level 4 ans
Level 4 KS3 Answers 1.
Completes all three grids correctly, ie
3
11 4
12 7
9
28
27
10
10
6
4
or
24
or
3
4
6 24
Completes the first two grids correctly
2
or Completes the third grid correctly and gives any two correct entries in the first two grids or Completes the third grid correctly, gives any one correct entry in the first grid, makes an error in the right hand entry of the second grid, but follows through correctly to give their product or
Gives any two correct entries in the first two grids
1 U1
or Completes the third grid correctly or Gives any one correct entry in the first grid, makes an error in the right hand entry of the second grid, but follows through correctly to give their product [3]
Hertfordshire La Schools
1
2.
(a)
Gives two different 3-digit multiples of 4
1
eg ▪
100 104
▪
132 236
(b)
Gives a 2-digit factor of 100, ie
1
10, 20, 25 or 50 Gives a different 2-digit factor of 100 from any credited for the first mark of part (b) ! Factors of 100 given that do not have 2 digits eg, for both marks in part (b) ▪ 100 1 ▪ 2 5 Mark as 0, 1
!
1
2-digit factors of 100 given within factor pairs eg, for both marks in part (b) ▪ 10 × 10 20 × 5 ▪ 25 × 4 50 × 2 Mark as 0, 1 Do not accept: negative factors [3]
Hertfordshire La Schools
2
3.
Completes all four entries in the table correctly, ie 4.95
5
24.75
3.20
13
41.60
1.95
10
19.50
Total:
or
2
85.85
Completes at least three entries in the table correctly
1 U1
or Completes all four entries correctly with some or all amounts of money given in pence ! For 1m, follow through Where the only error is in the total cost of balloons, for the overall total accept their total cost of balloons + 61.10 [2]
4.
Getting There (a)
64 and 864 675
1 1
(b)
2520 15
1 1 [4]
5.
Patterns on a grid (a)
Gives the correct coordinates, ie (2, 1)
1
(b)
Gives both pairs of coordinates in either order eg
1
(c)
(3, 3) (4, 4)
Gives both pairs of coordinates in either order eg
1
(16, 16) (17, 17)
Hertfordshire La Schools
3
(d)
Makes a correct decision and gives a correct explanation that shows or implies 14 and justifies that 16 more are needed eg
2
Yes, 12 + 22 + 32 + 42 = 30
There are enough because 1 + 4 + 9 = 14, 4 4 = 16 and 14 + 16 = 30
The next square is 16 tiles (4 by 4 square drawn) and you’ve used up 14 of them, so there’s just enough
You have 16 tiles left and 4 4 = 16; all the tiles are used
or States or implies that the next square uses 16 tiles eg
You need 16 to make the next square
Draws a 4 by 4 square with 16 cells
4 4 seen ! 16 not justified Accept only if the response makes it clear that exactly 30 tiles are used eg, for 2m accept Used 14, got another 16 so you will use up all the 30 tiles
1
30 14 = 16, so yes you have exactly the correct amount eg, for 2m or 1m, do not accept 14 used, 16 left so yes you can 30 14 = 16, so yes you have enough or States or implies that exactly 30 tiles will be used, but does not justify that 16 more are needed eg You need all 30 There would be no tiles left over It all adds up to 30
Hertfordshire La Schools
4
or Identifies the pattern of differences eg
+3, +5, +7 ! 4 by 4 square drawn correctly, but the number of squares incorrectly processed For 1m, Condone Do not accept their explanation could imply that 7 more squares are needed, ie a total of 21 eg
U1
so yes, there are enough [5]
6.
(a)
20, 28
1
36, 108
1
14, 14
1 or equivalent 2 ! First new term for each sequence correct, with second terms all incorrect or omitted Mark as 0, 0, 1
Hertfordshire La Schools
1
5
(b)
Indicates No and gives a correct explanation The most common correct explanations:
1 U1
Show that the rule does not work for the third term eg It doesn’t work for the second two numbers, 22 – 8 = 14 not 18 If it was subtract 8, the last number would be 14 It’s 22 – 4 = 18, not 22 – 8 22 – 18 = 4 not 8 Accept minimally acceptable explanation eg 22 – 8 = 14 When you take away 8, it should be 14 18 should be 14 The third number should be 14 22 – 8 ≠ 18 It’s 22 – 4 18 to 22 is 4 Do not accept incomplete or incorrect explanation eg 18 is wrong
It should be 14 It doesn’t work for 22 and 18 You subtract a different number the second time 8 – 22 = 14 22 – 8 = 15
State what the correct rule could be eg It should be divide by 2, then add 7 The rule is add 14 then halve it You take away half as much each time Accept minimally acceptable explanation eg ÷2+7 It’s take away 8, then take away 4 –8 and –4 You halve what you subtract
Hertfordshire La Schools
6
Do not accept incomplete or incorrect explanation eg You subtract a different number each time You subtract 4 The rule is subtract 4 Take away half [4]
7.
