Mixed Topic Worksheet Grades 8/9: Day 032
- 1
Question 1. The graph of y = cos x is reflected in the x-axis.
Write down the equation of the reflected graph and the image of the point (0, 1)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: y = -cos x
- B1: (0, -1)
Answer: y = -cos x; (0, -1)[2 marks] - 2
Question 2. Zara says that 5√6 is greater than 6√5.
Is Zara correct?
You must show your working.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 5√6 = √150
- M1: 6√5 = √180
- C1: No, 6√5 is greater
Answer: No: 5√6 = √150 and 6√5 = √180, so 6√5 is greater[3 marks] - 3
Question 3. ABCDEFGH is a cuboid.
M is the midpoint of GH.
Work out the length of AM.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: AM² = (16 ÷ 2)² + 7² + 6²
- M1: AM² = 64 + 49 + 36
- M1: AM = √149
- A1: AM = 12.2
Answer: 12.2[4 marks] - 4
Question 4. Work out the frequency density of each class.
15 < t ≤ 35: frequency 36
35 < t ≤ 40: frequency 14
40 < t ≤ 60: frequency 30Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width
- A1: 1.8
- A1: 2.8
- A1: 1.5
Answer: 1.8, 2.8, 1.5[4 marks] - 5
Question 5. The curve y = 2x² + bx + c has its minimum point at (3, -4)
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: y = 2(x - 3)² - 4
- M1: 2x² - 12x + 18 - 4
- A1: b = -12 and c = 14
Answer: b = -12, c = 14[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 032
- 1
Question 1. The graph of y = cos x is reflected in the x-axis.
[2 marks]
Write down the equation of the reflected graph and the image of the point (0, 1)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: y = -cos x
- B1: (0, -1)
Answer: y = -cos x; (0, -1) - 2
Question 2. Zara says that 5√6 is greater than 6√5.
[3 marks]
Is Zara correct?
You must show your working.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 5√6 = √150
- M1: 6√5 = √180
- C1: No, 6√5 is greater
Answer: No: 5√6 = √150 and 6√5 = √180, so 6√5 is greater - 3
Question 3. ABCDEFGH is a cuboid.
[4 marks]
M is the midpoint of GH.
Work out the length of AM.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: AM² = (16 ÷ 2)² + 7² + 6²
- M1: AM² = 64 + 49 + 36
- M1: AM = √149
- A1: AM = 12.2
Answer: 12.2 - 4
Question 4. Work out the frequency density of each class.
[4 marks]
15 < t ≤ 35: frequency 36
35 < t ≤ 40: frequency 14
40 < t ≤ 60: frequency 30Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width
- A1: 1.8
- A1: 2.8
- A1: 1.5
Answer: 1.8, 2.8, 1.5 - 5
Question 5. The curve y = 2x² + bx + c has its minimum point at (3, -4)
[3 marks]
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: y = 2(x - 3)² - 4
- M1: 2x² - 12x + 18 - 4
- A1: b = -12 and c = 14
Answer: b = -12, c = 14
Mixed Topic Worksheet Grades 8/9: Day 032
- 1
Question 1. The graph of y = cos x is reflected in the x-axis.
Write down the equation of the reflected graph and the image of the point (0, 1)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: y = -cos x
- B1: (0, -1)
Answer: y = -cos x; (0, -1)[2 marks] - 2
Question 2. Zara says that 5√6 is greater than 6√5.
Is Zara correct?
You must show your working.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 5√6 = √150
- M1: 6√5 = √180
- C1: No, 6√5 is greater
Answer: No: 5√6 = √150 and 6√5 = √180, so 6√5 is greater[3 marks] - 3
Question 3. ABCDEFGH is a cuboid.
M is the midpoint of GH.
Work out the length of AM.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: AM² = (16 ÷ 2)² + 7² + 6²
- M1: AM² = 64 + 49 + 36
- M1: AM = √149
- A1: AM = 12.2
Answer: 12.2[4 marks] - 4
Question 4. Work out the frequency density of each class.
15 < t ≤ 35: frequency 36
35 < t ≤ 40: frequency 14
40 < t ≤ 60: frequency 30Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width
- A1: 1.8
- A1: 2.8
- A1: 1.5
Answer: 1.8, 2.8, 1.5[4 marks] - 5
Question 5. The curve y = 2x² + bx + c has its minimum point at (3, -4)
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: y = 2(x - 3)² - 4
- M1: 2x² - 12x + 18 - 4
- A1: b = -12 and c = 14
Answer: b = -12, c = 14[3 marks]