PiXL AQA Style Pre Paper 2H Practice Answers

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1 PiXL AQA Style Pre Paper 2H Practice Answers This set of answers is not a conventional marking scheme; while it gives a basic allocation of marks, its main purpose it to help students understand how to do each question and how they can avoid making mistakes. As such, its format is rather different from that of a normal mark scheme. The following guidance is adapted from that issued by AQA Types of mark M A B Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. Working out Usually, if the question asks students to show working, marks are not awarded to students who show no working. As a general principle, where the questions does not ask students to show working, a correct answer is awarded full marks. However, if the answer is incorrect, students can still obtain method marks, assuming that they show some valid working out. An incorrect answer with no working out is always awarded zero. Premature approximation Rounding off too early can lead to inaccuracy in the final answer. This is normally penalised by 1 mark. Q Answer Mark Comments cm Multiply the diameter (here it is 12.6cm) by π Most scientific calculators will calculate operations in the correct order if the calculation is entered correctly. Here, is calculated first, then the result subtracted from (a) b 2 = 196 b = 44 5 (b) q = 4 From 2q = 686, divide by 2 before taking the cube root. q = 7

2 6 Uses Pythagoras for BC BC = Use the full decimal you obtained for BC; don t round off decimals prematurely cm 2 The final 0 must be present for 2 decimal places. 7 Either = and = or = 5.40 and = 5.59 (other variants possible) 1.5 l box ticked Either divide the price by the quantity (to find the cost of 1 litre or 1 ml) or divide the quantity by the price (to find the quantity per 1 or 1p). There are several alternatives (ml or litres, 1 or 1p); two are given here. Both divisions must be correct for the second mark. As well as ticking the box, write down your conclusion from the calculations. Of course, ticking a box (even the correct one) with no working out will get you no marks. 8 sin 2 = cos 67 cos 58 = cos ( 58 ) These two should be ticked. Other indications (eg T and F for true and false, but why bother not using the tick? Make sure your calculator is set in degrees litres = gallons or 100 km = 62.5 miles seen 62.5 miles (your number of miles) (your number of gallons) 42.4 mpg Correct answer, rounded sensibly. 10 (a) Sight of an attempt to find.7 10 and an attempt to divide the result by will get you the method mark. Be very careful entering negative powers for standard form. Make sure you know how to use the standard form key on your calculator. Correct answer. Other roundings accepted (b) Nitrogen This is the only gas with a mass bigger than Keith s total. 10 (c) % Add to to find the total mass (or just add all five masses together from scratch) ( ) (total you found before) 100 Correct answer. Other roundings accepted.

3 11 (a) cos(angle) = 2 6 Not enough just to identify trigonometry here; you must use the correct trigonometric ratio (sin, cos or tan) and make a fraction with the numbers. angle = which is pretty close to 70 The ladder is safe so remember to tick the ladder is safe box. As ever, no working here means no marks. 11 (b) sin25 =? 2 or? 2 = cos50? = 2 sin25 or? = cos 50 You could split the isosceles triangle down its line of symmetry and make two right angled triangles, or you could use the cosine rule. If your method is about right, you will be let off a small mistake here. For the second mark there won t be any mistakes in your working out. 2.5 m Round your answer to a sensible level of accuracy. 12 (a) After a % reduction, there is 97% left. 12 (b) (i) 1.05 seen, or 6210, or or or 210 or or = or = Any correct method to find interest for one of the two years - this may be implied by sight of any correct amount of interest, or the value after one year. Correct answer seen, or 6900, or = 180 and = 900 Works out the value of 6000 invested for 5 years at % simple interest, or writes down multiplier for % simple interest over 5 years. 12 (b) (ii) Any method to increase by 2.5% at least once = or = Very similar to the and marks for part (b) (i). There is no need to round the amounts (although rounding to the nearest penny would seem sensible). It is, however, possible to make the comparison without using the 6000 at all. The multiplier for % simple interest over 5 years is 1.15 (see above); the multiplier for the compound interest is = 1.155, which is bigger than This would give full marks. Compound interest greater Correct answer; you must, of course, have complete, correct working out.