(a)
Indicates a pair of numbers with a sum of 34
1
Indicates a pair of numbers with a product of 10
1
(b)
Indicates 12 Do not accept remainders other than 0.
1
(c)
Indicates 275
1
Indicates 368
1
Indicates 16 Do not accept remainders other than 0.
1 [6]
8.
(a)
Claire
1
(b)
Gives the names Claire then Tom
1 U1
Accept: unambiguous indication of name eg, for Claire • C [2]
9.
Gives a pair of numbers for a and b, such that b = a + 4
1
eg •
a=5
•
a = 1.5
b=9 b = 5.5 Do not accept: values embedded eg • 4+5=9 • a=4+5 b=9
Gives a pair of numbers for a and b, such that b = a + 4, different from any previously credited
1 U1 [2]
Hertfordshire La Schools
7
10.
What numbers? (a)
3
1
(b)
10
1 Do not accept incorrect statement eg, for part (a) n=3+5 [2]
11.
Recycling rubbish (a)
Gives a value between 6 and 16 inclusive Accept value qualified eg About 10
1
(b)
Indicates only Germany and Norway Accept unambiguous indication eg N, G
1
[2]
Hertfordshire La Schools
8
12.
Gives five numbers less than 6 eg
1
1 5
2 4
3
0.4 1 2
–7 0
!
!
!
Hertfordshire La Schools
4
Accept numbers repeated on the same spinner Numbers written outside the spinner or on lines between the sections of the spinner Accept provided the pupil’s intention is clear Zero Accept zero as an even number, but not as an odd number Accept zero as a multiple of 3 Negative integers Accept numbers of the form 2n as even, numbers of the form 2n + 1 as odd and numbers of the form 3n as multiples of 3, where n is an integer
9
Gives five numbers with more even numbers than odd numbers eg
1
15 14
2 58
9
4 6
2
10
!
8
Section(s) of the spinner left blank For the first mark, do not accept For the second and third marks, accept provided exactly five digits have been given and the statement is satisfied eg, for the second mark accept ■
26 4 7
4
eg, for the third mark accept ■
8
17
25
Hertfordshire La Schools
10
Gives five numbers that are not multiples of 3 eg
1
■
–1 26
100
8
11
[3]
13.
(a)
10
1 Do not accept: 10%
(b)
Completes the percentage bar chart correctly,
2
ie 50% labelled No 40% labelled Don’t know 10% labelled Yes, with bars in any order eg No 0%
or
20%
Don’t know 40%
60%
Yes
80%
100%
Indicates sections corresponding to 50%, 40% and 10% but fails to label, labels incorrectly or bars are not continuous
1
eg ? 0%
20%
40%
60%
?
?
?
80%
100%
or Shows or implies the values 50, 40 and 10 eg
0%
Hertfordshire La Schools
20%
40%
60%
80%
100%
11
or Indicates a correct bar for either Don’t know or Yes, and labels correctly Accept: unambiguous labelling eg • ? 0%
20%
? 40%
? 60%
? 80%
100%
! Lines not ruled or accurate Accept provided the pupil’s intention is clear [3]
14.
(a)
(b)
Gives A as (0, 6)
1
Gives C as (4, 3) ! Answers for A and C transposed but otherwise completely correct If this is the only error, ie gives A as (4, 3) and gives C as (0, 6), mark as 0, 1
1
Indicates point D on the graph at (2, 7) ! Point inaccurate, not labelled or marked only with the letter D Condone any unambiguous indication within 2mm of the correct intersection of the grid
1
[3]
15.
(a)
(b)
Gives a value greater than 62.5, but less than 63.5
1
Gives a value greater than 52.5, but less than 53.5 ! The two values in part (a) transposed but otherwise correct Mark as 0, 1
1
Indicates the correct point at (34, 72) ! Inaccurate indication Accept any unambiguous indication within 2mm of the correct intersection of the grid
1
[3]
Hertfordshire La Schools
12
16.
