Mixed Topic Worksheet Grades 6/7: Day 029
- 1
Question 1. Water is poured at a constant rate into an empty cylinder.
Describe the graph of the depth of the water against time.
Give a reason for your answer.Matching Shapes to Graphs▶ Show worked answerHide worked answer
- B1: a straight line going up from the origin
- B1: the cylinder is the same width all the way up, so the depth rises by the same amount each second
Answer: A straight line through the origin, because the width stays the same so the depth rises at a constant rate[2 marks] - 2
Question 2. A triangle has sides of length 3 cm, 4 cm and 5 cm.
The triangle is enlarged by scale factor -3.
Work out the perimeter of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: sides of the image are 3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15 (lengths are positive)
- A1: 9 + 12 + 15 = 36 cm
Answer: 36 cm[2 marks] - 3
Question 3. The times, in seconds, of two runners over 6 races are shown. Runner A: 12.1, 12.2, 12.2, 12.3, 12.4, 12.5. Runner B: 11.9, 12.0, 12.2, 12.4, 12.6, 13.8. Work out the interquartile range of each runner and state who is more consistent.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: A: 12.4-12.2; B: 12.6-12.0
- A1: A =0.2, B =0.6
- B1: Runner A
Answer: A: 0.2 s, B: 0.6 s; Runner A is more consistent[3 marks] - 4
Question 4. Solve 2x² + 7x + 3 = 0
Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: factorise: (2x + 1)(x + 3) = 0
- M1: 2x + 1 = 0 or x + 3 = 0
- A1: x = -1/2 or x = -3
Answer: x = -1/2 or x = -3[3 marks] - 5
Question 5. Express 0.dot3dot6 as a fraction in its simplest form.
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- M1: 99x = 36
- A1: x = dfrac411
Answer: dfrac411[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 029
- 1
Question 1. Water is poured at a constant rate into an empty cylinder.
[2 marks]
Describe the graph of the depth of the water against time.
Give a reason for your answer.Matching Shapes to Graphs▶ Show worked answerHide worked answer
- B1: a straight line going up from the origin
- B1: the cylinder is the same width all the way up, so the depth rises by the same amount each second
Answer: A straight line through the origin, because the width stays the same so the depth rises at a constant rate - 2
Question 2. A triangle has sides of length 3 cm, 4 cm and 5 cm.
[2 marks]
The triangle is enlarged by scale factor -3.
Work out the perimeter of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: sides of the image are 3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15 (lengths are positive)
- A1: 9 + 12 + 15 = 36 cm
Answer: 36 cm - 3
Question 3. The times, in seconds, of two runners over 6 races are shown. Runner A: 12.1, 12.2, 12.2, 12.3, 12.4, 12.5. Runner B: 11.9, 12.0, 12.2, 12.4, 12.6, 13.8. Work out the interquartile range of each runner and state who is more consistent.
[3 marks]Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: A: 12.4-12.2; B: 12.6-12.0
- A1: A =0.2, B =0.6
- B1: Runner A
Answer: A: 0.2 s, B: 0.6 s; Runner A is more consistent - 4
Question 4. Solve 2x² + 7x + 3 = 0
[3 marks]Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: factorise: (2x + 1)(x + 3) = 0
- M1: 2x + 1 = 0 or x + 3 = 0
- A1: x = -1/2 or x = -3
Answer: x = -1/2 or x = -3 - 5
Question 5. Express 0.dot3dot6 as a fraction in its simplest form.
[3 marks]
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- M1: 99x = 36
- A1: x = dfrac411
Answer: dfrac411
Mixed Topic Worksheet Grades 6/7: Day 029
- 1
Question 1. Water is poured at a constant rate into an empty cylinder.
Describe the graph of the depth of the water against time.
Give a reason for your answer.Matching Shapes to Graphs▶ Show worked answerHide worked answer
- B1: a straight line going up from the origin
- B1: the cylinder is the same width all the way up, so the depth rises by the same amount each second
Answer: A straight line through the origin, because the width stays the same so the depth rises at a constant rate[2 marks] - 2
Question 2. A triangle has sides of length 3 cm, 4 cm and 5 cm.
The triangle is enlarged by scale factor -3.
Work out the perimeter of the image.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: sides of the image are 3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15 (lengths are positive)
- A1: 9 + 12 + 15 = 36 cm
Answer: 36 cm[2 marks] - 3
Question 3. The times, in seconds, of two runners over 6 races are shown. Runner A: 12.1, 12.2, 12.2, 12.3, 12.4, 12.5. Runner B: 11.9, 12.0, 12.2, 12.4, 12.6, 13.8. Work out the interquartile range of each runner and state who is more consistent.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: A: 12.4-12.2; B: 12.6-12.0
- A1: A =0.2, B =0.6
- B1: Runner A
Answer: A: 0.2 s, B: 0.6 s; Runner A is more consistent[3 marks] - 4
Question 4. Solve 2x² + 7x + 3 = 0
Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: factorise: (2x + 1)(x + 3) = 0
- M1: 2x + 1 = 0 or x + 3 = 0
- A1: x = -1/2 or x = -3
Answer: x = -1/2 or x = -3[3 marks] - 5
Question 5. Express 0.dot3dot6 as a fraction in its simplest form.
You must show all your working.Writing Recurring Decimals as Fractions▶ Show worked answerHide worked answer
- M1: multiplies by 100 and subtracts x, so the recurring parts cancel
- M1: 99x = 36
- A1: x = dfrac411
Answer: dfrac411[3 marks]