Mixed Topic Worksheet Grades 8/9: Day 034
- 1
Question 1. The graph of y = x⁴ - 3x² + 5 is reflected.
Mia says, 'Reflecting the graph in the y-axis gives the same graph.'
Noah says, 'Reflecting the graph in the x-axis gives the same graph.'
Who is correct? You must show your working.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y-axis: (-x)⁴ - 3(-x)² + 5 = x⁴ - 3x² + 5
- M1: x-axis: y = -x⁴ + 3x² - 5, which is different
- C1: Mia is correct
Answer: Mia is correct[3 marks] - 2
Question 2. The table shows the frequency densities of a histogram of 100 values. Estimate the median.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 14, 44, so 6 more needed from 24
- M1: 20+dfrac624×20
- A1: 25
Answer: 25[3 marks] - 3
Question 3. ABCDEFGH is a cuboid.
The angle between AG and the plane ABCD is 34^°.
Work out CG. Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AC² = 11² + 7²
- M1: CG = AC × tan 34^°
- A1: CG = 8.8 from 13.04 × 0.6745
Answer: 8.8[3 marks] - 4
Question 4. PA and PB are tangents to a circle with centre O and radius 10 cm, touching it at A and B. OP = 26 cm. Work out the size of angle APB. Give your answer correct to 1 decimal place.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: sin(APO) = dfrac1026, using angle OAP = 90°
- B1: angle APO = 22.6° and OP bisects angle APB
- A1: 2 × 22.6 = 45.2°
Answer: 45.2°[3 marks] - 5
Question 5. Solve x²-3x-10 < 0
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: solve x²-3x-10 = 0, (x-5)(x+2) = 0
- A1: critical values x = -2 and x = 5
- A1: -2 < x < 5
Answer: -2 < x < 5[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 034
- 1
Question 1. The graph of y = x⁴ - 3x² + 5 is reflected.
[3 marks]
Mia says, 'Reflecting the graph in the y-axis gives the same graph.'
Noah says, 'Reflecting the graph in the x-axis gives the same graph.'
Who is correct? You must show your working.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y-axis: (-x)⁴ - 3(-x)² + 5 = x⁴ - 3x² + 5
- M1: x-axis: y = -x⁴ + 3x² - 5, which is different
- C1: Mia is correct
Answer: Mia is correct - 2
Question 2. The table shows the frequency densities of a histogram of 100 values. Estimate the median.
[3 marks]Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 14, 44, so 6 more needed from 24
- M1: 20+dfrac624×20
- A1: 25
Answer: 25 - 3
Question 3. ABCDEFGH is a cuboid.
[3 marks]
The angle between AG and the plane ABCD is 34^°.
Work out CG. Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AC² = 11² + 7²
- M1: CG = AC × tan 34^°
- A1: CG = 8.8 from 13.04 × 0.6745
Answer: 8.8 - 4
Question 4. PA and PB are tangents to a circle with centre O and radius 10 cm, touching it at A and B. OP = 26 cm. Work out the size of angle APB. Give your answer correct to 1 decimal place.
[3 marks]Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: sin(APO) = dfrac1026, using angle OAP = 90°
- B1: angle APO = 22.6° and OP bisects angle APB
- A1: 2 × 22.6 = 45.2°
Answer: 45.2° - 5
Question 5. Solve x²-3x-10 < 0
[3 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: solve x²-3x-10 = 0, (x-5)(x+2) = 0
- A1: critical values x = -2 and x = 5
- A1: -2 < x < 5
Answer: -2 < x < 5
Mixed Topic Worksheet Grades 8/9: Day 034
- 1
Question 1. The graph of y = x⁴ - 3x² + 5 is reflected.
Mia says, 'Reflecting the graph in the y-axis gives the same graph.'
Noah says, 'Reflecting the graph in the x-axis gives the same graph.'
Who is correct? You must show your working.Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y-axis: (-x)⁴ - 3(-x)² + 5 = x⁴ - 3x² + 5
- M1: x-axis: y = -x⁴ + 3x² - 5, which is different
- C1: Mia is correct
Answer: Mia is correct[3 marks] - 2
Question 2. The table shows the frequency densities of a histogram of 100 values. Estimate the median.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 14, 44, so 6 more needed from 24
- M1: 20+dfrac624×20
- A1: 25
Answer: 25[3 marks] - 3
Question 3. ABCDEFGH is a cuboid.
The angle between AG and the plane ABCD is 34^°.
Work out CG. Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AC² = 11² + 7²
- M1: CG = AC × tan 34^°
- A1: CG = 8.8 from 13.04 × 0.6745
Answer: 8.8[3 marks] - 4
Question 4. PA and PB are tangents to a circle with centre O and radius 10 cm, touching it at A and B. OP = 26 cm. Work out the size of angle APB. Give your answer correct to 1 decimal place.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: sin(APO) = dfrac1026, using angle OAP = 90°
- B1: angle APO = 22.6° and OP bisects angle APB
- A1: 2 × 22.6 = 45.2°
Answer: 45.2°[3 marks] - 5
Question 5. Solve x²-3x-10 < 0
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: solve x²-3x-10 = 0, (x-5)(x+2) = 0
- A1: critical values x = -2 and x = 5
- A1: -2 < x < 5
Answer: -2 < x < 5[3 marks]