that the three options are not equally likely cm 2 1 Award 1 mark for correct answer. Some students may not check the units carefully, or may add the two lengths rather than multiplying, or find the perimeter. 5 a cuboid b rhombus c hexagon d cone e cylinder 5 Award 1 mark for each correct and correctly spelled. 1 3 Students will be expected to spell the names correctly as they have been given a list to use. Some students may confuse cone and pyramid, and may not recognise the hexagon as it is irregular = 81 7 a 4 7 b 1 2 Award 1 mark for or equivalent calculation. 2 Award 1 mark for each correct. Students Accept 7 for b. 7 Some students may find 10% and 5% first and multiply up. may not realise immediately that the probability in b is 1. 8 The values 3.2 and 4.5 have been added without consideration with the order of magnitude AND The orders of magnitude have been added 2 Award 1 mark for each point. Alternative, sensible wordings are acceptable. Students may be confused by the fact that 7.7 is an incorrect value even though the two numbers are being added together. oundation Set E Paper 2 (Calculator) Mark scheme

2 together as though the two numbers are being multipled together rather than added. 9 a b 1 cm 3 cm 10 cm 1 cm 5 cm 6 cm 1 cm 1 cm 30 cm 2 cm 3 cm 5 cm 3 a Award 1 mark for correct answer. b Award 2 marks for 4 possible sets of dimensions with no repeats. Award 1 mark for 2 or 3 sets of possible dimensions. Students may not realise that their answer to part a can help them with b. They may not realise that they have given the same set of dimensions in a different order. Students often find this type of open-ended question difficult, as they do not know how many answers they need to find. 10 A = 2r(2r + 9) πr2 3 Award 1 mark for 2r(2r + 9) or equivalent, ignore subsequent working if this is wrongly expanded for this mark only. Award 1 mark for 1 2 πr2 The final mark is for adding two correct expressions and equating to A. Students usually do better on the rectangle part. or the semicircle, common errors are forgetting to halve 2r for the radius, forgetting to halve the area of the circle or using the circumference formula. 4 Award 1 mark for Volume = = cm 3 Density = = = 7.80 g/cm 3 Award 1 mark for dividing mass by their volume. Award 1 mark for (accept without units). Award 1 mark for correctly rounding and incorrect density. 12 a 6 Award 1 mark for each of a d correct. In e award 2 marks for 2n 1. Award 1 mark for 2n. Students may not use the correct volume formula and/or density formula. Students may give the final answer as 7.8, not realising the zero is needed as the question asks for 2 dp. Students may find the number of squares in pattern 6 by drawing. They may not consider the sequence as two sequences of different coloured squares, and so find part d difficult. oundation Set E Paper 2 (Calculator) Mark scheme

3 b White squares sequence is 1, 1, 3, 3, 5, 5,... 5 c Total squares sequence is 1, 3, 5, 7, 9, 11, d Black squares sequence is 0, 2, 2, 4, 4, 6, 6,... Always even e 2n 1 13 a (0, 0) b (0, 2) 2 Award 1 mark for each correct. Students tend to be more familiar with the shape of the curve y = x 2 than y = x 2 + k, so part b is likely to have more incorrect answers, such as (2, 0) and (0, 2) cm 3 1 Award 1 mark for correct answer. Students often confuse the conversion factors for lengths, areas and volumes. 15 a 3 : 2 (or 2 : 3) 4 a Award 2 marks for 2 : 3 or 3 : 2 A common error in b is to calculate b 60% Award 1 mark for 200 : 300 3/2 or 2/3 as a percentage. or 300 : 200 b Award 1 mark for 60%. Award 1 mark for % 16 a = a Award 2 marks for 0.15 Award 1 mark for equivalent. Some students will find it difficult to use the relative frequency to calculate the original number in b. oundation Set E Paper 2 (Calculator) Mark scheme

4 b 6 = 0.05 b Award 2 marks for 120. Award x x = 6 6 = mark for or equivalent c Award 2 marks for 84. c Award 1 mark for their 120 = y = 2x 3 2 Award 1 mark for an equation y = mx + c with intercept 3 or gradient 2. Students usually find the gradient harder than the intercept and occasionally use points that are not integers in gradient calculations depending where they decide to work from. 18 a 4.48 b 731 c 17.9 d a 6.4 cm b angle Q 20 a 5 6 = = 1 b 6 4 Award 1 mark for each correct. Students who do not use the power key are more likely to make errors with repeated multiplications. In c a common error is only to include 2 8 under the square root sign when keying it into the calculator. Some may make errors writing their answers to 3sf, for example giving 3 dp. 2 Award 1 mark for each correct. Students sometimes have difficulty identifying equal sides and angles when the triangles are flipped over as 3 a Award 2 marks for 1. Award 1 mark for total 30. b Award 1 mark for correct median for their data set of five values from a. here. Students sometimes have trouble when working backwards and forget that the total is the mean the number of data values. These students sometimes use a trial and improvement method or occasionally an algebraic approach e.g. x = = 4.0 (1 dp) 2 Award 1 mark for Do not accept 4. Students do not always realise they need to give the value in the decimal oundation Set E Paper 2 (Calculator) Mark scheme

5 place, even if it is zero a + 3c = (1) 3 Award 1 mark for a correct pair of Students who do not read the question a + 2c = (2) equations. Award 1 mark for carefully may waste time calculating 4a + 8c = (3) = (2) 4 either correct multiplication of an the values of both tickets. 5c = (3) (1) equation to give equal coefficients c = 3450 = 690 of one of the variables or a correct 5 substitution. Award 1 mark for the No, she has forgotten to make y the subject. The intercept should be 1 and the gradient should be 2. correct answer. 1 Award the mark for any equivalent answer. This is a common error so some students may think she is correct. 24 5( 1 + 6x) 1 Award 1 mark for correct answer. Taking out a negative common factor is more challenging and some students may have incorrect signs inside the brackets Award 1 mark for fx column completed with no more than 1 error, and 1 mark for fx = 275 (or correct sum of their fx column) allowing 1 error in the fx column. The most common error is to add up the frequencies and divide by = a or 20 km b tan R = R = = or a Award 3 marks for 20.2 or 20, accept with no units given. Award 1 mark for (= 410). Award 1 mark for their 410 b Award 4 marks for or 327. Students may not realise that West and South are at right angles. In part b some students may use sine or cos, with their value from part a. Some students may calculate the wrong angle, or forget to subtract it from 360 to give the bearing. oundation Set E Paper 2 (Calculator) Mark scheme

6 Award 1 mark for tan used. 13 Award 1 mark for tan R = 11 (= ). Award 1 mark for 32.9 or 33 Award 1 mark for 360 their Award marks for sine or cos used correctly with their PR from part a. 27 a 1000 (1 + x 100 )6 = a 6 b ( ) 100 = = 4 % (nearest 1000 whole number) 4 a Award 2 marks for correct answer. Award 1 mark for (1 + x 100 )6 b Award 2 marks for correct answer. Award 1 mark for seen. 4 a Award 2 marks for all correct. Award 1 mark for 2 correct expressions. b Award 2 marks for all correct. Award 1 mark for 2 correct expressions. Students may not see that they need to divide x by 100 and add 1 to get the multiplier. When a simplifying question is presented in a different format some students will struggle with this. Part b is likely to prove more challenging because students will be expected to work backwards to get to missing values. Students may make errors when dealing with negative signs in the powers. b oundation Set E Paper 2 (Calculator) Mark scheme

7 TOTAL OR PAPER IS 80 MARKS oundation Set E Paper 2 (Calculator) Mark scheme