Mixed Topic Worksheet Grades 8/9: Day 090
- 1
Question 1. Graph B is the image of y = f(x) after a translation.
B has equation y = f(x + a) + b, a and b integers. Work out a and b.Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: maximum moves from (-2, 4) to (1, 2): 3 right, 2 down
- A1: a = -3, b = -2
Answer: a = -3, b = -2[2 marks] - 2
Question 2. Some values of x and y are shown. x: 2, 4, 8 and y: 12, 6, 4. Zara says that y is inversely proportional to x. Is Zara correct? Show working to justify your answer.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: xy=24, 24, 32
- A1: No, xy is not constant
Answer: No, xy is 24, 24, 32, which is not constant[2 marks] - 3
Question 3. a = 6.3 and b = 4.8
Each value is correct to 1 decimal place.
Work out the lower bound of a × b
Give your answer correct to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 6.3 - 0.05 and 4.8 - 0.05
- M1: 6.25 × 4.75
- A1: 29.7
Answer: 29.7[3 marks] - 4
Question 4. ABCDEFGH is a cuboid with a square base ABCD.
AE = 9 cm
AG = 14 cm
Work out the length of AB.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: 14² = AB² + AB² + 9²
- M1: 2AB² = 14² - 9²
- M1: AB² = 115 ÷ 2
- M1: AB = √57.5
- A1: AB = 7.6
Answer: 7.6[5 marks] - 5
Question 5. A rectangular pen has a straight wall as one side.
40 m of fencing covers the other three sides.
The two sides at right angles to the wall are x metres long.
The area must be at least 150 m².
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(40 - 2x) ≥ 150
- M1: x² - 20x + 75 ≤ 0
- M1: (x - 5)(x - 15) ≤ 0
- A1: 5 ≤ x ≤ 15
Answer: 5 ≤ x ≤ 15[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 090
- 1
Question 1. Graph B is the image of y = f(x) after a translation.
[2 marks]
B has equation y = f(x + a) + b, a and b integers. Work out a and b.Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: maximum moves from (-2, 4) to (1, 2): 3 right, 2 down
- A1: a = -3, b = -2
Answer: a = -3, b = -2 - 2
Question 2. Some values of x and y are shown. x: 2, 4, 8 and y: 12, 6, 4. Zara says that y is inversely proportional to x. Is Zara correct? Show working to justify your answer.
[2 marks]Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: xy=24, 24, 32
- A1: No, xy is not constant
Answer: No, xy is 24, 24, 32, which is not constant - 3
Question 3. a = 6.3 and b = 4.8
[3 marks]
Each value is correct to 1 decimal place.
Work out the lower bound of a × b
Give your answer correct to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 6.3 - 0.05 and 4.8 - 0.05
- M1: 6.25 × 4.75
- A1: 29.7
Answer: 29.7 - 4
Question 4. ABCDEFGH is a cuboid with a square base ABCD.
[5 marks]
AE = 9 cm
AG = 14 cm
Work out the length of AB.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: 14² = AB² + AB² + 9²
- M1: 2AB² = 14² - 9²
- M1: AB² = 115 ÷ 2
- M1: AB = √57.5
- A1: AB = 7.6
Answer: 7.6 - 5
Question 5. A rectangular pen has a straight wall as one side.
[4 marks]
40 m of fencing covers the other three sides.
The two sides at right angles to the wall are x metres long.
The area must be at least 150 m².
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(40 - 2x) ≥ 150
- M1: x² - 20x + 75 ≤ 0
- M1: (x - 5)(x - 15) ≤ 0
- A1: 5 ≤ x ≤ 15
Answer: 5 ≤ x ≤ 15
Mixed Topic Worksheet Grades 8/9: Day 090
- 1
Question 1. Graph B is the image of y = f(x) after a translation.
B has equation y = f(x + a) + b, a and b integers. Work out a and b.Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: maximum moves from (-2, 4) to (1, 2): 3 right, 2 down
- A1: a = -3, b = -2
Answer: a = -3, b = -2[2 marks] - 2
Question 2. Some values of x and y are shown. x: 2, 4, 8 and y: 12, 6, 4. Zara says that y is inversely proportional to x. Is Zara correct? Show working to justify your answer.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: xy=24, 24, 32
- A1: No, xy is not constant
Answer: No, xy is 24, 24, 32, which is not constant[2 marks] - 3
Question 3. a = 6.3 and b = 4.8
Each value is correct to 1 decimal place.
Work out the lower bound of a × b
Give your answer correct to 3 significant figures.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: 6.3 - 0.05 and 4.8 - 0.05
- M1: 6.25 × 4.75
- A1: 29.7
Answer: 29.7[3 marks] - 4
Question 4. ABCDEFGH is a cuboid with a square base ABCD.
AE = 9 cm
AG = 14 cm
Work out the length of AB.
Give your answer to 1 decimal place.3D Pythagoras▶ Show worked answerHide worked answer
- M1: 14² = AB² + AB² + 9²
- M1: 2AB² = 14² - 9²
- M1: AB² = 115 ÷ 2
- M1: AB = √57.5
- A1: AB = 7.6
Answer: 7.6[5 marks] - 5
Question 5. A rectangular pen has a straight wall as one side.
40 m of fencing covers the other three sides.
The two sides at right angles to the wall are x metres long.
The area must be at least 150 m².
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x(40 - 2x) ≥ 150
- M1: x² - 20x + 75 ≤ 0
- M1: (x - 5)(x - 15) ≤ 0
- A1: 5 ≤ x ≤ 15
Answer: 5 ≤ x ≤ 15[4 marks]