GCSE MARKING SCHEME APPLICATIONS OF MATHEMATICS (LINKED PAIR PILOT) SUMMER WJEC CBAC Ltd.

Transcription

1 GCSE MARKING SCHEME APPLICATIONS OF MATHEMATICS (LINKED PAIR PILOT) SUMMER 2015 WJEC CBAC Ltd.

2 EAS Practice Papers SET2 Mathematics Numeracy Unit 1 Foundation Tier SET 2 Numeracy U1 FT Mark Comments B 1. Indicates the five correct dates. 8th, 1th, 15th, 2th and 25th. (April 201) For all five with no extras. B3 for four, for three, for two. Penalise extras as follows, -1 for 1 or 2, -2 for 3 or, -3 for 5 or and - for more than (only from marks gained). Strategy of looking at 12 out of 20 or equivalent. Strategy of looking at 5 out of 8 or equivalent Statement that both are correct. 2. 1st Diagram Circle : Square : 5 2nd Diagram Right Hand Circle : 7 Square : -15 Bottom Circle : -18 All parts (a) (b) marked at the same time To be viewed with diagram 3.(a) Missing inside segment = 2 Perimeter = = (cm) To be viewed with diagram (b) Area = OR (= 2 + 3) (= 72 12) = 0 cm2. a) Multiples of 7 b) 28 and 35 placed correctly 5. Any correct strategy for finding the need for paying for 9 bottles from Len s store AND 8 bottles from Deb s store 9 90(p) or 8 ( ) (p) or ( )8.10 or ( )8 810(p) or ( )8.10 AND ( )8 AND Deb s store Organisation and communication Accuracy of writing. Use overlay 2 rectangles cm by 3cm 1 rectangle cm by cm 2 rectangles cm by 3cm Makes a correct net S1 S1 7 5 S1 U1 3 S1 OC1 W1 Correct numbers must be compared for award of S1 marks. S0,S0, for an unsupported correct statement. FT from a negative answer in the square You must also check the diagram for any working. Must be seen in part (a). Attempt to add all sides of the shape. Use 2+2x for where x stands for their 2 S1, for methods that imply the '2', e.g C.A.O. Attempt to add all areas of the shape OR difference of areas C.A.O. Independent of all other marks. for either Or equivalent Or equivalent Or equivalent Use overlay (± 2mm) To gain each, each pair of rectangles must not be disjointed Penalise 1 only, if height of 1 cm used.

3 7. (2 x adult one-day tickets 2 x = ) 3 AND (2 x child one-day tickets 2x = ) 35 (2 x adult individual rides 2 x x 2.50 = ) 30 (2 x 8 child individual rides 2 x 8 x 2.50 = ) 0 (Tickets are )2 child one-day tickets and 12 (adult) individual ride tickets (Cost = = ) 5 8. (a)an attempt to find values that can be directly compared. Finding (Zac) 0/100(oe) (Josh) 2/100 (oe) (Lowri) 58/100 (oe) OR OR OR Most: Josh AND least: Lowri (b) (8 =) 8 (8 + 9 =) Ribbon marking for 12(a) and (b) (a) 0.15 ( )80 or equivalent OR an attempt to calculate 2 ( )22 (Total cost = ) 0.15 ( ) ( )22 or equivalent ( =) ( )00 (b) (Difference in price =) ( )00 ( )80 OR ( )120 (Percentage increase =) 120/80 100% or equivalent 25% To be viewed with diagram 10. Volume = ( ½) = 1500 (cm3) = 1500/1000 = 1 5 litres 5 5 Accept a sight of 78 Accept sight of 70 for 2nd and 3rd s. May be implied by answer of 5. FT their prices for the cheapest option. SC1 B0 if sight of ( )78 and ( )70 AND conclusion to buy individual ride tickets All %, OR all fractions with common denominator, OR all decimals, OR a valid combination e.g. Zac 3/5 = 0% = 0. All fractions must have the same denominator If only one error made, then FT. SC1 if most: Josh, AND least: Lowri with no supporting work. Alternative: FT their 8 n 5 = 8 n = 102 n = 17 FT their 102 Valid method for finding either 15% of ( )80 OR 2 ( )22 (implied by sight of ( )72 or ( ) 528 respectively) A complete correct method CAO Attempt to find difference in price. FT their (a) A complete correct method OR 00/80 100(%) (= 125%) 00/80 100(%) 100(%) 25(%) No need for the ½ for the. CAO FT 'their 1500'/1000 litres not required but A0 for incorrect units.

4 To be viewed with table 11. (a) ( ) 8.0 and 10:35 (a.m.) (b) Taxi fare is ( )17 - ( )27 Tube tickets cost ( )20 Compares ( )17 with ( )20 Compares ( )27 with ( )20 12.(a) All points plotted correctly (b)true TRUE To be viewed with diagram 13. Area trapezium = ½ 5 ( + 10) = 0 (cm2) Triangle: ½ 10 x = 0 (x = ) 8 (cm) F.T. their figures Per person solutions Taxi fare is ( )17 - ( )27 Divides any taxi fare by 5 Compares ( )3.0 with ( ) Compares ( )5.0 with ( ) 2 taxis (Maximum 3 marks available) Taxi fare is ( )3 - ( )5 Tube tickets cost ( )20 Taxi (always) more than tube Intention: closer to the correct intersection than to any others for indication of at least 3 correct points Penalise joining point to point -1 for any correct For equating their 0 (any value) with ½ 10 x FT correct evaluation from their 0 (their value) SC2 for an answer 8(cm) from area of trapezium = 5 ( + 10) = 80 followed by area of triangle =10 x = 80, or SC1 for a 2 stage method equating 10 x with 5 ( + 10) with error in calculating x A full one stage method 10 x = 5 ( + 10) or equivalent is correct for 3 marks.

