Foundation Session 4GCSE Maths Topics

Foundation Session 4GCSE Maths Topics

Solutions

Pictograms
Stem and Leaf Diagrams
Bar Charts
Pie Charts

Teaching example 1

1 (a) /   / 1 / B1 for two complete circles
(b) / London / 1 / B1 for ‘London’ or ‘14’
(c) / 7 / 1 / B1 for 7 cao

Teaching example 2

(a) / 1 2 8
2 6 8 8
3 1 4 4 4
4 2 3 / 2 / B2
(B1 for 1 line correct)
(b)
(c) / 34
31 / 1
1 / B1
B1
(d) / / 30 / 2 / M1, A1
(e) / 34 – 26 = , / 8 / 2 / M1, A1
(f) / The mean gets bigger, because the total amount of milk has increased. / 2 / B1, B1

Teaching example 3

(a) / 15 / 1 / B1
(b) / Volkswagen / 1 / B1
(c) / 105 / 1 / B1

Teaching example 4

(a) / The proportion of elms has decreased over the period. / 1 / B1
(b) / The proportion of beech trees has increased- this may be due to a reduction of elms./ The overall number of trees may have fallen. /We don't know the overall number of trees in 1950 and 2000. / 1 / B1

Teaching example 5

Student Questions

Question 1

Stranraer - Belfast / 1 / B1 cao
4 / 1 / B1 cao
It is the longest route. It takes twice as long as the second longest route, etc
Other factors may include the cost, the number of ferries on each route, the ease of getting to the port, competition from other ferries, etc / 2 / B2 for two sensible reasons
(B1 for one sensible reason)

Question 2

(b) / 4 | … 3 3 5 8 8
5 | … 1 2 3 5 / 2 / B2 cao
(B1 for both 4 | …3 and 5 | …1)
(c)(i) / 39 / 2 / B1 ft stem and leaf diagram if 8 or 9 values added
(ii) / 19 / B1 ft stem and leaf diagram if 8 or 9 values added

Question 3

(a) / 2 / B2
4
5
6
7
8
9 / 2
9
5 6 8 8 9
2 3 7
0 1 4 6 9
2
B1 if one error/ omission
B1 S/C if unordered
(b) / (i) 8th data, 73 / B1
84 – 68 =, (Not range) / (ii) 16 / 3 / M1, A1

Question 4

(a)
(b)
(c)
(d) / / 60o 36o
All angles correct(within 10) (any 2 sections correct B1),
Labels
Yes proportions are similar / 1
1
3
1 / B1
B1
B1 B1
B1
B1

Question 5

Question 6

(b) / 3, 5, 8, 10, 10 / 1 / B1
(c) / 10/360 x 360 or (360 –(30 +50 + 80))/2 or any correct method (M1) / 100o, 100o (both put in table)
(Correct answers in table without working gets both marks) / 2 / M1 A1
(d) / EITHER:All Angles correct +/-20 tolerance (B1 B1).
OR: Three angles correct (B1).
PLUS All sections labelled (B1). / 3 / B1 B1 B1
(e) / EITHER:
Good idea - A lot of cycles in motorised traffic.
OR: Not a good idea as only 12 lorries an hour.
OR: Not a good idea as the traffic is generally light.
OR: any equivalent sensible answer. / 1 / B1

Question 7

(a) / / correct bar length - 39 / 1 / B1 Tolerance half a unit.
(Correct answer one small line below 40)
Condone a different width/shading
(b) / 29 + 40 + 7 + 39 = / 115 / 2 / M1 for effort to add 4 figures which are above zero
A1 for correct answer
(c) / ANY TWO from:
BBC2 has the most repeats;
ITV has least repeats;
The number of repeats is different for each;
BBC2 and C4 have almost the same number of repeats.
Any sensible comparison of numbers of repeats. / 2 / B1:B1
There are a number of different satisfactory answers
Watch out for the same statement twice but written in different words
NOTE: Just figures is not enough
e.g ‘BBC2 40 ITV1 7’ B0 but ‘BBC2 40 but ITV1 7’ B1