Patterns (a)
Shows two rectangles in a pattern with only one line of symmetry, eg
1
(b)
Shows two rectangles in a pattern with rotation symmetry of order 2, eg
1
!
Lines of symmetry drawn Ignore
!
Rectangles not shaded Accept only if unambiguous
!
Edges of rectangles not explicit Pupils may use the edge of the grid or not show an edge when the rectangles are adjacent. Accept only if unambiguous
!
Rectangles placed within the grid but covering only parts of squares Accept provided the pupil’s intention is clear eg, for the first mark, accept
Hertfordshire La Schools
13
1
Rectangles placed with parts or all outside the grid Accept provided the pupil’s intention is clear eg, for the third mark, accept
!
Rectangles overlapping Accept only if unambiguous eg, for the third mark, accept
Incorrect size of rectangles Do not treat as a misread, ie do not accept Grid not taken to be part of the pattern [2]
17.
Gives the correct numerator, ie
1 6
6
Gives the correct numerator, ie
1 3
6
Hertfordshire La Schools
14
Gives the correct numerator, ie
1 3
3 [3]
18.
(a)
Indicates trapezium, ie
1
Accept unambiguous indication (b)
17
1 [2]
19.
Grid shapes (a)
B and E in either order Accept shape A given alongside a correct response
1
(b)
D and E in either order ! Responses for parts (a) and (b) transposed but otherwise correct Mark as 0; 1
1
(c)
30
1 Accept the given shape C excluded eg 29 more 29 [3]
20.
Matchboxes (a)
10.6
1
7.2
1
3(.0)
1 Accept equivalent fractions or decimals
Hertfordshire La Schools
15
(b)
8
1 !
Answer of 4 Accept only if it is clearly stated that another 4 boxes are needed eg, accept 4 more eg, do not accept 4 [4]
21.
Measuring Gives a correct explanation that shows the relationship between the volume of the jug and one litre eg
It’s 2 jugs
Fill the jug once, pour it in the bucket and fill it again
He uses 500 + 500
A jug is half a litre
Empty into the bucket twice
1
U1
Accept minimally acceptable explanation eg Fill it twice 500ml 2 Accept jug assumed to be calibrated eg Put 200ml in the jug, then repeat to give a total of 5 times [1]
Hertfordshire La Schools
16
Completes all three grids correctly, ie
3
11 4
12 7
9
28
27
10
10
6
4
or
24
or
3
4
6 24
Completes the first two grids correctly
2
or Completes the third grid correctly and gives any two correct entries in the first two grids or Completes the third grid correctly, gives any one correct entry in the first grid, makes an error in the right hand entry of the second grid, but follows through correctly to give their product or
Gives any two correct entries in the first two grids
1 U1
or Completes the third grid correctly or Gives any one correct entry in the first grid, makes an error in the right hand entry of the second grid, but follows through correctly to give their product [3]
Hertfordshire La Schools
1
2.
(a)
Gives two different 3-digit multiples of 4
1
eg ▪
100 104
▪
132 236
(b)
Gives a 2-digit factor of 100, ie
1
10, 20, 25 or 50 Gives a different 2-digit factor of 100 from any credited for the first mark of part (b) ! Factors of 100 given that do not have 2 digits eg, for both marks in part (b) ▪ 100 1 ▪ 2 5 Mark as 0, 1
!
1
2-digit factors of 100 given within factor pairs eg, for both marks in part (b) ▪ 10 × 10 20 × 5 ▪ 25 × 4 50 × 2 Mark as 0, 1 Do not accept: negative factors [3]
Hertfordshire La Schools
2
3.
Completes all four entries in the table correctly, ie 4.95
5
24.75
3.20
13
41.60
1.95
10
19.50
Total:
or
2
85.85
Completes at least three entries in the table correctly
1 U1
or Completes all four entries correctly with some or all amounts of money given in pence ! For 1m, follow through Where the only error is in the total cost of balloons, for the overall total accept their total cost of balloons + 61.10 [2]
4.
Getting There (a)
64 and 864 675
1 1
(b)
2520 15
1 1 [4]
5.
