Bar Charts & Pictograms: WJEC GCSE Higher June 2022 Unit 1 Q3

Higher June 2022 Unit 1 Q3

WJECHigherCurrent spec6 marksBar Charts & Pictograms Basic Probability Pie Charts

3. The children in year 5 and year 6 in a primary school took part in a survey.
The children were asked, “How many pets do you have?”
The results are shown in the pie chart and bar chart below.
No child in either year had more than 5 pets.

Year 5 pie chart with sectors No pets, 1 pet (a right angle), 2 pets, 3 pets, 4 pets and 5 pets; Year 6 bar chart of frequency against number of pets: 0 pets 6, 1 pet 8, 2 pets 5, 3 pets 3, 4 pets 2, 5 pets 1

There are 36 children in year 5.

One child is chosen at random from all the children in year 5 and year 6.
What is the probability that this child has no more than 1 pet? [6]

Mark scheme

Scheme	Marks	Comments
(0 pets angle =) 40(°) ± 2(°)	B1	Answers may be seen on diagrams
(Year 5: 0 pets =) \(\dfrac{40(^\circ) \pm 2(^\circ)}{360}\) × 36	M1	Or equivalent FT ‘their 40’
(Year 5: 0 pets =) 4	A1	Answer must be whole number and from correct working (e.g. not from 360 ÷ 90) An answer of 4 (may be seen as 4/36) implies B1M1A1, provided not from incorrect working.
(Year 5: 1 pet = ) 9	B1	May be seen as 9/36
(Probability no more than 1 pet =) \(\dfrac{27}{61}\) or equivalent ISW	B2	FT \(\dfrac{\text{‘their derived 4’} + \text{‘their derived 9’} + 6 + 8}{61}\) (no more than 1 pet) B1 for a numerator of 27 in a fraction < 1. FT ‘their derived 4’ + ‘their derived 9’ + 6 + 8 accurately evaluated as a numerator in a fraction < 1. B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘27 in 61’. If no marks awarded, award SC1 for sight of a correct 61. Special cases: If only 1 pet considered from Year 5 AND Year 6, an answer of \(\dfrac{17}{61}\) would gain B0 or B1 M0A0B1B2 FT \(\dfrac{\text{‘their derived 9’} + 8}{61}\) for B0 or B1 M0A0B0B2 Last B1 for a numerator of 17 in a fraction < 1. FT ‘their derived 9’ + 8 accurately evaluated as a numerator in a fraction < 1. Last B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘17 in 61’. If only 0 pets considered from Year 5 AND Year 6, an answer of \(\dfrac{10}{61}\) would gain B1M1A1B0B2 FT \(\dfrac{\text{‘their derived 4’} + 6}{61}\) for B1M1A0B0B2 Last B1 for a numerator of 10 in a fraction < 1. FT ‘their derived 4’ + 6 accurately evaluated as a numerator in a fraction < 1. Last B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘10 in 61’.

Alternative method 1

Scheme	Marks	Comments
(0 + 1 pet angle =) 130(°) ± 2(°)	B1	Answers may be seen on diagrams
(Year 5: 0 + 1 pet =) \(\dfrac{130(^\circ) \pm 2(^\circ)}{360}\) × 36	M1	Or equivalent FT ‘their 130’
(Year 5: 0 + 1 pet =) 13	A2	May be seen as 13/36 Award A1 for an answer not rounded.
(Probability no more than 1 pet =) \(\dfrac{27}{61}\) or equivalent ISW	B2	FT \(\dfrac{(\text{‘their derived 13’} + 6 + 8)}{61}\) B1 for a numerator of 27 in a fraction < 1. FT ‘their derived 13’ + 6 + 8 accurately evaluated as a numerator in a fraction < 1. B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘27 in 61’. If no marks awarded for the whole question, award SC1 for sight of a correct 61.

Alternative method 2

Scheme	Marks	Comments
(Each child is represented by \(\dfrac{360(^\circ)}{36}\) = ) 10(°)	B1	Answers may be seen on diagrams
(Year 5: 0 pets angle = 40(°) ± 2(°)	B1
(Year 5: 0 pets = \(\dfrac{40(^\circ) \pm 2(^\circ)}{10(^\circ)}\) = ) 4	B1	FT ‘their 40’ Answer must be whole number and from correct working (e.g. not from 360 ÷ 90) An answer of 4 (may be seen as 4/36) implies B1B1B1, provided not from incorrect working.
(Year 5: 1 pet = ) 9	B1	May be seen as 9/36
(Probability no more than 1 pet =) \(\dfrac{27}{61}\) or equivalent ISW	B2	FT \(\dfrac{(\text{‘their derived 4’} + \text{‘their derived 9’} + 6 + 8)}{61}\) B1 for a numerator of 27 in a fraction < 1. FT ‘their derived 4’ + ‘their derived 9’ + 6 + 8 accurately evaluated as a numerator in a fraction < 1 B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘27 in 61’. If no marks awarded, award SC1 for sight of a correct 61. Special cases: If only 1 pet considered from Year 5 AND Year 6, an answer of \(\dfrac{17}{61}\) would gain B0 or B1 M0A0B1B2 FT \(\dfrac{\text{‘their derived 9’} + 8}{61}\) for B0 or B1 M0A0B0B2 Last B1 for a numerator of 17 in a fraction < 1. FT ‘their derived 9’ + 8 accurately evaluated as a numerator in a fraction < 1. Last B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘17 in 61’. If only 0 pets considered from Year 5 AND Year 6, an answer of \(\dfrac{10}{61}\) would gain B1M1A1B0B2 FT \(\dfrac{\text{‘their derived 4’} + 6}{61}\) for B1M1A0B0B2 Last B1 for a numerator of 10 in a fraction < 1. FT ‘their derived 4’ + 6 accurately evaluated as a numerator in a fraction < 1. Last B1 for a denominator of 61 in a fraction < 1. Penalise incorrect notation −1. e.g. ‘10 in 61’.