Mixed Topic Worksheet Grades 8/9: Day 023
- 1
Question 1. Show that the equation x³ - 4x + 2 = 0 has a solution between x = 0 and x = 1
Change of Signs▶ Show worked answerHide worked answer
- M1: 0³ - 4(0) + 2 = 2 and 1³ - 4(1) + 2 = -1
- A1: there is a change of sign, so there is a solution between x = 0 and x = 1
Answer: f(0) = 2 > 0 and f(1) = -1 < 0: a change of sign, so a solution lies between 0 and 1[2 marks] - 2
Question 2. The table shows information about the masses, m kg, of 60 parcels.
Complete the table by working out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density = frequency ÷ class width
- A1: at least two correct frequency densities
- A1: 0.8, 2.4, 3.2, 0.8
Answer: 0.8, 2.4, 3.2, 0.8[3 marks] - 3
Question 3. The curve y = x² + 3x - 4 is reflected in the y-axis.
Write down the equation of the image.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replaces x with -x: y = (-x)² + 3(-x) - 4
- M1: (-x)² = x² and 3(-x) = -3x
- A1: y = x² - 3x - 4
Answer: y = x² - 3x - 4[3 marks] - 4
Question 4. Two fair dice are rolled. Given that the total score is at least 10, work out the probability that at least one die shows a 6.
Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: totals of 10 or more: (4,6) (5,5) (6,4) (5,6) (6,5) (6,6), so 6 outcomes
- M1: outcomes with a 6: 5
- A1: 5/6
Answer: 5/6[3 marks] - 5
Question 5. Write 3x² - 6x + 1 in the form a(x + p)² + q
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² - 2x) + 1
- M1: 3≤ft((x - 1)² - 1) + 1
- A1: 3(x - 1)² - 2
Answer: 3(x - 1)² - 2[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 023
- 1
Question 1. Show that the equation x³ - 4x + 2 = 0 has a solution between x = 0 and x = 1
[2 marks]Change of Signs▶ Show worked answerHide worked answer
- M1: 0³ - 4(0) + 2 = 2 and 1³ - 4(1) + 2 = -1
- A1: there is a change of sign, so there is a solution between x = 0 and x = 1
Answer: f(0) = 2 > 0 and f(1) = -1 < 0: a change of sign, so a solution lies between 0 and 1 - 2
Question 2. The table shows information about the masses, m kg, of 60 parcels.
[3 marks]
Complete the table by working out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density = frequency ÷ class width
- A1: at least two correct frequency densities
- A1: 0.8, 2.4, 3.2, 0.8
Answer: 0.8, 2.4, 3.2, 0.8 - 3
Question 3. The curve y = x² + 3x - 4 is reflected in the y-axis.
[3 marks]
Write down the equation of the image.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replaces x with -x: y = (-x)² + 3(-x) - 4
- M1: (-x)² = x² and 3(-x) = -3x
- A1: y = x² - 3x - 4
Answer: y = x² - 3x - 4 - 4
Question 4. Two fair dice are rolled. Given that the total score is at least 10, work out the probability that at least one die shows a 6.
[3 marks]Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: totals of 10 or more: (4,6) (5,5) (6,4) (5,6) (6,5) (6,6), so 6 outcomes
- M1: outcomes with a 6: 5
- A1: 5/6
Answer: 5/6 - 5
Question 5. Write 3x² - 6x + 1 in the form a(x + p)² + q
[3 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² - 2x) + 1
- M1: 3≤ft((x - 1)² - 1) + 1
- A1: 3(x - 1)² - 2
Answer: 3(x - 1)² - 2
Mixed Topic Worksheet Grades 8/9: Day 023
- 1
Question 1. Show that the equation x³ - 4x + 2 = 0 has a solution between x = 0 and x = 1
Change of Signs▶ Show worked answerHide worked answer
- M1: 0³ - 4(0) + 2 = 2 and 1³ - 4(1) + 2 = -1
- A1: there is a change of sign, so there is a solution between x = 0 and x = 1
Answer: f(0) = 2 > 0 and f(1) = -1 < 0: a change of sign, so a solution lies between 0 and 1[2 marks] - 2
Question 2. The table shows information about the masses, m kg, of 60 parcels.
Complete the table by working out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density = frequency ÷ class width
- A1: at least two correct frequency densities
- A1: 0.8, 2.4, 3.2, 0.8
Answer: 0.8, 2.4, 3.2, 0.8[3 marks] - 3
Question 3. The curve y = x² + 3x - 4 is reflected in the y-axis.
Write down the equation of the image.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replaces x with -x: y = (-x)² + 3(-x) - 4
- M1: (-x)² = x² and 3(-x) = -3x
- A1: y = x² - 3x - 4
Answer: y = x² - 3x - 4[3 marks] - 4
Question 4. Two fair dice are rolled. Given that the total score is at least 10, work out the probability that at least one die shows a 6.
Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: totals of 10 or more: (4,6) (5,5) (6,4) (5,6) (6,5) (6,6), so 6 outcomes
- M1: outcomes with a 6: 5
- A1: 5/6
Answer: 5/6[3 marks] - 5
Question 5. Write 3x² - 6x + 1 in the form a(x + p)² + q
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3(x² - 2x) + 1
- M1: 3≤ft((x - 1)² - 1) + 1
- A1: 3(x - 1)² - 2
Answer: 3(x - 1)² - 2[3 marks]