Mixed Topic Worksheet Grades 6/7: Day 038
- 1
Question 1. 75 customers: 45 buy a hot drink, 38 buy a snack and 20 buy both. One customer is chosen at random. Work out the probability, as a percentage to 1 decimal place, that the customer buys a hot drink only.
Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: hot drink only =45-20=25
- A1: 25/75=33.3%
Answer: 33.3%[2 marks] - 2
Question 2. Show that an estimate for dfrac√80.6 × 3.90.41 is 90 Use the nearest square number for the root and round the other numbers to 1 significant figure.
Estimating Roots▶ Show worked answerHide worked answer
- M1: √81 = 9
- M1: dfrac9 × 40.4
- A1: 36 ÷ 0.4 = 90
Answer: 90[3 marks] - 3
Question 3. Triangle T has vertices (1, 2), (3, 2) and (1, 3).
T is enlarged by scale factor -2, centre (0, 0).
Write down the coordinates of the vertices of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B1: (-2, -4)
- B1: (-6, -4)
- B1: (-2, -6)
Answer: (-2, -4), (-6, -4) and (-2, -6)[3 marks] - 4
Question 4. Sian finds the nth term of the sequence
5 qquad 12 qquad 23 qquad 38 qquad ldots
She writes: second difference is 4, so the nth term is 4n² + n
Is Sian correct? You must show your working.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: 4 × 2² + 2 = 18
- A1: 18 is not 12, so No
Answer: No: the 2nd term of 4n² + n is 18, not 12[2 marks] - 5
Question 5. ABC is an isosceles triangle with AB = AC.
Work out the length of BC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: BC² = 10.4² + 10.4² - 2 × 10.4 × 10.4 × cos 44^°
- M1: BC² = 216.32 - 155.61 = 60.71
- A1: BC = 7.8
Answer: 7.8 cm[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 038
- 1
Question 1. 75 customers: 45 buy a hot drink, 38 buy a snack and 20 buy both. One customer is chosen at random. Work out the probability, as a percentage to 1 decimal place, that the customer buys a hot drink only.
[2 marks]Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: hot drink only =45-20=25
- A1: 25/75=33.3%
Answer: 33.3% - 2
Question 2. Show that an estimate for dfrac√80.6 × 3.90.41 is 90 Use the nearest square number for the root and round the other numbers to 1 significant figure.
[3 marks]Estimating Roots▶ Show worked answerHide worked answer
- M1: √81 = 9
- M1: dfrac9 × 40.4
- A1: 36 ÷ 0.4 = 90
Answer: 90 - 3
Question 3. Triangle T has vertices (1, 2), (3, 2) and (1, 3).
[3 marks]
T is enlarged by scale factor -2, centre (0, 0).
Write down the coordinates of the vertices of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B1: (-2, -4)
- B1: (-6, -4)
- B1: (-2, -6)
Answer: (-2, -4), (-6, -4) and (-2, -6) - 4
Question 4. Sian finds the nth term of the sequence
[2 marks]
5 qquad 12 qquad 23 qquad 38 qquad ldots
She writes: second difference is 4, so the nth term is 4n² + n
Is Sian correct? You must show your working.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: 4 × 2² + 2 = 18
- A1: 18 is not 12, so No
Answer: No: the 2nd term of 4n² + n is 18, not 12 - 5
Question 5. ABC is an isosceles triangle with AB = AC.
[3 marks]
Work out the length of BC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: BC² = 10.4² + 10.4² - 2 × 10.4 × 10.4 × cos 44^°
- M1: BC² = 216.32 - 155.61 = 60.71
- A1: BC = 7.8
Answer: 7.8 cm
Mixed Topic Worksheet Grades 6/7: Day 038
- 1
Question 1. 75 customers: 45 buy a hot drink, 38 buy a snack and 20 buy both. One customer is chosen at random. Work out the probability, as a percentage to 1 decimal place, that the customer buys a hot drink only.
Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: hot drink only =45-20=25
- A1: 25/75=33.3%
Answer: 33.3%[2 marks] - 2
Question 2. Show that an estimate for dfrac√80.6 × 3.90.41 is 90 Use the nearest square number for the root and round the other numbers to 1 significant figure.
Estimating Roots▶ Show worked answerHide worked answer
- M1: √81 = 9
- M1: dfrac9 × 40.4
- A1: 36 ÷ 0.4 = 90
Answer: 90[3 marks] - 3
Question 3. Triangle T has vertices (1, 2), (3, 2) and (1, 3).
T is enlarged by scale factor -2, centre (0, 0).
Write down the coordinates of the vertices of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B1: (-2, -4)
- B1: (-6, -4)
- B1: (-2, -6)
Answer: (-2, -4), (-6, -4) and (-2, -6)[3 marks] - 4
Question 4. Sian finds the nth term of the sequence
5 qquad 12 qquad 23 qquad 38 qquad ldots
She writes: second difference is 4, so the nth term is 4n² + n
Is Sian correct? You must show your working.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: 4 × 2² + 2 = 18
- A1: 18 is not 12, so No
Answer: No: the 2nd term of 4n² + n is 18, not 12[2 marks] - 5
Question 5. ABC is an isosceles triangle with AB = AC.
Work out the length of BC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: BC² = 10.4² + 10.4² - 2 × 10.4 × 10.4 × cos 44^°
- M1: BC² = 216.32 - 155.61 = 60.71
- A1: BC = 7.8
Answer: 7.8 cm[3 marks]