5 EAS Practice Papers SET2 Mathematics Numeracy Unit 1 Intermediate Tier SET 2 Numeracy U1 IT Mark Comments All parts (a) (b) marked at the same time To be viewed with diagram 1.(a) Missing inside segment = 2 Perimeter = = (cm) To be viewed with diagram (b) Area = OR (= 2 + 3) (= 72 12) = 0 cm2 To be viewed with table 2. (a) ( ) 8.0 and 10:35 (a.m.) (b) Taxi fare is ( )17 - ( )27 Tube tickets cost ( )20 Compares ( )17 with ( )20 Compares ( )27 with ( )20 3. (a)travel dates = 15th 22rd (November) (b) (month before =) Sight of 15th October (three weeks before =) 2th September (c) (Eastplane based in the) UK with valid reason (d) (AF112) = 0:25(+1) 22:0 (= 7hrs 5 min) (Flight time =) 7h 5m h = 3h 5m (e) Explanation referring to the flight time being exactly hours OR need to take into account time difference of hours S1 U1 8 You must also check the diagram for any working. Must be seen in part (a). Attempt to add all sides of the shape. Use 2+2x for where x stands for their 2 S1, for methods that imply the '2', e.g C.A.O. Attempt to add all areas of the shape OR difference of areas C.A.O. Independent of all other marks. F.T. their figures Per person solutions Taxi fare is ( )17 - ( )27 Divides any taxi fare by 5 Compares ( )3.0 with ( ) Compares ( )5.0 with ( ) 2 taxis (Maximum 3 marks available) Taxi fare is ( )3 - ( )5 Tube tickets cost ( )20 Taxi (always) more than tube Look at calendar for indication for this part of the question Award for any indication e.g. start holiday on 15th November. FT for subtracting a month from their 15th Nov 15th October could be implied FT for subtracting 3 weeks from their 15th Oct If no marks gained SC1 for subtracting 3 weeks then subtracting a month (25th October; 25th September) OR for subtracting weeks rather than a calendar month (25th October; 27th September) Reason could include reference to: 0 minute turnaround at Moscow; outward flight code EP01 followed with return flight code EP02; first flight of the day, etc Be generous with this mark. Condone reference to Outward and Inward above timetables. -hrs might be implied by both times given as London or Moscow times (gains second ). (look for 02:25(+1), 02:0(+1) ) FT their 7hrs 5 min Could refer to needing to add hours to the difference (0 hours). Ignore further extraneous explanation.

6 .(a) All points plotted correctly (b) Line of best fit with points above and below (c)true TRUE 5. No, Yes, No Far Flung: No and most expensive or most often late Statement that implies Celtic Flights is more reliable than Roly Air. Ribbon-marking for parts (a) and (b) (a) 0 15 ( )80 or equivalent OR an attempt to calculate 2 ( )22 (Total cost = ) 0 15 ( ) ( )22 or equivalent ( =) ( )00 Organisation and communication Accuracy of writing (b) (Difference in price =) ( )00 ( )80 OR ( )120 (Percentage increase =) 120/80 100(%) or equivalent 25(%) 3 OC1 W1 8 Intention: closer to the correct intersection than to any others for indication of at least 3 correct points Penalise joining point to point -1 The line must be fit for purpose, it should not pass through the intersection of the axes Ignore also joining point to point for any correct Accept percentages used within comparison Do not accept percentages quoted without interpretation. Accept statements such as only 7% as a comparison No with statement of 1 of the 2 reasons Unambiguous and not contradicted. In either reason box for Celtic Flights or Roly Air Valid method for finding either 15% of ( )80 OR 2 ( )22 (implied by sight of ( )72 or ( ) 528 respectively) A complete correct method CAO Attempt to find difference in price. FT their (a) A complete correct method OR 00/80 100(%) (= 125%) 00/80 100(%) 100(%) 25(%)

7 7. (a) Neither school can be accommodated in the Red block OR equivalent statement (b) A correct allocation of rooms Red block - females Teachers S 2 Room C (8) 8 Room A () Room D () Corridor Room B () Room E() Teachers L 2 Room F (8) 8 B3 If incomplete or incorrect award for a correct allocation of rooms for girls S = 8,8 and L =,,, OR S =,, and L =,8,8 OR S =,,8 and L =,,8 (no need to fill number in room as all beds used) for correct possible allocation of rooms for boys e.g. S=,,8,8 and L = 10,10 (many combinations) for correct possible allocation of beds for boys e.g. S =,,7,7 and L = 10,8 (many combinations) Be aware that there are multiple correct answers for allocation of rooms. Need to check no. of beds used for boys as not at full capacity. Green block - males Teachers Room A S () 2 Room B (8) Teachers L 2 Room C (10) Room D () Corridor Room E(8) Room F (10) 8. A comment that states that it may appear that reported crime has decreased because the axes are not perpendicular. 2 Accept any wording that suggests this. if only refers to the misunderstanding. if only refers to the reason.

