📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 060

Grades 8/9Calculator

  1. Question 1. y = x³ - 2x + 1 is reflected in the y-axis. Write down the equation of the image.

    Show worked answerHide worked answer
    1. M1: x becomes -x
    2. A1: y = -x³ + 2x + 1
    Answer: y = -x³ + 2x + 1
    Reflections in the x- & y-Axes
    [2 marks]

  2. Question 2. ABCDEFGH is a cuboid.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: DB² = 11² + 6²
    2. M1: DF² = DB² + 5²
    3. A1: DF = 13.5 from DF² = 182
    Answer: 13.5
    3D Pythagoras
    11 cm5 cmADBCFGEH6 cm
    [3 marks]

  3. Question 3. A car travels 410 km, correct to the nearest 10 km, using 38 litres of petrol, correct to the nearest litre.
    Kai says the lower bound of the distance per litre is 405 ÷ 37.5 = 10.8 km.
    Is Kai correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 410 - 5 and 38 + 0.5
    2. M1: 405 ÷ 38.5 = 10.5
    3. C1: Kai used the lower bound of the volume of petrol, so Kai is not correct
    Answer: No
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. AB is a diameter of a circle with centre O. C is a point on the circle and angle AOC = 100°. Work out the size of angle CAB. Give reasons.

    Show worked answerHide worked answer
    1. M1: OA = OC (radii), so triangle OAC is isosceles
    2. M1: (180 - 100) ÷ 2
    3. A1: 40°
    Answer: 40°
    Combining Circle Theorems
    [3 marks]

  5. Question 5. Solve x²+5x > 2x+18

    Show worked answerHide worked answer
    1. M1: collect the terms, x²+3x-18 > 0
    2. M1: solve (x+6)(x-3) = 0, so x = -6 and x = 3
    3. A1: x < -6 or x > 3
    Answer: x < -6 or x > 3
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 060

Grades 8/9Calculator

  1. Question 1. y = x³ - 2x + 1 is reflected in the y-axis. Write down the equation of the image.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: x becomes -x
    2. A1: y = -x³ + 2x + 1
    Answer: y = -x³ + 2x + 1
    Reflections in the x- & y-Axes

  2. Question 2. ABCDEFGH is a cuboid.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    [3 marks]
    11 cm5 cmADBCFGEH6 cm
    Show worked answerHide worked answer
    1. M1: DB² = 11² + 6²
    2. M1: DF² = DB² + 5²
    3. A1: DF = 13.5 from DF² = 182
    Answer: 13.5
    3D Pythagoras

  3. Question 3. A car travels 410 km, correct to the nearest 10 km, using 38 litres of petrol, correct to the nearest litre.
    Kai says the lower bound of the distance per litre is 405 ÷ 37.5 = 10.8 km.
    Is Kai correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 410 - 5 and 38 + 0.5
    2. M1: 405 ÷ 38.5 = 10.5
    3. C1: Kai used the lower bound of the volume of petrol, so Kai is not correct
    Answer: No
    Combining Upper & Lower Bounds

  4. Question 4. AB is a diameter of a circle with centre O. C is a point on the circle and angle AOC = 100°. Work out the size of angle CAB. Give reasons.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: OA = OC (radii), so triangle OAC is isosceles
    2. M1: (180 - 100) ÷ 2
    3. A1: 40°
    Answer: 40°
    Combining Circle Theorems

  5. Question 5. Solve x²+5x > 2x+18

    [3 marks]
    Show worked answerHide worked answer
    1. M1: collect the terms, x²+3x-18 > 0
    2. M1: solve (x+6)(x-3) = 0, so x = -6 and x = 3
    3. A1: x < -6 or x > 3
    Answer: x < -6 or x > 3
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 060

Grades 8/9Calculator

  1. Question 1. y = x³ - 2x + 1 is reflected in the y-axis. Write down the equation of the image.

    Show worked answerHide worked answer
    1. M1: x becomes -x
    2. A1: y = -x³ + 2x + 1
    Answer: y = -x³ + 2x + 1
    Reflections in the x- & y-Axes
    [2 marks]

  2. Question 2. ABCDEFGH is a cuboid.
    Work out the length of DF.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: DB² = 11² + 6²
    2. M1: DF² = DB² + 5²
    3. A1: DF = 13.5 from DF² = 182
    Answer: 13.5
    3D Pythagoras
    11 cm5 cmADBCFGEH6 cm
    [3 marks]

  3. Question 3. A car travels 410 km, correct to the nearest 10 km, using 38 litres of petrol, correct to the nearest litre.
    Kai says the lower bound of the distance per litre is 405 ÷ 37.5 = 10.8 km.
    Is Kai correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 410 - 5 and 38 + 0.5
    2. M1: 405 ÷ 38.5 = 10.5
    3. C1: Kai used the lower bound of the volume of petrol, so Kai is not correct
    Answer: No
    Combining Upper & Lower Bounds
    [3 marks]

  4. Question 4. AB is a diameter of a circle with centre O. C is a point on the circle and angle AOC = 100°. Work out the size of angle CAB. Give reasons.

    Show worked answerHide worked answer
    1. M1: OA = OC (radii), so triangle OAC is isosceles
    2. M1: (180 - 100) ÷ 2
    3. A1: 40°
    Answer: 40°
    Combining Circle Theorems
    [3 marks]

  5. Question 5. Solve x²+5x > 2x+18

    Show worked answerHide worked answer
    1. M1: collect the terms, x²+3x-18 > 0
    2. M1: solve (x+6)(x-3) = 0, so x = -6 and x = 3
    3. A1: x < -6 or x > 3
    Answer: x < -6 or x > 3
    Solving Quadratic Inequalities
    [3 marks]