Mixed Topic Worksheet Grades 6/7: Day 054
- 1
Question 1. Solve dfrac3x + 14 = dfracx + 72
Solving Harder Equations▶ Show worked answerHide worked answer
- M1: Multiplies both sides by 4: 3x + 1 = 2(x + 7)
- M1: Expands the bracket: 3x + 1 = 2x + 14
- M1: Collects: 3x - 2x = 14 - 1
- A1: x = 13
Answer: x = 13[4 marks] - 2
Question 2. The number x = 0.1010010001ldots continues in this pattern: after each 1 there is one more 0 than after the previous 1.
Nisha says that x is rational because it has a pattern.
Ravi says that x is irrational.
Who is correct? Give a reason.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: the digits 1, 0, 1, 0, 0, 1, 0, 0, 0, 1 have a growing run of zeros, so no block of digits repeats
- M1: x = 0.1010010001ldots never terminates or recurs, so x ≠ dfracab for integers a and b
- A1: Ravi
Answer: Ravi. The digits never repeat in a fixed block, so x cannot be written as a fraction.[3 marks] - 3
Question 3. The diagram shows a regular hexagon with sides of length 8 cm.
Work out the area of the hexagon.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the centre angle of each triangle is 360 ÷ 6 = 60^°
- M1: one triangle has area 1/2 × 8 × 8 × sin 60^°
- M1: six triangles, 6 × 27.7
- A1: 166.3
Answer: 166.3 cm²[4 marks] - 4
Question 4. A circle has equation x² + y² = 36
Write down the radius of the circle and the coordinates of the four points where the circle crosses the axes.Sketching Circles▶ Show worked answerHide worked answer
- M1: Radius = √36 = 6
- A1: (6, 0), (-6, 0), (0, 6) and (0, -6)
Answer: Radius 6; (6, 0), (-6, 0), (0, 6), (0, -6)[2 marks] - 5
Question 5. Triangle PQR has
Area = 53 cm²
PQ = 14 cm
Angle QPR = 57^°
Work out the length of PR.
Give your answer to 1 decimal place.Calculating Side Lengths Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 53 = 1/2 × 14 × PR × sin 57^°
- A1: 9.0
Answer: 9.0 cm[2 marks]
Mixed Topic Worksheet Grades 6/7: Day 054
- 1
Question 1. Solve dfrac3x + 14 = dfracx + 72
[4 marks]Solving Harder Equations▶ Show worked answerHide worked answer
- M1: Multiplies both sides by 4: 3x + 1 = 2(x + 7)
- M1: Expands the bracket: 3x + 1 = 2x + 14
- M1: Collects: 3x - 2x = 14 - 1
- A1: x = 13
Answer: x = 13 - 2
Question 2. The number x = 0.1010010001ldots continues in this pattern: after each 1 there is one more 0 than after the previous 1.
[3 marks]
Nisha says that x is rational because it has a pattern.
Ravi says that x is irrational.
Who is correct? Give a reason.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: the digits 1, 0, 1, 0, 0, 1, 0, 0, 0, 1 have a growing run of zeros, so no block of digits repeats
- M1: x = 0.1010010001ldots never terminates or recurs, so x ≠ dfracab for integers a and b
- A1: Ravi
Answer: Ravi. The digits never repeat in a fixed block, so x cannot be written as a fraction. - 3
Question 3. The diagram shows a regular hexagon with sides of length 8 cm.
[4 marks]
Work out the area of the hexagon.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the centre angle of each triangle is 360 ÷ 6 = 60^°
- M1: one triangle has area 1/2 × 8 × 8 × sin 60^°
- M1: six triangles, 6 × 27.7
- A1: 166.3
Answer: 166.3 cm² - 4
Question 4. A circle has equation x² + y² = 36
[2 marks]
Write down the radius of the circle and the coordinates of the four points where the circle crosses the axes.Sketching Circles▶ Show worked answerHide worked answer
- M1: Radius = √36 = 6
- A1: (6, 0), (-6, 0), (0, 6) and (0, -6)
Answer: Radius 6; (6, 0), (-6, 0), (0, 6), (0, -6) - 5
Question 5. Triangle PQR has
[2 marks]
Area = 53 cm²
PQ = 14 cm
Angle QPR = 57^°
Work out the length of PR.
Give your answer to 1 decimal place.Calculating Side Lengths Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 53 = 1/2 × 14 × PR × sin 57^°
- A1: 9.0
Answer: 9.0 cm
Mixed Topic Worksheet Grades 6/7: Day 054
- 1
Question 1. Solve dfrac3x + 14 = dfracx + 72
Solving Harder Equations▶ Show worked answerHide worked answer
- M1: Multiplies both sides by 4: 3x + 1 = 2(x + 7)
- M1: Expands the bracket: 3x + 1 = 2x + 14
- M1: Collects: 3x - 2x = 14 - 1
- A1: x = 13
Answer: x = 13[4 marks] - 2
Question 2. The number x = 0.1010010001ldots continues in this pattern: after each 1 there is one more 0 than after the previous 1.
Nisha says that x is rational because it has a pattern.
Ravi says that x is irrational.
Who is correct? Give a reason.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: the digits 1, 0, 1, 0, 0, 1, 0, 0, 0, 1 have a growing run of zeros, so no block of digits repeats
- M1: x = 0.1010010001ldots never terminates or recurs, so x ≠ dfracab for integers a and b
- A1: Ravi
Answer: Ravi. The digits never repeat in a fixed block, so x cannot be written as a fraction.[3 marks] - 3
Question 3. The diagram shows a regular hexagon with sides of length 8 cm.
Work out the area of the hexagon.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the centre angle of each triangle is 360 ÷ 6 = 60^°
- M1: one triangle has area 1/2 × 8 × 8 × sin 60^°
- M1: six triangles, 6 × 27.7
- A1: 166.3
Answer: 166.3 cm²[4 marks] - 4
Question 4. A circle has equation x² + y² = 36
Write down the radius of the circle and the coordinates of the four points where the circle crosses the axes.Sketching Circles▶ Show worked answerHide worked answer
- M1: Radius = √36 = 6
- A1: (6, 0), (-6, 0), (0, 6) and (0, -6)
Answer: Radius 6; (6, 0), (-6, 0), (0, 6), (0, -6)[2 marks] - 5
Question 5. Triangle PQR has
Area = 53 cm²
PQ = 14 cm
Angle QPR = 57^°
Work out the length of PR.
Give your answer to 1 decimal place.Calculating Side Lengths Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 53 = 1/2 × 14 × PR × sin 57^°
- A1: 9.0
Answer: 9.0 cm[2 marks]