8 9. Method 1 (total profit = total selling price total cost price) (Money taken for full-price fruit cakes =) ¾ x 20 x ( ) (= ( )90) (Money taken for reduced-price fruit cakes =) 5 x 0.7 x ( ) (= ( )21) (Total money taken for chocolate cakes =) 13 x ( ) x ( )1 (= ( )28) (Total cost =) 20 x ( ) x ( )1 ( =( )75) (Profit =) ( ) [ ] - ( )75 = ( ) OR Method 2 (total profit = fruit cake profit + chocolate cake profit (Full-price fruit cake profit =) ¾ x 20 x ( ) - ¾ x 20 x ( )3 OR ¾ x 20 x ( )( - 3) (= ( )5) (Reduced-price fruit cake profit =) 5 x 0.7 x ( ) - 5 x ( )3 OR 5 x (0.7 x ( ) - ( )3) (=( )) (Full-price chocolate cake profit =) 13 x ( )2-13 x ( )1 OR 13 x ( )(2 1) (=( )13) (Reduced-price chocolate cake profit = 0) (Total profit =) ( ) [ (+0)] = ( ) 10. (a) All 9 numbers placed correctly OR B3 Or equivalent e.g. ( ) 0.0 x 5 x 7 FT from their ¾ x 20 Consideration of + 2 x ( )1 can be implicit FT provided at least awarded C.A.O. for sight of 5 x 0.7 x ( ) or ( )1.20 FT from their ¾ x 20 FT provided at least awarded C.A.O. for any 7 or 8 numbers placed correctly, the other numbers omitted or incorrectly placed, OR for any 5 or numbers placed correctly, the other numbers omitted or incorrectly placed. Any ambiguous duplicates are marked as an incorrect placement for that number (b) Venn diagram 2 AND full reason, e.g. multiples of are a subset of multiples of 2 and there is a multiple of 2 which is a multiple of 5, or set B is a subset of set A, and set A intersects with set C, or A & B share some of the numbers, but C only shares numbers with A, or C & B have nothing in common, and B shares everything with A E2 5 OR selects Venn diagram 2 and explains why the other 2 Venn diagrams are not selected for choice of Venn diagram 2 AND a partial reason, i.e. only mentions 1 aspect or attempts an explanation e.g. times table is within 2 times table, or shows which of A are within times table, or 22 is in A but not in C, or no multiples of in C OR for selection of Venn diagram 2 and explains why 1 of the other 2 Venn diagrams are not selected Accept informal words such as within for subset, overlap for intersection

9 11. Straight lines parallel to all verticals and horizontals, with lines of radius distance away from the steps (+2mm) All inner steps, locus turn at 90 vertex All outer steps, arcs with wheel radius (+2mm) 12. (a) Reason, e.g. outside the bookshop (b) Two boxes if you are 30 (c) Suitable question with at least 3 boxes, no overlaps or gaps and prices from a low value upwards (to maybe 20) considered or a number of boxes given but concentrated at lower prices x Class A has 12 girls Class B has 18 girls There are twice as many girls as boys in class B, or ⅓ of class B boys, or ⅔ of class B girls Class B has 9 boys 5 for straight lines, or series of points (>), parallel to 2 verticals/horizontals, radius distance away (+2mm), OR straight lines parallel to all verticals and horizontals but not radius distance away Do not accept curves with free hand sketches for arcs with wheel radius (+2mm) at 2 outer steps, OR intention of arcs at all outer steps but not necessarily at wheel radius If B5 penalise extra lines drawn -1 Accept reference to people not buying, but checking out ready for downloading, showcasing, or that older people are more likely these days to buy from shops than younger people Do not accept reference to groups under 20 and over 0. Or refers to widths groups for younger or older people, or unequal groups. Allow overlap(s). Ignore incorrect response if correct response is given. Do not accept doesn t give options for under 20s or over 0s, or 2 options for 20 year olds Suitable question with at least 3 boxes, with either consistent overlaps or gaps OR a suitable range of prices is not considered, OR for suitable choice of groups with no gaps or overlaps but without a suitable question being asked Examples of consistent overlaps or gaps: 0-5, 5-10, 10 - under 5, - 10, 11-15, 1 - over 5, over 10, over 20 * *however possible if asked to tick only one box FT 1½ their 12 correctly evaluated (but NOT 1½ ) Sight of 18 implies first, OR Class B: Angle girls 20 ±2 and angle boys 120 ±2 This may be implied from their numbers of girls and boys in class B Note: ⅓ of 18 does not imply ⅓ of class B boys, hence B0 18 is ⅔, implies CAO

10 15. (a) (Millet) 3 850/10 255(g) (b)attempt to find unit cost e.g. for 1kg (For the 250g bag, 1kg costs) 1.9 (For the 300g bag, 1kg costs) 1.80 (For the kg bag, 1kg costs) 1.90 Considering buying 10 or more 300g bags S1 CAO OR for one correct costing for 5kg e.g. ( )7(.)0 + 9(p) = ( )9(.)5 OR At least 2 combinations of bags to a total of 5kg OR any 2 correct costings for buying 5kg OR stating any 3 possible combinations of bags to 5kg 250g 300g kg Cost = = = = 9.08 Working with or choice of 15 of the 300g bags, or with an answer of 1(. ), 17 or 1, or trials including 15 or 1 or 17 of the 300g bags (Cheapest way to buy 5kg is 15 (300g bags) at 5(p) + 2 (250g bag) at 9(p) = ( )8(.) (p) ) = ( )9(.)08 1(a)(i) 2950 (miles) 3050 (miles) 79.5(hours) or 79 ½ (hours) or 79 h 30 min 80.5(hours) or 80½(hours) or 80 h 30 min (b)(ii) Volume scale factor 27 Length scale factor 3 of larger pebbles needed (15/3 = ) OR equivalent, e.g. repeated additions or multiples, All correct entries for any 2 correct entries Do not accept 79.3 or 80.3 as 2 correct entries, allow this as equivalent to counting 1 correct entry FT their greatest distance divided by their least time, provided distance >3000 and time < 80 Accept sight of Allow for sight of 5/2 or 27 provided not connected to irrelevant working Accept Allow for sight of 3 provided not connected to irrelevant working Award of the 2nd implies also the 1st SC2 only for an answer of 5 without relevant working

