Mixed Topic Worksheet Grades 6/7: Day 036
- 1
Question 1. The volume of the cylinder is 590 cm³. Work out the height, h cm, of the cylinder.
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 4² × h = 590
- M1: h = 590 ÷ (π × 4²)
- A1: 11.7
Answer: 11.7[3 marks] - 2
Question 2. A phone case comes in 6 colours.
Each colour comes in 3 sizes.
Each size comes with a matt or a gloss finish.
Work out the total number of different phone cases.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 6 × 3 × 2
- A1: 36
Answer: 36[2 marks] - 3
Question 3. A rectangle has length (3 + √5) cm and width (3 - √5) cm. Show that the area of the rectangle is a rational number.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: (3 + √5)(3 - √5) = 9 - 3√5 + 3√5 - 5
- M1: the √5 terms cancel, leaving 9 - 5
- A1: 4, which is rational
Answer: 4 cm², which is rational[3 marks] - 4
Question 4. A(-5, 12) and B(5, -12) are the ends of a diameter of a circle.
Find the equation of the circle.General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: the centre is the midpoint of AB: (0, 0)
- M1: r² = 5² + 12² = 169
- A1: x² + y² = 169
Answer: x² + y² = 169[3 marks] - 5
Question 5. 4(x + a) + b(x - 2) equiv 7x + 2
Work out the values of a and b.Equating Coefficients▶ Show worked answerHide worked answer
- M1: x terms: 4 + b = 7
- M1: numbers: 4a - 2b = 2
- A1: a = 2, b = 3
Answer: a = 2, b = 3[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 036
- 1
Question 1. The volume of the cylinder is 590 cm³. Work out the height, h cm, of the cylinder.
[3 marks]
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 4² × h = 590
- M1: h = 590 ÷ (π × 4²)
- A1: 11.7
Answer: 11.7 - 2
Question 2. A phone case comes in 6 colours.
[2 marks]
Each colour comes in 3 sizes.
Each size comes with a matt or a gloss finish.
Work out the total number of different phone cases.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 6 × 3 × 2
- A1: 36
Answer: 36 - 3
Question 3. A rectangle has length (3 + √5) cm and width (3 - √5) cm. Show that the area of the rectangle is a rational number.
[3 marks]Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: (3 + √5)(3 - √5) = 9 - 3√5 + 3√5 - 5
- M1: the √5 terms cancel, leaving 9 - 5
- A1: 4, which is rational
Answer: 4 cm², which is rational - 4
Question 4. A(-5, 12) and B(5, -12) are the ends of a diameter of a circle.
[3 marks]
Find the equation of the circle.General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: the centre is the midpoint of AB: (0, 0)
- M1: r² = 5² + 12² = 169
- A1: x² + y² = 169
Answer: x² + y² = 169 - 5
Question 5. 4(x + a) + b(x - 2) equiv 7x + 2
[3 marks]
Work out the values of a and b.Equating Coefficients▶ Show worked answerHide worked answer
- M1: x terms: 4 + b = 7
- M1: numbers: 4a - 2b = 2
- A1: a = 2, b = 3
Answer: a = 2, b = 3
Mixed Topic Worksheet Grades 6/7: Day 036
- 1
Question 1. The volume of the cylinder is 590 cm³. Work out the height, h cm, of the cylinder.
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 4² × h = 590
- M1: h = 590 ÷ (π × 4²)
- A1: 11.7
Answer: 11.7[3 marks] - 2
Question 2. A phone case comes in 6 colours.
Each colour comes in 3 sizes.
Each size comes with a matt or a gloss finish.
Work out the total number of different phone cases.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 6 × 3 × 2
- A1: 36
Answer: 36[2 marks] - 3
Question 3. A rectangle has length (3 + √5) cm and width (3 - √5) cm. Show that the area of the rectangle is a rational number.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: (3 + √5)(3 - √5) = 9 - 3√5 + 3√5 - 5
- M1: the √5 terms cancel, leaving 9 - 5
- A1: 4, which is rational
Answer: 4 cm², which is rational[3 marks] - 4
Question 4. A(-5, 12) and B(5, -12) are the ends of a diameter of a circle.
Find the equation of the circle.General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: the centre is the midpoint of AB: (0, 0)
- M1: r² = 5² + 12² = 169
- A1: x² + y² = 169
Answer: x² + y² = 169[3 marks] - 5
Question 5. 4(x + a) + b(x - 2) equiv 7x + 2
Work out the values of a and b.Equating Coefficients▶ Show worked answerHide worked answer
- M1: x terms: 4 + b = 7
- M1: numbers: 4a - 2b = 2
- A1: a = 2, b = 3
Answer: a = 2, b = 3[3 marks]