Patterns on a grid (a)
Gives the correct coordinates, ie (2, 1)
1
(b)
Gives both pairs of coordinates in either order eg
1
(c)
(3, 3) (4, 4)
Gives both pairs of coordinates in either order eg
1
(16, 16) (17, 17)
Hertfordshire La Schools
3
(d)
Makes a correct decision and gives a correct explanation that shows or implies 14 and justifies that 16 more are needed eg
2
Yes, 12 + 22 + 32 + 42 = 30
There are enough because 1 + 4 + 9 = 14, 4 4 = 16 and 14 + 16 = 30
The next square is 16 tiles (4 by 4 square drawn) and you’ve used up 14 of them, so there’s just enough
You have 16 tiles left and 4 4 = 16; all the tiles are used
or States or implies that the next square uses 16 tiles eg
You need 16 to make the next square
Draws a 4 by 4 square with 16 cells
4 4 seen ! 16 not justified Accept only if the response makes it clear that exactly 30 tiles are used eg, for 2m accept Used 14, got another 16 so you will use up all the 30 tiles
1
30 14 = 16, so yes you have exactly the correct amount eg, for 2m or 1m, do not accept 14 used, 16 left so yes you can 30 14 = 16, so yes you have enough or States or implies that exactly 30 tiles will be used, but does not justify that 16 more are needed eg You need all 30 There would be no tiles left over It all adds up to 30
Hertfordshire La Schools
4
or Identifies the pattern of differences eg
+3, +5, +7 ! 4 by 4 square drawn correctly, but the number of squares incorrectly processed For 1m, Condone Do not accept their explanation could imply that 7 more squares are needed, ie a total of 21 eg
U1
so yes, there are enough [5]
6.
(a)
20, 28
1
36, 108
1
14, 14
1 or equivalent 2 ! First new term for each sequence correct, with second terms all incorrect or omitted Mark as 0, 0, 1
Hertfordshire La Schools
1
5
(b)
Indicates No and gives a correct explanation The most common correct explanations:
1 U1
Show that the rule does not work for the third term eg It doesn’t work for the second two numbers, 22 – 8 = 14 not 18 If it was subtract 8, the last number would be 14 It’s 22 – 4 = 18, not 22 – 8 22 – 18 = 4 not 8 Accept minimally acceptable explanation eg 22 – 8 = 14 When you take away 8, it should be 14 18 should be 14 The third number should be 14 22 – 8 ≠ 18 It’s 22 – 4 18 to 22 is 4 Do not accept incomplete or incorrect explanation eg 18 is wrong
It should be 14 It doesn’t work for 22 and 18 You subtract a different number the second time 8 – 22 = 14 22 – 8 = 15
State what the correct rule could be eg It should be divide by 2, then add 7 The rule is add 14 then halve it You take away half as much each time Accept minimally acceptable explanation eg ÷2+7 It’s take away 8, then take away 4 –8 and –4 You halve what you subtract
Hertfordshire La Schools
6
Do not accept incomplete or incorrect explanation eg You subtract a different number each time You subtract 4 The rule is subtract 4 Take away half [4]
7.
(a)
Indicates a pair of numbers with a sum of 34
1
Indicates a pair of numbers with a product of 10
1
(b)
Indicates 12 Do not accept remainders other than 0.
1
(c)
Indicates 275
1
Indicates 368
1
Indicates 16 Do not accept remainders other than 0.
1 [6]
8.
(a)
Claire
1
(b)
Gives the names Claire then Tom
1 U1
Accept: unambiguous indication of name eg, for Claire • C [2]
9.
Gives a pair of numbers for a and b, such that b = a + 4
1
eg •
a=5
•
a = 1.5
b=9 b = 5.5 Do not accept: values embedded eg • 4+5=9 • a=4+5 b=9
Gives a pair of numbers for a and b, such that b = a + 4, different from any previously credited
1 U1 [2]
Hertfordshire La Schools
7
10.
What numbers? (a)
3
1
(b)
10
1 Do not accept incorrect statement eg, for part (a) n=3+5 [2]
11.
Recycling rubbish (a)
Gives a value between 6 and 16 inclusive Accept value qualified eg About 10
1
(b)
Indicates only Germany and Norway Accept unambiguous indication eg N, G
1
[2]
Hertfordshire La Schools
8
12.
Gives five numbers less than 6 eg
1
1 5
2 4
3
0.4 1 2
–7 0
!
!
!
Hertfordshire La Schools
4
Accept numbers repeated on the same spinner Numbers written outside the spinner or on lines between the sections of the spinner Accept provided the pupil’s intention is clear Zero Accept zero as an even number, but not as an odd number Accept zero as a multiple of 3 Negative integers Accept numbers of the form 2n as even, numbers of the form 2n + 1 as odd and numbers of the form 3n as multiples of 3, where n is an integer
9
Gives five numbers with more even numbers than odd numbers eg
1
15 14
2 58
9
4 6
2
10
!