11 EAS Practice Papers SET2 Mathematics Numeracy Unit 1 Higher Tier SET 2 Numeracy U1 HT Mark Comments 1. (a)travel dates = 15th 22rd (November) (b) (month before =) Sight of 15th October (three weeks before =) 2th September (c) (Eastplane based in the) UK with valid reason (d) (AF112) = 0:25(+1) 22:0 (= 7hrs 5 min) (Flight time =) 7h 5m h = 3h 5m (e) Explanation referring to the flight time being exactly hours OR need to take into account time difference of hours 2.(a) All points plotted correctly (b) Line of best fit with points above and below (c)true TRUE 3. No, Yes, No Far Flung: No and most expensive or most often late Statement that implies Celtic Flights is more reliable than Roly Air 8 3 Look at calendar for indication for this part of the question Award for any indication e.g. start holiday on 15th November. FT for subtracting a month from their 15th Nov 15th October could be implied FT for subtracting 3 weeks from their 15th Oct If no marks gained SC1 for subtracting 3 weeks then subtracting a month (25th October; 25th September) OR for subtracting weeks rather than a calendar month (25th October; 27th September) Reason could include reference to: 0 minute turnaround at Moscow; outward flight code EP01 followed with return flight code EP02; first flight of the day, etc Be generous with this mark. Condone reference to Outward and Inward above timetables. -hrs might be implied by both times given as London or Moscow times (gains second ). (look for 02:25(+1), 02:0(+1) ) FT their 7hrs 5 min Could refer to needing to add hours to the difference (0 hours). Ignore further extraneous explanation. Intention: closer to the correct intersection than to any others for indication of at least 3 correct points Penalise joining point to point -1 The line must be fit for purpose, it should not pass through the intersection of the axes Ignore also joining point to point for any correct Accept percentages used within comparison Do not accept percentages quoted without interpretation. Accept statements such as only 7% as a comparison No with statement of 1 of the 2 reasons Unambiguous and not contradicted. In either reason box for Celtic Flights or Roly Air

12 . Ribbon-marking for parts (a) and (b) (a) 0 15 ( )80 or equivalent OR an attempt to calculate 2 ( )22 (Total cost = ) 0 15 ( ) ( )22 or equivalent ( =) ( )00 Organisation and communication Accuracy of writing (b) (Difference in price =) ( )00 ( )80 OR ( )120 (Percentage increase =) 120/80 100(%) or equivalent 25(%) 5. (a) Neither school can be accommodated in the Red block OC1 W1 8 Valid method for finding either 15% of ( )80 OR 2 ( )22 (implied by sight of ( )72 or ( ) 528 respectively) A complete correct method CAO Attempt to find difference in price. FT their (a) A complete correct method OR 00/80 100(%) (= 125%) 00/80 100(%) 100(%) 25(%) OR equivalent statement (b) A correct allocation of rooms Red block - females Teachers S 2 Room C (8) 8 Room A () Room D () Corridor Room B () Room E() Teachers L 2 Room F (8) 8 B3 If incomplete or incorrect award for a correct allocation of rooms for girls S = 8,8 and L =,,, OR S =,, and L =,8,8 OR S =,,8 and L =,,8 (no need to fill number in room as all beds used) for correct possible allocation of rooms for boys e.g. S=,,8,8 and L = 10,10 (many combinations) for correct possible allocation of beds for boys e.g. S =,,7,7 and L = 10,8 (many combinations) Be aware that there are multiple correct answers for allocation of rooms. Need to check no. of beds used for boys as not at full capacity. Green block - males Teachers Room A S () 2 Room C (10) Room D () Corridor Room B (8) Room E(8) Teachers L 2 Room F (10). A comment that states that it may appear that reported crime has decreased because the axes are not perpendicular. 2 Accept any wording that suggests this. if only refers to the misunderstanding. if only refers to the reason.

13 7. Method 1 (total profit = total selling price total cost price) (Money taken for full-price fruit cakes =) ¾ x 20 x ( ) (= ( )90) (Money taken for reduced-price fruit cakes =) 5 x 0.7 x ( ) (= ( )21) (Total money taken for chocolate cakes =) 13 x ( ) x ( )1 (= ( )28) (Total cost =) 20 x ( ) x ( )1 ( =( )75) (Profit =) ( ) [ ] - ( )75 = ( ) OR Method 2 (total profit = fruit cake profit + chocolate cake profit (Full-price fruit cake profit =) ¾ x 20 x ( ) - ¾ x 20 x ( )3 OR ¾ x 20 x ( )( - 3) (= ( )5) (Reduced-price fruit cake profit =) 5 x 0.7 x ( ) - 5 x ( )3 OR 5 x (0.7 x ( ) - ( )3) (=( )) (Full-price chocolate cake profit =) 13 x ( )2-13 x ( )1 OR 13 x ( )(2 1) (=( )13) (Reduced-price chocolate cake profit = 0) (Total profit =) ( ) [ (+0)] = ( ) 8. (a) All 9 numbers placed correctly OR B3 Or equivalent e.g. ( ) 0.0 x 5 x 7 FT from their ¾ x 20 Consideration of + 2 x ( )1 can be implicit FT provided at least awarded C.A.O. for sight of 5 x 0.7 x ( ) or ( )1.20 FT from their ¾ x 20 FT provided at least awarded C.A.O. for any 7 or 8 numbers placed correctly, the other numbers omitted or incorrectly placed, OR for any 5 or numbers placed correctly, the other numbers omitted or incorrectly placed. Any ambiguous duplicates are marked as an incorrect placement for that number (b) Venn diagram 2 AND full reason, e.g. multiples of are a subset of multiples of 2 and there is a multiple of 2 which is a multiple of 5, or set B is a subset of set A, and set A intersects with set C, or A & B share some of the numbers, but C only shares numbers with A, or C & B have nothing in common, and B shares everything with A E2 5 OR selects Venn diagram 2 and explains why the other 2 Venn diagrams are not selected for choice of Venn diagram 2 AND a partial reason, i.e. only mentions 1 aspect or attempts an explanation e.g. times table is within 2 times table, or shows which of A are within times table, or 22 is in A but not in C, or no multiples of in C OR for selection of Venn diagram 2 and explains why 1 of the other 2 Venn diagrams are not selected Accept informal words such as within for subset, overlap for intersection

