Mixed Topic Worksheet Grades 6/7: Day 005
- 1
Question 1. The nth term of a sequence is 3n + 2.
Is 50 a term of this sequence? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: 3n + 2 = 50, so 3n = 48
- M1: n = 16, a whole number
- A1: Yes, 50 is the 16th term
Answer: Yes: 3n + 2 = 50 gives n = 16[3 marks] - 2
Question 2. Sam draws a box plot for these 7 numbers.
3 quad 5 quad 8 quad 10 quad 16 quad 21 quad 24
He makes one mistake. Describe his mistake and write down the correct value.Drawing Box Plots▶ Show worked answerHide worked answer
- M1: (7 + 1) ÷ 4 = 2, so the quartiles are the 2nd and 6th values, 5 and 21, and the median is the 4th value, 10
- B1: the upper quartile is drawn at 16
- B1: the correct upper quartile is 21 (the 6th value)
Answer: The upper quartile is drawn at 16; the correct upper quartile is 21[3 marks] - 3
Question 3. Two cones are similar.
The volume of the small cone is 40 cm³.
Work out the volume of the large cone.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 6 ÷ 4 = 1.5
- M1: 1.5³ × 40
- A1: 135
Answer: 135 cm³[3 marks] - 4
Question 4. Here is triangle XYZ.
Sam wants to work out the length x.
Should Sam use the sine rule or the cosine rule?
Give a reason for your answer.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- B1: the cosine rule
- B1: two sides and the angle between them are known, and no side opposite a known angle is given
Answer: The cosine rule, because two sides and the angle between them are known[2 marks] - 5
Question 5. A cumulative frequency graph for 120 values shows a lower quartile of 31, a median of 40 and an upper quartile of 52. Work out how many values lie between 40 and 52.
Cumulative Frequency Median & IQR▶ Show worked answerHide worked answer
- M1: 120 values, so a quarter is 120 ÷ 4
- A1: 30
Answer: 30[2 marks]
Mixed Topic Worksheet Grades 6/7: Day 005
- 1
Question 1. The nth term of a sequence is 3n + 2.
[3 marks]
Is 50 a term of this sequence? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: 3n + 2 = 50, so 3n = 48
- M1: n = 16, a whole number
- A1: Yes, 50 is the 16th term
Answer: Yes: 3n + 2 = 50 gives n = 16 - 2
Question 2. Sam draws a box plot for these 7 numbers.
[3 marks]
3 quad 5 quad 8 quad 10 quad 16 quad 21 quad 24
He makes one mistake. Describe his mistake and write down the correct value.Drawing Box Plots▶ Show worked answerHide worked answer
- M1: (7 + 1) ÷ 4 = 2, so the quartiles are the 2nd and 6th values, 5 and 21, and the median is the 4th value, 10
- B1: the upper quartile is drawn at 16
- B1: the correct upper quartile is 21 (the 6th value)
Answer: The upper quartile is drawn at 16; the correct upper quartile is 21 - 3
Question 3. Two cones are similar.
[3 marks]
The volume of the small cone is 40 cm³.
Work out the volume of the large cone.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 6 ÷ 4 = 1.5
- M1: 1.5³ × 40
- A1: 135
Answer: 135 cm³ - 4
Question 4. Here is triangle XYZ.
[2 marks]
Sam wants to work out the length x.
Should Sam use the sine rule or the cosine rule?
Give a reason for your answer.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- B1: the cosine rule
- B1: two sides and the angle between them are known, and no side opposite a known angle is given
Answer: The cosine rule, because two sides and the angle between them are known - 5
Question 5. A cumulative frequency graph for 120 values shows a lower quartile of 31, a median of 40 and an upper quartile of 52. Work out how many values lie between 40 and 52.
[2 marks]Cumulative Frequency Median & IQR▶ Show worked answerHide worked answer
- M1: 120 values, so a quarter is 120 ÷ 4
- A1: 30
Answer: 30
Mixed Topic Worksheet Grades 6/7: Day 005
- 1
Question 1. The nth term of a sequence is 3n + 2.
Is 50 a term of this sequence? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: 3n + 2 = 50, so 3n = 48
- M1: n = 16, a whole number
- A1: Yes, 50 is the 16th term
Answer: Yes: 3n + 2 = 50 gives n = 16[3 marks] - 2
Question 2. Sam draws a box plot for these 7 numbers.
3 quad 5 quad 8 quad 10 quad 16 quad 21 quad 24
He makes one mistake. Describe his mistake and write down the correct value.Drawing Box Plots▶ Show worked answerHide worked answer
- M1: (7 + 1) ÷ 4 = 2, so the quartiles are the 2nd and 6th values, 5 and 21, and the median is the 4th value, 10
- B1: the upper quartile is drawn at 16
- B1: the correct upper quartile is 21 (the 6th value)
Answer: The upper quartile is drawn at 16; the correct upper quartile is 21[3 marks] - 3
Question 3. Two cones are similar.
The volume of the small cone is 40 cm³.
Work out the volume of the large cone.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 6 ÷ 4 = 1.5
- M1: 1.5³ × 40
- A1: 135
Answer: 135 cm³[3 marks] - 4
Question 4. Here is triangle XYZ.
Sam wants to work out the length x.
Should Sam use the sine rule or the cosine rule?
Give a reason for your answer.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- B1: the cosine rule
- B1: two sides and the angle between them are known, and no side opposite a known angle is given
Answer: The cosine rule, because two sides and the angle between them are known[2 marks] - 5
Question 5. A cumulative frequency graph for 120 values shows a lower quartile of 31, a median of 40 and an upper quartile of 52. Work out how many values lie between 40 and 52.
Cumulative Frequency Median & IQR▶ Show worked answerHide worked answer
- M1: 120 values, so a quarter is 120 ÷ 4
- A1: 30
Answer: 30[2 marks]