Question Working Answer Mark AO Notes Grade 1 79 298 – 78 987 = 311 kWh used. 80 kWh × 20.95 pence = 1676 pence = £16.76 311 – 80 = 231 231 × 10.80 pence = 2494.80 pence = £24.948 Total bill = £16.76 + £24.948 = £41. 708 Assumption that if you average consumption over the year April will be representative. £41.71 Yes M1 B1 B1 B1 A1 C1 2 M1 for subtracting the given readings to find the amount of electricity used B1 multiplying 80 by 20.95 or for writing down £16.76 B1 for subtracting 80 from 311 and then finding the cost of the remainder used by multiplying by 10.80 or for writing down £24.948 B1 for adding the two amounts found together or writing down £41.708 A1 for converting to pounds correctly C1 for assumption made such as that given or showing that the standing order is higher than the cost of electricity used in April oe assumptions stated B 6
12 a b c i Jupiter ii Pluto iii Pluto iv Jupiter v Uranus vi Earth and Venus Diameter and mass increase with distance from the Sun until you reach Jupiter. Diameter and mass then decrease with distance from the Sun. B2 B6 C3 2 B1 for correct distance column B1 for correct diameter column B1 cao B1 cao B1 cao B1 cao B1 cao B1 cao C3 for clarity of explanation and of finding some trend within the data M 11 13 a b c d Sometimes true – not true for fractions or negative numbers. Always true (positive × positive = positive, Negative × negative = positive). False – you can’t find the square root of a negative number using real numbers. Always true – The cube root of a positive number is positive and the cube root of a negative number is negative. B1 C1 B1 C1 B1 C1 B1 C1 2 B1 for sometimes C1 for correct explanation B1 for always true C1 for correct explanation B1 for false C1 for correct explanation B1 for always true C1 for correct explanation M 8
14 i ii 56 ÷ 5-3 = 5(6 - -3) = 5 or =59 56 × 5-3 = 5(6+-3) = 53 or == 53 27 × 48 = n4 × 2c Using prime factors: 27 = 33 48 = 24 × 3 So 27 × 48 = 34 × 24 The power represents the reciprocal of squaring so take the square root. So n = 3 and c = 4 M2 M2 C2 M2 B2 A2 C1 2 M1 for showing subtraction of indices M1 for recognising 6 – –3 = 6 +3 or M1 for showing each number as a product of factors M1 for combining them to give all the 5s as numerators M1 for showing the indices are added M1 for recognising 6 + –3 = 6 – 3 or M1 for showing each number as a product of factors M1 for combining them to give all the 5s as numerators C1 for showing square root C1 for clear explanation M1 for finding the prime factors of each number M1 for stating each number as the product of the prime factors B1 for 27 expressed as product of prime factors in index form B1 for 48 expressed as product of prime factors in index form A1 for n = 23 cao A1 for c = 4 cao C1 for clear communication of solution M 11
17 So of the residential land is used for services. m2 = 13.75% 13.75% of the total area is used for services. C1 M1 A1 M1 A1 2 3 C1 for recognising and stating of residential development is used for the services M1 for multiplying by A1 oe M1 for finding above fraction of 15 and multiplying by 100 A1 accept 14 or 13.8 M 5
32 2.5 × 103 = 2500 Too small 2.5 × 104 = 25 000 2.5 × 105 = 250 000 Too big n = 4 M1 A1 2 M1 for using trial and improvement A1 for correct answer H 2 33 a b c d e f g h i j 0.6 0.9 1.3 0.3 0.1 1.2 1.5 1.4 2.1 3.5 B1 B1 B1 B1 B1 B1 B1 B1 B1 B1 2 cao cao cao cao cao cao cao cao cao cao H 10 34 Try a = 3, b = 4 = = = 5 a + b = 7 Statement is false. M1 A1 C1 2 M1 for finding an example which disproves the statement A1 for stating it is false C1 for clear communication of the solution H 3 35 For example: 2÷ = The cancels from numerator and denominator leaving 2, an integer. B1 P1 C1 2 B1 for a correct division of two surds P1 for showing how the surds will leave an integer answer C1 for clear communicating of method used H 3 36 a b For example: 3 + and 3 – For example: and B1 B1 2 B1 for a correct possible pair of surds B1 for a correct possible pair of surds H 2
37 is more than 1 and less than 2, since = 1 and = 2. So 1 + is more than 2 and less than 3. C1 C1 2 C1 for explaining the integer range for C1 for explaining how this relates to the 2 and 3 metres H 2 38 a b Earth diameter = 1.2756 × 104 km So radius = 6.378 × 103 Population = 7.185004 × 109 Surface area sphere = 4πr2 Surface area of the earth =4 x π x(6.378 x 103)2 = 5.1118593 x 108 km2 Per person = =0.07114622 km2 0.07 km2 It reduces the total surface area by 30% of the total. Multiply the area per person by 0.3. The revised answer is 0.021 km2. M1 A1 M1 M1 A1 M1 A1 C1 C2 2 M1 for halving diameter A1 for correct radius M1 for applying correct formula M1 for using correct formula with correct data cao not rounded Correct division of surface area by population A1 correct answer rounded to 1 or 2 sf C1 for a clear communication of solution C2 for a clear explanation of how the percentage makes a difference H 10
d e give an improper fraction. But any decimal with n recurring digits can be changed to a fraction by multiplying by 10n and eliminating the infinite part. a = 2.727 272….. 100a = 272.7272……. 100a – a = 270 99a = 270 a = a = 27.27272….. 100a = 2727.272……. 100a – a = 2700 99a = 2700 a = which is × 10 C1 C1 C1 M1 A1 A1 C1 C1 for clear explanation of easy C1 for clear explanation of more difficult C1 for clear explanation for any recurring decimal M1 for correct method of converting recurring decimal to fraction cao cao C1 clear communication of full answer. 11
41 Using the sine rule: = sin B = 35 × To maximise the angle we need to maximise this calculation by using the upper bound of sin 61° and 35 cm and the lower bound of 42 cm: sin B = 35.5 × sin B = 0.751 759 2 B = sin-1 0.751 759 2 B = 48.742 997° B = 48.7 (3sf) M2 B1 C1 B1 B1 B1 2 M2 showing how the sine rule is applied in this situation B1 for setting the equation with sinB as subject C1 for clear explanation of how we maximise the calculation B1 for calculation used with correct bounds B1 for correct value not rounded B1 for correct answer to 2 or 3 sf H 7