14 9. Straight lines parallel to all verticals and horizontals, with lines of radius distance away from the steps (+2mm) All inner steps, locus turn at 90 vertex All outer steps, arcs with wheel radius (+2mm) 10. (a) Reason, e.g. outside the bookshop (b) Two boxes if you are 30 (c) Suitable question with at least 3 boxes, no overlaps or gaps and prices from a low value upwards (to maybe 20) considered or a number of boxes given but concentrated at lower prices x Class A has 12 girls Class B has 18 girls There are twice as many girls as boys in class B, or ⅓ of class B boys, or ⅔ of class B girls Class B has 9 boys 5 2 for straight lines, or series of points (>), parallel to 2 verticals/horizontals, radius distance away (+2mm), OR straight lines parallel to all verticals and horizontals but not radius distance away Do not accept curves with free hand sketches for arcs with wheel radius (+2mm) at 2 outer steps, OR intention of arcs at all outer steps but not necessarily at wheel radius If B5 penalise extra lines drawn -1 Accept reference to people not buying, but checking out ready for downloading, showcasing, or that older people are more likely these days to buy from shops than younger people Do not accept reference to groups under 20 and over 0. Or refers to widths groups for younger or older people, or unequal groups. Allow overlap(s). Ignore incorrect response if correct response is given. Do not accept doesn t give options for under 20s or over 0s, or 2 options for 20 year olds Suitable question with at least 3 boxes, with either consistent overlaps or gaps OR a suitable range of prices is not considered, OR for suitable choice of groups with no gaps or overlaps but without a suitable question being asked Examples of consistent overlaps or gaps: 0-5, 5-10, 10 - under 5, - 10, 11-15, 1 - over 5, over 10, over 20 * *however possible if asked to tick only one box FT 1½ their 12 correctly evaluated (but NOT 1½ ) Sight of 18 implies first, OR Class B: Angle girls 20 ±2 and angle boys 120 ±2 This may be implied from their numbers of girls and boys in class B Note: ⅓ of 18 does not imply ⅓ of class B boys, hence B0 18 is ⅔, implies CAO

15 13. (a) (Millet) 3 850/10 255(g) (b)attempt to find unit cost e.g. for 1kg (For the 250g bag, 1kg costs) 1.9 (For the 300g bag, 1kg costs) 1.80 (For the kg bag, 1kg costs) 1.90 Considering buying 10 or more 300g bags Working with or choice of 15 of the 300g bags, or with an answer of 1(. ), 17 or 1, or trials including 15 or 1 or 17 of the 300g bags (Cheapest way to buy 5kg is 15 (300g bags) at 5(p) + 2 (250g bag) at 9(p) = ( )8(.) (p) ) = ( )9(.)08 1(a)(i) 2950 (miles) 3050 (miles) 79.5(hours) or 79 ½ (hours) or 79 h 30 min 80.5(hours) or 80½(hours) or 80 h 30 min (b)(ii) Volume scale factor 27 Length scale factor 3 of larger pebbles needed (15/3 = ) 5 S1 3 3 CAO OR for one correct costing for 5kg e.g. ( )7(.)0 + 9(p) = ( )9(.)5 OR At least 2 combinations of bags to a total of 5kg OR any 2 correct costings for buying 5kg OR stating any 3 possible combinations of bags to 5kg 250g 300g kg Cost = = = = 9.08 OR equivalent, e.g. repeated additions or multiples, All correct entries for any 2 correct entries Do not accept 79.3 or 80.3 as 2 correct entries, allow this as equivalent to counting 1 correct entry FT their greatest distance divided by their least time, provided distance >3000 and time < 80 Accept sight of Allow for sight of 5/2 or 27 provided not connected to irrelevant working Accept Allow for sight of 3 provided not connected to irrelevant working Award of the 2nd implies also the 1st SC2 only for an answer of 5 without relevant working

16 1(a) Axis labelled frequency density with a uniform scale from 0 to 5(minimum) Frequency densities 1.8, 2.2, 5, 0., 0.2 Correct histogram M2 Do not accept a scale using less than half the paper or for scales to 100 FT for their uniform scale for any 3 correct frequency densities (b) Explanation: Median is in the group 0<t 0 Estimate so we don t know, or (Estimate of the) median is, or It (may be) is nearer 0 than 0 17.(a) x = x = 3... with an attempt to subtract 33/90 (=11/30) or 33/990 or equivalent (b) 2/3 (c) = 9 Each E mark is independent. Accept median is in same group Accept median could be towards the lower end of the median group. Or 10x and 100x, or equivalent. Or an alternative method. CAO (3 3/9 gets A0) for (3/2) -1 or 1/(3/2) or 1/1 5 or (8/27) 1/3 or (3 8 /3 27) or 3 (8 /27) B0 for 8/27 1/3 or 8 1/3 /27 FT from one incorrect term

17 EAS Practice Papers SET2 Mathematics-Numeracy Unit 2 Foundation Tier SET 2 Numeracy U2 FT Mark Comments To be viewed with diagram Parts (a) & (b) marked at the same time 1 (a) Pointer showing 320g 1. (b) Reading 20 (g) One cube weighs (20 320)/5 if calculation shown and F.T. their pointer. OR for sight of 320 in the working but nothing on their diagram OR 20 shown on their diagram. Pointer drawn takes precedence over written value(s) Pointer nearer correct mark than the ones each side of it = 0 (g) 2. Person Should have flu vaccination? Yes or No Reason B Complete method, subtraction and division FT 'their 20 and 320 Allow, SC1 for 20/5 = 12 (g) Unsupported 12 (g) gets M0,A0 Award for each correct response and valid reason. Denise Ye Is a diabetic Jack David 3. (a)(i) Church (2, 5) Yes No Is over 5 and/or has a chest condition Does not meet any requirements or equivalent, OR gives at least 2 reasons for not having the flu jab. Alys Yes Is pregnant Castle (-, -3) (ii) Skating park (S) plotted at (3, 0) (b) (i) 5 (minutes) (ii) ¾ (hours) + 20 (mins) (hours) Changing all to hours OR all to mins correctly 155 mins or 2 hrs 35 mins or 2.58(3...)hours ISW 7 Award SC2 for ALL CORRECT reasons with ALL INCORRECT Yes/No. If no marks awarded, award SC1 for Yes, Yes, No, Yes Reverse coordinates B0 throughout (c) Accept any indication of (3, 0) For adding the 3 times given. FT their 5 minutes Either OR ¾ + 1/ or equivalent Do not accept 0.3 for 1/3 for but allow for If units used they must be correct. Do not accept 2.35 but allow 2:35

