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

Mixed Topic Worksheet Grades 8/9: Day 063

Grades 8/9Non-calculator

  1. Question 1. On a histogram the bar for 20 < x ≤ 30 has frequency density 4.8 and the bar for 30 < x ≤ 50 has frequency density 3. Elsa says the class 20 < x ≤ 30 has more values. Is she correct? Show your working.

    Show worked answerHide worked answer
    1. M1: 4.8×10=48 and 3×20=60
    2. B1: No
    3. B1: the class 30 < x ≤ 50 has more (60 against 48)
    Answer: No: 20 < x ≤ 30 has 48 values, 30 < x ≤ 50 has 60
    Interpreting Histograms
    [3 marks]

  2. Question 2. By completing the square, solve x² + 4x - 1 = 0. Give your answers in surd form.

    Show worked answerHide worked answer
    1. M1: (x + 2)² - 5 = 0
    2. M1 A1: x = -2 ± √5
    Answer: x = -2 + √5 or x = -2 - √5
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  3. Question 3. PA and PB are tangents to a circle with centre O, touching it at A and B. C is a point on the major arc AB. Angle OAB = 28°. Work out the size of angle ACB. Give reasons.

    Show worked answerHide worked answer
    1. M1: OA = OB so angle OBA = 28° and angle AOB = 180 - 2 × 28
    2. M1: angle ACB = AOB ÷ 2 = 124 ÷ 2
    3. A1: 62°
    Answer: 62°
    Combining Circle Theorems
    [3 marks]

  4. Question 4. Simplify fully dfracx²+7x+10x²-1÷dfracx+5x-1

    Show worked answerHide worked answer
    1. M1: dfracx²+7x+10x²-1×dfracx-1x+5
    2. M2: (x+2)(x+5) and (x-1)(x+1), cancels (x+5) and (x-1)
    3. A1: dfracx+2x+1
    Answer: dfracx+2x+1
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  5. Question 5. Beth rationalises dfrac32 + √5 and gets dfrac32 + √5 × dfrac2 - √52 - √5 = dfrac6 - 3√54 + 5 = dfrac2 - √53 This is wrong. Work out the correct answer.

    Show worked answerHide worked answer
    1. M1: 4 - 5 = -1
    2. A1: dfrac6 - 3√5-1 = 3√5 - 6
    Answer: 3√5 - 6
    Rationalising Denominators of the Form a ± √b
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 063

Grades 8/9Non-calculator

  1. Question 1. On a histogram the bar for 20 < x ≤ 30 has frequency density 4.8 and the bar for 30 < x ≤ 50 has frequency density 3. Elsa says the class 20 < x ≤ 30 has more values. Is she correct? Show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 4.8×10=48 and 3×20=60
    2. B1: No
    3. B1: the class 30 < x ≤ 50 has more (60 against 48)
    Answer: No: 20 < x ≤ 30 has 48 values, 30 < x ≤ 50 has 60
    Interpreting Histograms

  2. Question 2. By completing the square, solve x² + 4x - 1 = 0. Give your answers in surd form.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (x + 2)² - 5 = 0
    2. M1 A1: x = -2 ± √5
    Answer: x = -2 + √5 or x = -2 - √5
    Solving Quadratics by Completing the Square (a = 1)

  3. Question 3. PA and PB are tangents to a circle with centre O, touching it at A and B. C is a point on the major arc AB. Angle OAB = 28°. Work out the size of angle ACB. Give reasons.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: OA = OB so angle OBA = 28° and angle AOB = 180 - 2 × 28
    2. M1: angle ACB = AOB ÷ 2 = 124 ÷ 2
    3. A1: 62°
    Answer: 62°
    Combining Circle Theorems

  4. Question 4. Simplify fully dfracx²+7x+10x²-1÷dfracx+5x-1

    [4 marks]
    Show worked answerHide worked answer
    1. M1: dfracx²+7x+10x²-1×dfracx-1x+5
    2. M2: (x+2)(x+5) and (x-1)(x+1), cancels (x+5) and (x-1)
    3. A1: dfracx+2x+1
    Answer: dfracx+2x+1
    Multiplying & Dividing Algebraic Fractions

  5. Question 5. Beth rationalises dfrac32 + √5 and gets dfrac32 + √5 × dfrac2 - √52 - √5 = dfrac6 - 3√54 + 5 = dfrac2 - √53 This is wrong. Work out the correct answer.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 4 - 5 = -1
    2. A1: dfrac6 - 3√5-1 = 3√5 - 6
    Answer: 3√5 - 6
    Rationalising Denominators of the Form a ± √b
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 063

Grades 8/9Non-calculator

  1. Question 1. On a histogram the bar for 20 < x ≤ 30 has frequency density 4.8 and the bar for 30 < x ≤ 50 has frequency density 3. Elsa says the class 20 < x ≤ 30 has more values. Is she correct? Show your working.

    Show worked answerHide worked answer
    1. M1: 4.8×10=48 and 3×20=60
    2. B1: No
    3. B1: the class 30 < x ≤ 50 has more (60 against 48)
    Answer: No: 20 < x ≤ 30 has 48 values, 30 < x ≤ 50 has 60
    Interpreting Histograms
    [3 marks]

  2. Question 2. By completing the square, solve x² + 4x - 1 = 0. Give your answers in surd form.

    Show worked answerHide worked answer
    1. M1: (x + 2)² - 5 = 0
    2. M1 A1: x = -2 ± √5
    Answer: x = -2 + √5 or x = -2 - √5
    Solving Quadratics by Completing the Square (a = 1)
    [3 marks]

  3. Question 3. PA and PB are tangents to a circle with centre O, touching it at A and B. C is a point on the major arc AB. Angle OAB = 28°. Work out the size of angle ACB. Give reasons.

    Show worked answerHide worked answer
    1. M1: OA = OB so angle OBA = 28° and angle AOB = 180 - 2 × 28
    2. M1: angle ACB = AOB ÷ 2 = 124 ÷ 2
    3. A1: 62°
    Answer: 62°
    Combining Circle Theorems
    [3 marks]

  4. Question 4. Simplify fully dfracx²+7x+10x²-1÷dfracx+5x-1

    Show worked answerHide worked answer
    1. M1: dfracx²+7x+10x²-1×dfracx-1x+5
    2. M2: (x+2)(x+5) and (x-1)(x+1), cancels (x+5) and (x-1)
    3. A1: dfracx+2x+1
    Answer: dfracx+2x+1
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  5. Question 5. Beth rationalises dfrac32 + √5 and gets dfrac32 + √5 × dfrac2 - √52 - √5 = dfrac6 - 3√54 + 5 = dfrac2 - √53 This is wrong. Work out the correct answer.

    Show worked answerHide worked answer
    1. M1: 4 - 5 = -1
    2. A1: dfrac6 - 3√5-1 = 3√5 - 6
    Answer: 3√5 - 6
    Rationalising Denominators of the Form a ± √b
    [2 marks]