Mixed Topic Worksheet Grades 8/9: Day 029
- 1
Question 1. Write down the coordinates of the maximum point of y = sin x for 0° ≤ x ≤ 360°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: maximum value 1
- B1: (90, 1)
Answer: (90, 1)[2 marks] - 2
Question 2. The line y = -x + 4 and the curve y = x² - 5x + 8
Ali says they meet at two points.
Is Ali correct? Show your working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - 5x + 8 = -x + 4
- M1: (x - 2)² = 0
- A1: No, one solution x = 2, so one point (2, 2)
Answer: No, they meet at one point only, (2, 2)[3 marks] - 3
Question 3. Prove that the product of two consecutive odd numbers is always 1 less than a multiple of 4.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (2n+1)(2n+3)
- M1: = 4n²+8n+3
- C1: = 4(n²+2n+1) - 1, which is 1 less than a multiple of 4
Answer: 4(n²+2n+1)-1, so 1 less than a multiple of 4[3 marks] - 4
Question 4. Numbered tiles are in a bag. One tile is taken at random and kept out, then a second. Work out the probability that the product of the two numbers is a multiple of 3.
Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: P(multiple of 3) = 1 - P(neither is)
- B1: 6 tiles are multiples of 3, so 15 - 6 = 9 are not
- M1: 9/15 × 8/14 = 72/210
- M1: 1 - 72/210
- A1: 23/35
Answer: 23/35[5 marks] - 5
Question 5. Here is a speed-time graph for a tram for the first 6 seconds. Use 3 rectangles of equal width, each as high as the speed at the midpoint of its strip, to estimate the distance travelled in the 6 seconds.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: midpoints at 1, 3, 5 seconds, speeds 5, 9, 5
- M1: 2 × (5 + 9 + 5)
- A1: 38 m
Answer: 38 m[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 029
- 1
Question 1. Write down the coordinates of the maximum point of y = sin x for 0° ≤ x ≤ 360°.
[2 marks]Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: maximum value 1
- B1: (90, 1)
Answer: (90, 1) - 2
Question 2. The line y = -x + 4 and the curve y = x² - 5x + 8
[3 marks]
Ali says they meet at two points.
Is Ali correct? Show your working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - 5x + 8 = -x + 4
- M1: (x - 2)² = 0
- A1: No, one solution x = 2, so one point (2, 2)
Answer: No, they meet at one point only, (2, 2) - 3
Question 3. Prove that the product of two consecutive odd numbers is always 1 less than a multiple of 4.
[3 marks]Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (2n+1)(2n+3)
- M1: = 4n²+8n+3
- C1: = 4(n²+2n+1) - 1, which is 1 less than a multiple of 4
Answer: 4(n²+2n+1)-1, so 1 less than a multiple of 4 - 4
Question 4. Numbered tiles are in a bag. One tile is taken at random and kept out, then a second. Work out the probability that the product of the two numbers is a multiple of 3.
[5 marks]Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: P(multiple of 3) = 1 - P(neither is)
- B1: 6 tiles are multiples of 3, so 15 - 6 = 9 are not
- M1: 9/15 × 8/14 = 72/210
- M1: 1 - 72/210
- A1: 23/35
Answer: 23/35 - 5
Question 5. Here is a speed-time graph for a tram for the first 6 seconds. Use 3 rectangles of equal width, each as high as the speed at the midpoint of its strip, to estimate the distance travelled in the 6 seconds.
[3 marks]Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: midpoints at 1, 3, 5 seconds, speeds 5, 9, 5
- M1: 2 × (5 + 9 + 5)
- A1: 38 m
Answer: 38 m
Mixed Topic Worksheet Grades 8/9: Day 029
- 1
Question 1. Write down the coordinates of the maximum point of y = sin x for 0° ≤ x ≤ 360°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- B1: maximum value 1
- B1: (90, 1)
Answer: (90, 1)[2 marks] - 2
Question 2. The line y = -x + 4 and the curve y = x² - 5x + 8
Ali says they meet at two points.
Is Ali correct? Show your working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - 5x + 8 = -x + 4
- M1: (x - 2)² = 0
- A1: No, one solution x = 2, so one point (2, 2)
Answer: No, they meet at one point only, (2, 2)[3 marks] - 3
Question 3. Prove that the product of two consecutive odd numbers is always 1 less than a multiple of 4.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (2n+1)(2n+3)
- M1: = 4n²+8n+3
- C1: = 4(n²+2n+1) - 1, which is 1 less than a multiple of 4
Answer: 4(n²+2n+1)-1, so 1 less than a multiple of 4[3 marks] - 4
Question 4. Numbered tiles are in a bag. One tile is taken at random and kept out, then a second. Work out the probability that the product of the two numbers is a multiple of 3.
Conditional Probability with Tree Diagrams▶ Show worked answerHide worked answer
- M1: P(multiple of 3) = 1 - P(neither is)
- B1: 6 tiles are multiples of 3, so 15 - 6 = 9 are not
- M1: 9/15 × 8/14 = 72/210
- M1: 1 - 72/210
- A1: 23/35
Answer: 23/35[5 marks] - 5
Question 5. Here is a speed-time graph for a tram for the first 6 seconds. Use 3 rectangles of equal width, each as high as the speed at the midpoint of its strip, to estimate the distance travelled in the 6 seconds.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: midpoints at 1, 3, 5 seconds, speeds 5, 9, 5
- M1: 2 × (5 + 9 + 5)
- A1: 38 m
Answer: 38 m[3 marks]