18 . (a) Working towards 13 & 12 boxes or Engaging with buy 1 get 1 half price 13 x ( )27.(0) or 12 x ( )13.8(0) ( )358.8(0) ( )15.(0) ( )52.(0) (b) A, B & D circled S1 7 FT their ( )358.8(0) + their ( )15.(0) If M0 awarded allow SC1 for sight of ( )13.8(0). Possible S1 can still be awarded. Alternative method: Cost of 2 boxes = 1.5 x 27.0.: cost of 2 boxes = 12 x 1.5 x 27.0 = 9.80 Total cost including 25th Box = Award for any 2 correct nets circled and C not circled 5. (Annual cost of units) (p) 020(p) or ( )0.2(0) (Fixed charge per year =) ( )83.7 (cost of units + fixed charge per year 8) 12 ( or ) (Monthly payment=) ( )53.33 or 5333(p) To be viewed with diagram Parts (a) to (e) marked at the same time. (a) (Day) 2 (b) 3 (days) (c) 2 (days) (d) 17.5 (mm) OR 17½ (mm) (e)(i) (=70) or (=3.5) or (=.2857 ) or (=3.212 ) or equivalent Not correct stated or implied with correct interpretation of their appropriate calculation (ii) Notices that the pictogram is number of cases not prices/costs 5 7 Alternative mark scheme- Monthly cost (Monthly cost of units=) (p) ( )50.35 or 5035(p) (Monthly discount=)(8 12=)( ) ( )0.2(0) (= ) (Monthly payment=)( )53.33 or 5333(p) Allow 'on day 1, day 2 and day ' Allow 'on day 1 and day Depends on Alternative: Sunday = 90 and Wednesday = 50 leading to either 90/50 or 0/50 which indicates 80% more sold on Sunday rather than 0% Do not accept /90 = % is incorrect, hence B0 Wednesday sales 55.5 % of Friday sales, is incorrect, hence E0 Accept no as implied within a suitable explanation

19 7. (a) ( of necklaces is) = 27 (necklaces) ( of yellow beads is =) 270 ( of black beads is 27 =) 12 (b) Deciding to make two bracelets 8 bags of purple beads 3 bags of green beads 8. Parts (a) & (b) marked at the same time (a) 11 8 (cm) = 118 (km) To be viewed with diagram (b) Use Overlay Bearing 097º from A Bearing 32º from B Point (X) U1 Note: Sight of 270 (yellow) or 12 (black) implies, FT their consistent derived correctly evaluated FT their consistent derived 27 correctly evaluated OR sight of needing 8 purple or 18 green Reversed answer: 3 purple bags and 8 green bags following correct working award, SC1. Note intention to match 72s is incorrect working. If no marks, allow SC2 for bracelets with 1 bags of purple beads and bags of green beads, OR SC1 for other possible number of bracelets with the number of whole bags of purple and green correctly evaluated in the correct ratio Allow inclusive (Ignore km here) FT their km not required but A0 for incorrect units Unsupported answers within inc get,,. Unsupported answers outside inclusive get 0. Allow ±2 Allow ±2 F.T. if at least awarded. Unambiguous dots within the boundaries of the overlay can get the s. One unambiguous dot within the box gets all 3 marks. Watch out for line segments. An unambiguous point of intersection does not require X.

20 9. (Time driving = 2hrs 15min + 1hr 5min) = (hours) or 20(min) (Av. Speed =) 200 = 50 m.p.h. U1 for sight of either 2(hrs) 15(min) or 135(min) OR 1(hr) 5(min) or 105(min) Alternative method hours 25min - 25min = (hours) for sight of (hrs) 25(min) or 25(min). F.T. their time. Do not penalise if they incorrectly note their F.T. time (e.g. use 3 3 for 3hrs 30 min). A0 if they have incorrectly used their F.T. time. Independent of other marks. Allow any unambiguous correct notation. 200 / 20 = 0 83(33..). m.p.min gains,,u / 20 = 0 83(33..). m.p.h gains,,u / 20 = 0 83(33...) gains,,u (a) A correct combination with cost. A different combination with cost. Organisation and communication Accuracy of writing (seconds) OC1 W1 for a correct possible choice with no cost or an incorrect cost. for an incorrect combination of at least four containers with a correct cost. for a different correct possible choice with no cost or an incorrect cost. for a different incorrect combination of at least four containers with a correct cost. Small Medium Large Cost 0 1 ( ) ( ) 0 2 ( ) ( ) ( )52 Award for other multiples of 2 eg 8 (seconds) OR for listing multiples of 8 AND multiples of. 5

21 Parts (a) & (b) marked at the same time 12. (a) 23 (years) (b) TRUE FALES TRUE 13. (cost of room) (5 x 2 = ) ( )120 (total cost of meals) 27 x 15 ( )158 (total money spent) ( )799 (total money collected from tickets) 15 x 35 ( )5390 (Money given to charity) ( ) Comes from 7-2 for any correct FT their 120 and their 158 but not 2 and 27. FT their correct total collected their total money spent Unsupported correct answer implies all previous marks. Alternative method (cost of room) (5 x 2 = ) ( )120 (Difference in meal and ticket price) = ( )8 (Total money from this difference) 8 x 15 = ( )1232 (total money spent) ( )1 (Money given to charity) ( )591