8
Section(s) of the spinner left blank For the first mark, do not accept For the second and third marks, accept provided exactly five digits have been given and the statement is satisfied eg, for the second mark accept ■
26 4 7
4
eg, for the third mark accept ■
8
17
25
Hertfordshire La Schools
10
Gives five numbers that are not multiples of 3 eg
1
■
–1 26
100
8
11
[3]
13.
(a)
10
1 Do not accept: 10%
(b)
Completes the percentage bar chart correctly,
2
ie 50% labelled No 40% labelled Don’t know 10% labelled Yes, with bars in any order eg No 0%
or
20%
Don’t know 40%
60%
Yes
80%
100%
Indicates sections corresponding to 50%, 40% and 10% but fails to label, labels incorrectly or bars are not continuous
1
eg ? 0%
20%
40%
60%
?
?
?
80%
100%
or Shows or implies the values 50, 40 and 10 eg
0%
Hertfordshire La Schools
20%
40%
60%
80%
100%
11
or Indicates a correct bar for either Don’t know or Yes, and labels correctly Accept: unambiguous labelling eg • ? 0%
20%
? 40%
? 60%
? 80%
100%
! Lines not ruled or accurate Accept provided the pupil’s intention is clear [3]
14.
(a)
(b)
Gives A as (0, 6)
1
Gives C as (4, 3) ! Answers for A and C transposed but otherwise completely correct If this is the only error, ie gives A as (4, 3) and gives C as (0, 6), mark as 0, 1
1
Indicates point D on the graph at (2, 7) ! Point inaccurate, not labelled or marked only with the letter D Condone any unambiguous indication within 2mm of the correct intersection of the grid
1
[3]
15.
(a)
(b)
Gives a value greater than 62.5, but less than 63.5
1
Gives a value greater than 52.5, but less than 53.5 ! The two values in part (a) transposed but otherwise correct Mark as 0, 1
1
Indicates the correct point at (34, 72) ! Inaccurate indication Accept any unambiguous indication within 2mm of the correct intersection of the grid
1
[3]
Hertfordshire La Schools
12
16.
Patterns (a)
Shows two rectangles in a pattern with only one line of symmetry, eg
1
(b)
Shows two rectangles in a pattern with rotation symmetry of order 2, eg
1
!
Lines of symmetry drawn Ignore
!
Rectangles not shaded Accept only if unambiguous
!
Edges of rectangles not explicit Pupils may use the edge of the grid or not show an edge when the rectangles are adjacent. Accept only if unambiguous
!
Rectangles placed within the grid but covering only parts of squares Accept provided the pupil’s intention is clear eg, for the first mark, accept
Hertfordshire La Schools
13
1
Rectangles placed with parts or all outside the grid Accept provided the pupil’s intention is clear eg, for the third mark, accept
!
Rectangles overlapping Accept only if unambiguous eg, for the third mark, accept
Incorrect size of rectangles Do not treat as a misread, ie do not accept Grid not taken to be part of the pattern [2]
17.
Gives the correct numerator, ie
1 6
6
Gives the correct numerator, ie
1 3
6
Hertfordshire La Schools
14
Gives the correct numerator, ie
1 3
3 [3]
18.
(a)
Indicates trapezium, ie
1
Accept unambiguous indication (b)
17
1 [2]
19.
Grid shapes (a)
B and E in either order Accept shape A given alongside a correct response
1
(b)
D and E in either order ! Responses for parts (a) and (b) transposed but otherwise correct Mark as 0; 1
1
(c)
30
1 Accept the given shape C excluded eg 29 more 29 [3]
20.
Matchboxes (a)
10.6
1
7.2
1
3(.0)
1 Accept equivalent fractions or decimals
Hertfordshire La Schools
15
(b)
8
1 !
Answer of 4 Accept only if it is clearly stated that another 4 boxes are needed eg, accept 4 more eg, do not accept 4 [4]
21.
Measuring Gives a correct explanation that shows the relationship between the volume of the jug and one litre eg
It’s 2 jugs
Fill the jug once, pour it in the bucket and fill it again
He uses 500 + 500
A jug is half a litre
Empty into the bucket twice
1
U1
Accept minimally acceptable explanation eg Fill it twice 500ml 2 Accept jug assumed to be calibrated eg Put 200ml in the jug, then repeat to give a total of 5 times [1]
Hertfordshire La Schools
16
