Mixed Topic Worksheet Grades 8/9: Day 068
- 1
Question 1. A pyramid has a square base of side 8 cm. Its apex is 6 cm above the centre. Work out the angle between a sloping edge and the base. Give your answer to 1 decimal place.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: half diagonal 4√2, tan θ = frac64√2
- A1: 46.7°
Answer: 46.7°[2 marks] - 2
Question 2. The curve y = x² - 5 is translated 2 units to the left.
Find the equation of the translated curve.
Give your answer in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replace x with x + 2: y = (x + 2)² - 5
- M1: x² + 4x + 4 - 5
- A1: y = x² + 4x - 1
Answer: y = x² + 4x - 1[3 marks] - 3
Question 3. A car travels 75 km, correct to the nearest 5 km.
The time taken is 2.4 hours, correct to 1 decimal place.
Ana says the average speed was definitely greater than 30 km/h.
Is Ana correct?
You must show your working.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 75 - 2.5 and 2.4 + 0.05
- M1: 72.5 ÷ 2.45
- A1: 29.59...
- C1: 29.59... < 30, so No
Answer: No: the lower bound of the speed is 72.5 ÷ 2.45 = 29.59... km/h, which is less than 30 km/h.[4 marks] - 4
Question 4. Solve the simultaneous equations
x² + y² = 61
x² - y² = 11Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 2x² = 72
- M1: y² = 61 - 36 = 25
- A1: x = ± 6 and y = ± 5
- A1: all four pairs of values
Answer: (6, 5), (6, -5), (-6, 5) and (-6, -5)[4 marks] - 5
Question 5. Solve 3x² + 5x - 4 = 0 by completing the square. Give your solutions to 2 decimal places.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3≤ft(x + frac56)² - 25/12 - 4 = 0
- M1: ≤ft(x + frac56)² = 73/36
- A1: x = 0.59 or x = -2.26
Answer: x = 0.59 or x = -2.26[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 068
- 1
Question 1. A pyramid has a square base of side 8 cm. Its apex is 6 cm above the centre. Work out the angle between a sloping edge and the base. Give your answer to 1 decimal place.
[2 marks]3D Trigonometry▶ Show worked answerHide worked answer
- M1: half diagonal 4√2, tan θ = frac64√2
- A1: 46.7°
Answer: 46.7° - 2
Question 2. The curve y = x² - 5 is translated 2 units to the left.
[3 marks]
Find the equation of the translated curve.
Give your answer in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replace x with x + 2: y = (x + 2)² - 5
- M1: x² + 4x + 4 - 5
- A1: y = x² + 4x - 1
Answer: y = x² + 4x - 1 - 3
Question 3. A car travels 75 km, correct to the nearest 5 km.
[4 marks]
The time taken is 2.4 hours, correct to 1 decimal place.
Ana says the average speed was definitely greater than 30 km/h.
Is Ana correct?
You must show your working.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 75 - 2.5 and 2.4 + 0.05
- M1: 72.5 ÷ 2.45
- A1: 29.59...
- C1: 29.59... < 30, so No
Answer: No: the lower bound of the speed is 72.5 ÷ 2.45 = 29.59... km/h, which is less than 30 km/h. - 4
Question 4. Solve the simultaneous equations
[4 marks]
x² + y² = 61
x² - y² = 11Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 2x² = 72
- M1: y² = 61 - 36 = 25
- A1: x = ± 6 and y = ± 5
- A1: all four pairs of values
Answer: (6, 5), (6, -5), (-6, 5) and (-6, -5) - 5
Question 5. Solve 3x² + 5x - 4 = 0 by completing the square. Give your solutions to 2 decimal places.
[3 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3≤ft(x + frac56)² - 25/12 - 4 = 0
- M1: ≤ft(x + frac56)² = 73/36
- A1: x = 0.59 or x = -2.26
Answer: x = 0.59 or x = -2.26
Mixed Topic Worksheet Grades 8/9: Day 068
- 1
Question 1. A pyramid has a square base of side 8 cm. Its apex is 6 cm above the centre. Work out the angle between a sloping edge and the base. Give your answer to 1 decimal place.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: half diagonal 4√2, tan θ = frac64√2
- A1: 46.7°
Answer: 46.7°[2 marks] - 2
Question 2. The curve y = x² - 5 is translated 2 units to the left.
Find the equation of the translated curve.
Give your answer in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: replace x with x + 2: y = (x + 2)² - 5
- M1: x² + 4x + 4 - 5
- A1: y = x² + 4x - 1
Answer: y = x² + 4x - 1[3 marks] - 3
Question 3. A car travels 75 km, correct to the nearest 5 km.
The time taken is 2.4 hours, correct to 1 decimal place.
Ana says the average speed was definitely greater than 30 km/h.
Is Ana correct?
You must show your working.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 75 - 2.5 and 2.4 + 0.05
- M1: 72.5 ÷ 2.45
- A1: 29.59...
- C1: 29.59... < 30, so No
Answer: No: the lower bound of the speed is 72.5 ÷ 2.45 = 29.59... km/h, which is less than 30 km/h.[4 marks] - 4
Question 4. Solve the simultaneous equations
x² + y² = 61
x² - y² = 11Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 2x² = 72
- M1: y² = 61 - 36 = 25
- A1: x = ± 6 and y = ± 5
- A1: all four pairs of values
Answer: (6, 5), (6, -5), (-6, 5) and (-6, -5)[4 marks] - 5
Question 5. Solve 3x² + 5x - 4 = 0 by completing the square. Give your solutions to 2 decimal places.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 3≤ft(x + frac56)² - 25/12 - 4 = 0
- M1: ≤ft(x + frac56)² = 73/36
- A1: x = 0.59 or x = -2.26
Answer: x = 0.59 or x = -2.26[3 marks]