22 EAS Practice Papers SET2 Mathematics Numeracy Unit 2 Intermediate Tier SET 2 Numeracy U2 IT Mark Comments Parts (a) & (b) marked at the same time 1. (a) (i) 23 (years) Comes from 7-2 (b) TRUE FALES TRUE 2. 2 (seconds) for any correct Award for other multiples of 2 eg 8 (seconds) OR for listing multiples of 8 AND multiples of. 3. (Time driving = 2hrs 15min + 1hr 5min) = (hours) or 20(min) (Av. Speed =) 200 = 50 m.p.h..use overlay Position at 135 from ship A. Position at 215 from ship B. Position marked OR two intersecting lines. 5. (Annual cost of units) (p) 020(p) or ( )0.2(0) (Fixed charge per year =) ( )83.7 (cost of units + fixed charge per year 8) 12 ( or ) (Monthly payment=) ( )53.33 or 5333(p) 5 U1 8 for sight of either 2(hrs) 15(min) or 135(min) OR 1(hr) 5(min) or 105(min) Alternative method hours 25min - 25min = (hours) for sight of (hrs) 25(min) or 25(min). F.T. their time. Do not penalise if they incorrectly note their F.T. time (e.g. use 3 3 for 3hrs 30 min). A0 if they have incorrectly used their F.T. time. Independent of other marks. Allow any unambiguous correct notation. 200 / 20 = 0 83(33..). m.p.min gains,,u / 20 = 0 83(33..). m.p.h gains,,u / 20 = 0 83(33...) gains,,u0. ± 2 (use overlay). Allow the M marks for dots, crosses or any unambiguous indication that the correct bearings have been offered. F.T. if at least and two intersecting lines. (Lines must originate from ship A and ship B respectively) Alternative mark scheme- Monthly cost (Monthly cost of units=) (p) ( )50.35 or 5035(p) (Monthly discount=)(8 12=)( ) ( )0.2(0) (= ) (Monthly payment=)( )53.33 or 5333(p)

23 . (cost of room) (5 x 2 = ) ( )120 (total cost of meals) 27 x 15 ( )158 (total money spent) ( )799 (total money collected from tickets) 15 x 35 ( )5390 (Money given to charity) ( )591 7(a), 7, 80 (b) Correct cumulative frequency diagram, points plotted at upper bounds and joined by a curve or straight line (c) Median 58 reading from graph Low quartile 55.5 reading from graph Upper quartile 1 reading from graph Interquartile range 5.5 (d) Range ends correctly indicated (50(cm) and 8(cm)) Median line correctly indicated (approx. 58 ) UQ and LQ correctly indicated (approx. 1 & 55.5) 8. (Salary received) ( ) = ( )21000 (Cost of petrol) 8000 ( ) 25 0 = ( )1250 (New salary received) = ( )1000 (Loss) ( ) ( ) ( )1000 Organisation and communication Accuracy of writing = ( ) OC1 W1 9 FT their 120 and their 158 but not 2 and 27. FT their correct total collected their total money spent Unsupported correct answer implies all previous marks. Alternative method (cost of room) (5 x 2 = ) ( )120 (Difference in meal and ticket price) = ( )8 (Total money from this difference) 8 x 15 = ( )1232 (total money spent) ( )1 (Money given to charity) ( )591 Accuracy: nearer the intersection of correct lines than any others FT only if cumulative in (a) for points correct but not joined, OR correct apart from 0.5 translation, OR if one error in plotting but joined correctly FT from their cumulative entries. Not cumulative means no FT. Accuracy of readings ±0.5 FT their UQ their LQ correctly evaluated. Independent FT In (d) FT consistent previous misread of scale Whiskers should be shown If incorrect then FT their median If incorrect then FT their UQ and LQ reading Or F.T. 2/3 their F.T. their three stated values. (Look for or )

24 9. Taxable income ( =)( )305 0% tax to be paid on ( ) x (=51) 0. x (=31) ( ) 51AND ( )31 Claudia s tax should be ( ) (a) Suitable uniform scales starting at zero, with axes labelled. Correct grouped frequency diagram. [Heights of 80,0,52,32,1] (b) Sight of the mid-points 0.5, 1.5, 2.5, 3.5 &.5 Sum of mid-points freq = 20 = 1.8(5) (hours) or equivalent. 1 < t 2 (hours) 11.TRUE TRUE TRUE 12. (Volume of block =) (=00) (cm3) (Density of metal =) OR OR = 2.75 OR OR 2750 Appropriate unit g/cm3 kg/cm3 kg/m3 13. (a) (Vol. cuboid =) OR (Vol. cylinder =) π (Vol. cuboid) = 320 (Vol. cylinder) = 31( 7..) (Larger volume in the cuboid by) 73(.3 ) cm3 (b) (S. Area cuboid =) 18x10+2x182 OR (S. Area cylinder =) 2 π π 122 = 138 (cm2) = 132( 5... cm2).:square based tin uses less metal m1 U1 U1 FT taxable income 32255, i.e. their correctly evaluated FT 0. ( their ) provided their 305 > 32255, also FT ( =) giving (=7998) FT sum of their 51 + their 31 provided at least 1 of these values is correct and M2 awarded (Note: = 19) for 1 error in heights of bars. If no marks awarded, SC1 for a frequency polygon with all correct heights. FT their mid-points provided they are within the limits of each group, including the limits themselves. ISW. Accept 1.9. Allow 2 if 1.85 has been seen. Allow 1 to 2 hours. for any correct FT 1100 or 1.1 their volume provided it is a product. Volume may be given in another metric unit. Accept 315 to 318 inclusive OR 1008 π for vol. of cylinder FT their values, if gained. For sight of cm3 anywhere within the answer. Accept 131 to inclusive OR 5 π for S. Area cylinder FT if at least gained

25 = π x d or 2.7 = 2 x π x r or r = 2.7/π Diagonal = 8.95 to 8.5(0 ) (cm) diagonal 2 = side 2 + side 2 side 2 = diagonal 2 /2 side length = (.009 cm) Perimeter = 2.(.cm) Accept rounded or truncated FT their diagonal Do not FT from inappropriate truncation or incorrect rounding (e.g. from d = 8.) Answer here for should round to.01 FT provided both M marks awarded for x their side length

