Mixed Topic Worksheet Grades 8/9: Day 011
- 1
Question 1. How many times does the graph of y = tan x cross the line y = 2 for 0° ≤ x ≤ 360°?
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: each branch of tan x rises through every value once
- A1: 2
Answer: 2[2 marks] - 2
Question 2. The product of two consecutive integers is added to the larger of the two integers.
Prove algebraically that the result is a square number.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 1) + (n + 1)
- A1: n² + 2n + 1
- C1: (n + 1)², which is a square number
Answer: (n + 1)²[3 marks] - 3
Question 3. A class of 30 students has 14 girls. 18 students play the piano and 10 of them are girls. A student who does not play the piano is chosen. Work out the probability that this student is a girl.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: students who do not play = 30 - 18 = 12
- M1: girls who do not play = 14 - 10 = 4
- A1: 4/12 = 1/3
Answer: 1/3[3 marks] - 4
Question 4. The table shows the frequency densities of a histogram. Estimate the median.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 15, 25, 40, 20 so total 100 and median is the 50th value
- M1: 10+dfrac1040×10
- A1: 12.5
Answer: 12.5[3 marks] - 5
Question 5. Here is a speed-time graph for a motorbike. Use 3 trapezia of equal width to work out an estimate for the distance travelled between 2 seconds and 8 seconds.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: the strips are 2 seconds wide, with speeds read at 2, 4, 6 and 8 seconds
- M1: dfrac12 × 2 × (24 + 32) + dfrac12 × 2 × (32 + 24) + dfrac12 × 2 × (24 + 0)
- A1: 136 m
Answer: 136 m[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 011
- 1
Question 1. How many times does the graph of y = tan x cross the line y = 2 for 0° ≤ x ≤ 360°?
[2 marks]Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: each branch of tan x rises through every value once
- A1: 2
Answer: 2 - 2
Question 2. The product of two consecutive integers is added to the larger of the two integers.
[3 marks]
Prove algebraically that the result is a square number.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 1) + (n + 1)
- A1: n² + 2n + 1
- C1: (n + 1)², which is a square number
Answer: (n + 1)² - 3
Question 3. A class of 30 students has 14 girls. 18 students play the piano and 10 of them are girls. A student who does not play the piano is chosen. Work out the probability that this student is a girl.
[3 marks]Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: students who do not play = 30 - 18 = 12
- M1: girls who do not play = 14 - 10 = 4
- A1: 4/12 = 1/3
Answer: 1/3 - 4
Question 4. The table shows the frequency densities of a histogram. Estimate the median.
[3 marks]Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 15, 25, 40, 20 so total 100 and median is the 50th value
- M1: 10+dfrac1040×10
- A1: 12.5
Answer: 12.5 - 5
Question 5. Here is a speed-time graph for a motorbike. Use 3 trapezia of equal width to work out an estimate for the distance travelled between 2 seconds and 8 seconds.
[3 marks]Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: the strips are 2 seconds wide, with speeds read at 2, 4, 6 and 8 seconds
- M1: dfrac12 × 2 × (24 + 32) + dfrac12 × 2 × (32 + 24) + dfrac12 × 2 × (24 + 0)
- A1: 136 m
Answer: 136 m
Mixed Topic Worksheet Grades 8/9: Day 011
- 1
Question 1. How many times does the graph of y = tan x cross the line y = 2 for 0° ≤ x ≤ 360°?
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: each branch of tan x rises through every value once
- A1: 2
Answer: 2[2 marks] - 2
Question 2. The product of two consecutive integers is added to the larger of the two integers.
Prove algebraically that the result is a square number.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 1) + (n + 1)
- A1: n² + 2n + 1
- C1: (n + 1)², which is a square number
Answer: (n + 1)²[3 marks] - 3
Question 3. A class of 30 students has 14 girls. 18 students play the piano and 10 of them are girls. A student who does not play the piano is chosen. Work out the probability that this student is a girl.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: students who do not play = 30 - 18 = 12
- M1: girls who do not play = 14 - 10 = 4
- A1: 4/12 = 1/3
Answer: 1/3[3 marks] - 4
Question 4. The table shows the frequency densities of a histogram. Estimate the median.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 15, 25, 40, 20 so total 100 and median is the 50th value
- M1: 10+dfrac1040×10
- A1: 12.5
Answer: 12.5[3 marks] - 5
Question 5. Here is a speed-time graph for a motorbike. Use 3 trapezia of equal width to work out an estimate for the distance travelled between 2 seconds and 8 seconds.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: the strips are 2 seconds wide, with speeds read at 2, 4, 6 and 8 seconds
- M1: dfrac12 × 2 × (24 + 32) + dfrac12 × 2 × (32 + 24) + dfrac12 × 2 × (24 + 0)
- A1: 136 m
Answer: 136 m[3 marks]