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

Mixed Topic Worksheet Grades 4/5: Day 042

Grades 4/5Calculator

  1. Question 1. Jo works out the size of angle x in triangle ABC.
    Jo writes
    360 - 58 - 67 = 235
    So x = 235^°
    Work out the correct size of angle x.

    Show worked answerHide worked answer
    1. M1: 180 - 58 - 67 (the angles in a triangle add up to 180^°, not 360^°)
    2. A1: 55
    Answer: 55
    Angles in Triangles
    x58°67°ABCNot drawn accurately
    [2 marks]

  2. Question 2. The graph of y = x² + 7 crosses the y-axis at the point (0, k). Work out the value of k.

    Show worked answerHide worked answer
    1. B1: 7 (substitute x = 0, so x² = 0)
    Answer: 7
    y-Intercepts of Quadratics
    [1 mark]

  3. Question 3. A plant has grown to 130% of its original height.
    It is now 52 cm tall.
    Work out its original height.

    Show worked answerHide worked answer
    1. M1: 52 / 1.3
    2. A1: 40 cm
    Answer: 40 cm
    Percentages Greater than 100
    [2 marks]

  4. Question 4. A plane flies 80 km from A to B on a bearing of 040^°.
    Work out how far north of A the point B is.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: north = 80 × cos 40°
    2. A1: 61.3
    Answer: 61.3 km
    Bearings Problems Involving SOH, CAH, TOA
    N040°80 kmABNot drawn accurately
    [2 marks]

  5. Question 5. ABCD is a rectangle.
    The diagonal AC is drawn.
    Angle BAC = 36^°
    (a) Show that triangle ABC is congruent to triangle CDA.
    Give a reason for each statement. [3]
    (b) Write down the size of angle DCA. [1]

    Show worked answerHide worked answer
    1. (a) B1: AB = CD
    2. (a) B1: right angles at B and D and AC is the common hypotenuse
    3. (a) B1: RHS
    4. (b) B1: 36
    Answer: (a) AB = CD; right angles at B and D; AC common (RHS); (b) 36
    Identifying Congruent Triangles
    11 cm8 cm36°ABCDNot drawn accurately
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 4/5: Day 042

Grades 4/5Calculator

  1. Question 1. Jo works out the size of angle x in triangle ABC.
    Jo writes
    360 - 58 - 67 = 235
    So x = 235^°
    Work out the correct size of angle x.

    [2 marks]
    x58°67°ABCNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 180 - 58 - 67 (the angles in a triangle add up to 180^°, not 360^°)
    2. A1: 55
    Answer: 55
    Angles in Triangles

  2. Question 2. The graph of y = x² + 7 crosses the y-axis at the point (0, k). Work out the value of k.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: 7 (substitute x = 0, so x² = 0)
    Answer: 7
    y-Intercepts of Quadratics

  3. Question 3. A plant has grown to 130% of its original height.
    It is now 52 cm tall.
    Work out its original height.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 52 / 1.3
    2. A1: 40 cm
    Answer: 40 cm
    Percentages Greater than 100

  4. Question 4. A plane flies 80 km from A to B on a bearing of 040^°.
    Work out how far north of A the point B is.
    Give your answer to 1 decimal place.

    [2 marks]
    N040°80 kmABNot drawn accurately
    Show worked answerHide worked answer
    1. M1: north = 80 × cos 40°
    2. A1: 61.3
    Answer: 61.3 km
    Bearings Problems Involving SOH, CAH, TOA

  5. Question 5. ABCD is a rectangle.
    The diagonal AC is drawn.
    Angle BAC = 36^°
    (a) Show that triangle ABC is congruent to triangle CDA.
    Give a reason for each statement. [3]
    (b) Write down the size of angle DCA. [1]

    [4 marks]
    11 cm8 cm36°ABCDNot drawn accurately
    Show worked answerHide worked answer
    1. (a) B1: AB = CD
    2. (a) B1: right angles at B and D and AC is the common hypotenuse
    3. (a) B1: RHS
    4. (b) B1: 36
    Answer: (a) AB = CD; right angles at B and D; AC common (RHS); (b) 36
    Identifying Congruent Triangles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 4/5: Day 042

Grades 4/5Calculator

  1. Question 1. Jo works out the size of angle x in triangle ABC.
    Jo writes
    360 - 58 - 67 = 235
    So x = 235^°
    Work out the correct size of angle x.

    Show worked answerHide worked answer
    1. M1: 180 - 58 - 67 (the angles in a triangle add up to 180^°, not 360^°)
    2. A1: 55
    Answer: 55
    Angles in Triangles
    x58°67°ABCNot drawn accurately
    [2 marks]

  2. Question 2. The graph of y = x² + 7 crosses the y-axis at the point (0, k). Work out the value of k.

    Show worked answerHide worked answer
    1. B1: 7 (substitute x = 0, so x² = 0)
    Answer: 7
    y-Intercepts of Quadratics
    [1 mark]

  3. Question 3. A plant has grown to 130% of its original height.
    It is now 52 cm tall.
    Work out its original height.

    Show worked answerHide worked answer
    1. M1: 52 / 1.3
    2. A1: 40 cm
    Answer: 40 cm
    Percentages Greater than 100
    [2 marks]

  4. Question 4. A plane flies 80 km from A to B on a bearing of 040^°.
    Work out how far north of A the point B is.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: north = 80 × cos 40°
    2. A1: 61.3
    Answer: 61.3 km
    Bearings Problems Involving SOH, CAH, TOA
    N040°80 kmABNot drawn accurately
    [2 marks]

  5. Question 5. ABCD is a rectangle.
    The diagonal AC is drawn.
    Angle BAC = 36^°
    (a) Show that triangle ABC is congruent to triangle CDA.
    Give a reason for each statement. [3]
    (b) Write down the size of angle DCA. [1]

    Show worked answerHide worked answer
    1. (a) B1: AB = CD
    2. (a) B1: right angles at B and D and AC is the common hypotenuse
    3. (a) B1: RHS
    4. (b) B1: 36
    Answer: (a) AB = CD; right angles at B and D; AC common (RHS); (b) 36
    Identifying Congruent Triangles
    11 cm8 cm36°ABCDNot drawn accurately
    [4 marks]