26 EAS Practice Papers SET2 Mathematics Numeracy Unit 2 Higher Tier SET 2 Numeracy U2 HT Mark Comments 1.Use overlay Position at 135 from ship A. Position at 215 from ship B. Position marked OR two intersecting lines. 2(a), 7, 80 (b) Correct cumulative frequency diagram, points plotted at upper bounds and joined by a curve or straight line (c) Median 58 reading from graph Low quartile 55.5 reading from graph Upper quartile 1 reading from graph Interquartile range 5.5 ± 2 (use overlay). Allow the M marks for dots, crosses or any unambiguous indication that the correct bearings have been offered. F.T. if at least and two intersecting lines. (Lines must originate from ship A and ship B respectively) Accuracy: nearer the intersection of correct lines than any others FT only if cumulative in (a) for points correct but not joined, OR correct apart from 0.5 translation, OR if one error in plotting but joined correctly FT from their cumulative entries. Not cumulative means no FT. Accuracy of readings ±0.5 FT their UQ their LQ correctly evaluated. (d) Range ends correctly indicated (50(cm) and 8(cm)) Median line correctly indicated (approx. 58 ) UQ and LQ correctly indicated (approx. 1 & 55.5) 10 Independent FT In (d) FT consistent previous misread of scale Whiskers should be shown If incorrect then FT their median If incorrect then FT their UQ and LQ readings 3. (Salary received) ( ) = ( )21000 (Cost of petrol) 8000 ( ) 25 0 = ( )1250 (New salary received) = ( )1000 (Loss) ( ) ( ) ( )1000 Organisation and communication Accuracy of writing = ( )5750. Taxable income ( =)( )305 0% tax to be paid on ( ) x (=51) 0. x (=31) ( ) 51AND ( )31 Claudia s tax should be ( )1077 OC1 W1 9 Or F.T. 2/3 their F.T. their three stated values. (Look for or ) FT taxable income 32255, i.e. their correctly evaluated FT 0. ( their ) provided their 305 > 32255, also FT ( =) giving (=7998) FT sum of their 51 + their 31 provided at least 1 of these values is correct and M2 awarded (Note: = 19)

27 5. (a) Suitable uniform scales starting at zero, with axes labelled. Correct grouped frequency diagram. [Heights of 80,0,52,32,1] (b) Sight of the mid-points 0.5, 1.5, 2.5, 3.5 &.5 Sum of mid-points freq = 20 = 1.8(5) (hours) or equivalent. 1 < t 2 (hours).true TRUE TRUE 7. (Volume of block =) (=00) (cm3) (Density of metal =) OR OR = 2.75 OR OR 2750 Appropriate unit g/cm3 kg/cm3 kg/m3 8. (a) (Vol. cuboid =) OR (Vol. cylinder =) π (Vol. cuboid) = 320 (Vol. cylinder) = 31( 7..) (Larger volume in the cuboid by) 73(.3 ) cm3 (b) (S. Area cuboid =) 18x10+2x182 OR (S. Area cylinder =) 2 π π 122 = 138 (cm2) = 132( 5... cm2).:square based tin uses less metal m1 U1 U1 for 1 error in heights of bars. If no marks awarded, SC1 for a frequency polygon with all correct heights. FT their mid-points provided they are within the limits of each group, including the limits themselves. ISW. Accept 1.9. Allow 2 if 1.85 has been seen. Allow 1 to 2 hours. for any correct FT 1100 or 1.1 their volume provided it is a product. Volume may be given in another metric unit. Accept 315 to 318 inclusive OR 1008 π for vol. of cylinder FT their values, if gained. For sight of cm3 anywhere within the answer. Accept 131 to inclusive OR 5 π for S. Area cylinder FT if at least gained = π x d or 2.7 = 2 x π x r or r = 2.7/π Diagonal = 8.95 to 8.5(0 ) (cm) diagonal 2 = side 2 + side 2 side 2 = diagonal 2 /2 side length = (.009 cm) Perimeter = 2.(.cm) Accept rounded or truncated FT their diagonal Do not FT from inappropriate truncation or incorrect rounding (e.g. from d = 8.) Answer here for should round to.01 FT provided both M marks awarded for x their side length

28 10(a) 5.2/100 x 50 or 0.05 x 50 or 23.(0) ( ) x 50 ( ) Conclusion, e.g. Yes as more than 550 (b)(i) 0.08 (ii) Greater AND a reason, e.g. interest is accumulated through the year (each three months) (iii) Use of n = ( /) -1 AER.98(%) (iv) Explanation, based on need for fair comparison of interest rates 11. Π /30 OR Π /30 Π /30 - Π /30 Answer 12(cm2) or answers in the range to (cm2) 12(a) 0 (b) Tangent drawn at t = 3.5 Method, difference y / difference x Evaluated estimated answer from their reasonable tangent (c)(i) Finding v values: (0,) 1, 29, 2, 30 Split into areas and attempt to sum Correct substitution into trapezium rule (c)(ii) 0.18(km) 18 (metres) A May be embedded in further calculation Method of adding on different amounts, year period, following attempts to calculate 5.2% Example of working without truncation or rounding: (50+23.(0) =73.(0) 73.(0) = , or = = ) Accept (7.) and SC1 for depreciation 33.5(099..), but no FT for a conclusion Simple interest answer of 53.(0) is awarded only the FT from their compounded amount provided, and FT from simple interest from an answer of 53.(0) being < 550 CAO Correct substitution in the formula given for rounded or truncated, or incorrect rounding or truncation of the AER percentage. Mark final answer (box takes priority) Allow percentage of interest paid annually, must mention year or annual Seen in working Or equivalent The values used must be correct, do not allow 27/3.5 May not be from a tangent, but must be from use of differences, e.g. curve used to form a right-angled triangle (Approximately 3.3 (m/min2) Sight of (0,) 1, 29, 2, 30 Sight of the sum of products or an attempt substitution of their 5 values in the trapezium rule Or equivalent. ( ) or ( ) FT their values for v provided at least 3 values are correct, OR 2 areas correct in sum of possible FT their (i)/1000 evaluated correctly