4 1 (a) You get half way to final answer; could be rearranging as far as x = 100 4x or x 100 4x (in other words, an attempt to move the 4x and the 100, even if they are incorrect, followed by a cube root) or a partial cube root (eg x 100 4x before getting stuck). Correct answer; you must, of course, have complete, correct working out. 1 (b) Use the iteration once and obtain the first value after or Find two values that both round off to the same amount to 2 decimal places. 4.5 Correct answer, must be to 2 decimal places. 85% or 0.85 used The sale price is 85% of the original; do not work out 15% of the sale price or 4.8 seen If 85% is 408, this will work out what 1% is, from which you can find 100% (a) 0 < t = = 5 Median is higher than 0 15 (b) Mid values seen Use the middle of each interval. Should be 7.5, 22.5, 7.5 and 52.5, but 8, 2, 8 and 5 would be accepted (had the question said that the times were to the nearest minute, they would have been correct anyway). If your method is right, you will be let off a small mistake here. Again, use of 8, 2, 8 and 5 for the mid values would be accepted. Whatever you get for the total time must be divided by the number of contestants. With 8, 2, 8 and 5, this would be minutes Could be rounded to 2. (2.6 with 8, 2, 8 and 5 ) 16 4 π Use the formula to find the volume of the object. Volume is m. 200 (whatever you got for the volume) 870 kg/m g/cm and The object will float in water but not in oil box ticked. Divide mass by volume to find density Correct answer; you must have complete, correct working out for this last mark.

5 17 (a) Area of path is 4 x x + 2 4x Any method to find the area of the path. This one is based on four squares (one at each corner) and two pairs of rectangles along the sides of the lawn. 4x x = 50 (Whatever you obtained for the area, simplified) = 50m 2 Reaches 2x 2 +11x 25 = 0 Correct answer; you must have complete, correct working out for this last mark. 17 (b) ( 25) m or 17 cm Even if you got (a) wrong, or you couldn t do it, you can still get full marks for (b). Whatever you do, use the printed equation, not yours if it is different. Any rounding instruction ( to the nearest centimetre ) when solving a quadratic is code for you need to use the formula. The first mark is for a good attempt, but it may have errors. No errors here; be careful with the minus signs. Best to discard the negative solution too, being the width of the path minutes 42.5 seconds = 42.5 seconds or 5 minutes seconds = seconds m or m or 5 minutes 42.5 seconds or 5 minutes seconds or 42.5 seconds or seconds = (slowest possible) or = (fastest possible) 4.8 m/s, because both bounds round to this amount. Either conversion seen anywhere. Remember that entering 5.42 on your calculator will not give you 5 minutes 42 seconds. There are 60 seconds in a minute, but your calculator is working in 10s, 100s, etc. Any lower or upper bound seen for the length of the course or the time taken. Either lower or upper bound for speed calculated. Both bounds now calculated correctly. This has less to do with the number and more to do with your justification for it. Make sure it is clear why you chose to use 2 decimal places. If the speed is only calculated using then 1 special case mark is awarded and no more. Although speed = distance time is part of this, the question is really all about bounds.

6 19 (a) Attempts sine rule: x sin50 = 8.5 sin68 x = 8.5 sin50 sin68 For allow minor errors. Completely correct 7.02cm Correct answer. Other roundings accepted. 19 (b) Attempts cosine rule For the lengths can appear in any position. cos(angle) = = cos(angle) and attempts to rearrange to find cos(angle) Reaches cos(angle) = 6 84 Must now be set up to find the angle between the 7cm and 6cm sides Correct answer. Other roundings accepted. Ratio of volumes 5 : or volume of screw A is 5 volume of screw B or volume of screw A is volume of screw B 5 or equivalent (eg 0.6, 60%, etc). 20 Ratio of lengths 5 : or scale factor of lengths is 0. 6 or Any use of a cube root to get to the ratio of the lengths. 4cm or 4cm or 4cm 5 or equivalent.7cm or ) Assume that t = 12 (but you can have if you wish) (2082 for ) and Yes, the population will be greater than 2000 ticked.