Mixed Topic Worksheet Grades 8/9: Day 042
- 1
Question 1. The point (4, -3) lies on y = f(x). Write down a point that lies on y = f(-x).
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x-coordinate changes sign
- A1: (-4, -3)
Answer: (-4, -3)[2 marks] - 2
Question 2. Solve 2sin x = 1.4 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: sin x = 0.7, so x = sin⁻¹0.7
- M1: 180^° - 44.4^°
- A1: 44.4^° and 135.6^°
Answer: x = 44.4^° and x = 135.6^°[3 marks] - 3
Question 3. The smallest and the largest of three consecutive positive integers are multiplied together.
The result is 255.
Use algebra to work out the three integers.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 2) = 255
- M1: n² + 2n - 255 = 0 so (n + 17)(n - 15) = 0
- A1: n = 15 so the integers are 15, 16 and 17
Answer: 15, 16 and 17[3 marks] - 4
Question 4. Marc runs 5 km, to the nearest km, in 25 minutes, to the nearest minute. Marc says his speed was less than 14 km/h. Is Marc correct? You must show your working.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: greatest speed uses the upper bound of distance and lower bound of time
- A1: 5.5 ÷ (24.5 ÷ 60) = 13.47 km/h
- C1: 13.47 < 14, so Marc is correct
Answer: Yes: greatest speed is 13.47 km/h, which is less than 14[3 marks] - 5
Question 5. The inequality x² + 8x + k > 0 is true for every value of x.
Work out the possible values of k.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + 8x + k = (x + 4)² + k - 16
- M1: (x + 4)² ≥ 0 with equality at x = -4, so k - 16 must be above 0
- A1: k > 16, strict because the expression must not be 0 at x = -4
Answer: k > 16[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 042
- 1
Question 1. The point (4, -3) lies on y = f(x). Write down a point that lies on y = f(-x).
[2 marks]Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x-coordinate changes sign
- A1: (-4, -3)
Answer: (-4, -3) - 2
Question 2. Solve 2sin x = 1.4 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place
[3 marks]Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: sin x = 0.7, so x = sin⁻¹0.7
- M1: 180^° - 44.4^°
- A1: 44.4^° and 135.6^°
Answer: x = 44.4^° and x = 135.6^° - 3
Question 3. The smallest and the largest of three consecutive positive integers are multiplied together.
[3 marks]
The result is 255.
Use algebra to work out the three integers.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 2) = 255
- M1: n² + 2n - 255 = 0 so (n + 17)(n - 15) = 0
- A1: n = 15 so the integers are 15, 16 and 17
Answer: 15, 16 and 17 - 4
Question 4. Marc runs 5 km, to the nearest km, in 25 minutes, to the nearest minute. Marc says his speed was less than 14 km/h. Is Marc correct? You must show your working.
[3 marks]Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: greatest speed uses the upper bound of distance and lower bound of time
- A1: 5.5 ÷ (24.5 ÷ 60) = 13.47 km/h
- C1: 13.47 < 14, so Marc is correct
Answer: Yes: greatest speed is 13.47 km/h, which is less than 14 - 5
Question 5. The inequality x² + 8x + k > 0 is true for every value of x.
[3 marks]
Work out the possible values of k.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + 8x + k = (x + 4)² + k - 16
- M1: (x + 4)² ≥ 0 with equality at x = -4, so k - 16 must be above 0
- A1: k > 16, strict because the expression must not be 0 at x = -4
Answer: k > 16
Mixed Topic Worksheet Grades 8/9: Day 042
- 1
Question 1. The point (4, -3) lies on y = f(x). Write down a point that lies on y = f(-x).
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x-coordinate changes sign
- A1: (-4, -3)
Answer: (-4, -3)[2 marks] - 2
Question 2. Solve 2sin x = 1.4 for 0^° ≤ x ≤ 360^°. Give your answers correct to 1 decimal place
Solving Trigonometric Equations Using a Graph▶ Show worked answerHide worked answer
- M1: sin x = 0.7, so x = sin⁻¹0.7
- M1: 180^° - 44.4^°
- A1: 44.4^° and 135.6^°
Answer: x = 44.4^° and x = 135.6^°[3 marks] - 3
Question 3. The smallest and the largest of three consecutive positive integers are multiplied together.
The result is 255.
Use algebra to work out the three integers.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n(n + 2) = 255
- M1: n² + 2n - 255 = 0 so (n + 17)(n - 15) = 0
- A1: n = 15 so the integers are 15, 16 and 17
Answer: 15, 16 and 17[3 marks] - 4
Question 4. Marc runs 5 km, to the nearest km, in 25 minutes, to the nearest minute. Marc says his speed was less than 14 km/h. Is Marc correct? You must show your working.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: greatest speed uses the upper bound of distance and lower bound of time
- A1: 5.5 ÷ (24.5 ÷ 60) = 13.47 km/h
- C1: 13.47 < 14, so Marc is correct
Answer: Yes: greatest speed is 13.47 km/h, which is less than 14[3 marks] - 5
Question 5. The inequality x² + 8x + k > 0 is true for every value of x.
Work out the possible values of k.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + 8x + k = (x + 4)² + k - 16
- M1: (x + 4)² ≥ 0 with equality at x = -4, so k - 16 must be above 0
- A1: k > 16, strict because the expression must not be 0 at x = -4
Answer: k > 16[3 marks]