Mixed Topic Worksheet Grades 8/9: Day 051
- 1
Question 1. The graph of y = tan x is translated 40° to the right. Write down the equation of the asymptote between x = 0° and x = 180° of the new graph.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: original asymptote at x = 90°
- A1: x = 130°
Answer: x = 130°[2 marks] - 2
Question 2. The table shows information about the lengths, x cm, of 91 ropes.
A histogram is drawn for this information.
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: at least two correct
- A1: 0.8, 2.6, 2.2, 1.3
Answer: 0.8, 2.6, 2.2, 1.3[3 marks] - 3
Question 3. How many integers x satisfy x² - 4x - 12 ≤ 0?
Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x - 6)(x + 2) = 0 so critical values -2 and 6
- M1: -2 ≤ x ≤ 6
- A1: 9
Answer: 9[3 marks] - 4
Question 4. TA is a tangent to a circle at A. B and C are points on the circle, with C in the alternate segment to angle TAB. Angle TAB = (5x - 10)° and angle ACB = (3x + 10)°. Work out the value of x.
Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TAB = angle ACB (alternate segment theorem)
- M1: 5x - 10 = 3x + 10
- A1: x = 10
Answer: x = 10[3 marks] - 5
Question 5. Chen says that the solution of x²-6x-3 < 0 is -1 < x < 7. Is Chen correct? You must show your working.
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: substitute x = -1, (-1)²-6(-1)-3 = 4
- A1: 4 is not less than 0, so x = -1 is not in the solution
- C1: Chen is not correct
Answer: No. At x = -1, (-1)²-6(-1)-3 = 4, which is not less than 0[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 051
- 1
Question 1. The graph of y = tan x is translated 40° to the right. Write down the equation of the asymptote between x = 0° and x = 180° of the new graph.
[2 marks]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: original asymptote at x = 90°
- A1: x = 130°
Answer: x = 130° - 2
Question 2. The table shows information about the lengths, x cm, of 91 ropes.
[3 marks]
A histogram is drawn for this information.
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: at least two correct
- A1: 0.8, 2.6, 2.2, 1.3
Answer: 0.8, 2.6, 2.2, 1.3 - 3
Question 3. How many integers x satisfy x² - 4x - 12 ≤ 0?
[3 marks]Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x - 6)(x + 2) = 0 so critical values -2 and 6
- M1: -2 ≤ x ≤ 6
- A1: 9
Answer: 9 - 4
Question 4. TA is a tangent to a circle at A. B and C are points on the circle, with C in the alternate segment to angle TAB. Angle TAB = (5x - 10)° and angle ACB = (3x + 10)°. Work out the value of x.
[3 marks]Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TAB = angle ACB (alternate segment theorem)
- M1: 5x - 10 = 3x + 10
- A1: x = 10
Answer: x = 10 - 5
Question 5. Chen says that the solution of x²-6x-3 < 0 is -1 < x < 7. Is Chen correct? You must show your working.
[3 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: substitute x = -1, (-1)²-6(-1)-3 = 4
- A1: 4 is not less than 0, so x = -1 is not in the solution
- C1: Chen is not correct
Answer: No. At x = -1, (-1)²-6(-1)-3 = 4, which is not less than 0
Mixed Topic Worksheet Grades 8/9: Day 051
- 1
Question 1. The graph of y = tan x is translated 40° to the right. Write down the equation of the asymptote between x = 0° and x = 180° of the new graph.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: original asymptote at x = 90°
- A1: x = 130°
Answer: x = 130°[2 marks] - 2
Question 2. The table shows information about the lengths, x cm, of 91 ropes.
A histogram is drawn for this information.
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: at least two correct
- A1: 0.8, 2.6, 2.2, 1.3
Answer: 0.8, 2.6, 2.2, 1.3[3 marks] - 3
Question 3. How many integers x satisfy x² - 4x - 12 ≤ 0?
Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (x - 6)(x + 2) = 0 so critical values -2 and 6
- M1: -2 ≤ x ≤ 6
- A1: 9
Answer: 9[3 marks] - 4
Question 4. TA is a tangent to a circle at A. B and C are points on the circle, with C in the alternate segment to angle TAB. Angle TAB = (5x - 10)° and angle ACB = (3x + 10)°. Work out the value of x.
Circle Theorems▶ Show worked answerHide worked answer
- B1: angle TAB = angle ACB (alternate segment theorem)
- M1: 5x - 10 = 3x + 10
- A1: x = 10
Answer: x = 10[3 marks] - 5
Question 5. Chen says that the solution of x²-6x-3 < 0 is -1 < x < 7. Is Chen correct? You must show your working.
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: substitute x = -1, (-1)²-6(-1)-3 = 4
- A1: 4 is not less than 0, so x = -1 is not in the solution
- C1: Chen is not correct
Answer: No. At x = -1, (-1)²-6(-1)-3 = 4, which is not less than 0[3 marks]