Mixed Topic Worksheet Grades 6/7: Day 078
- 1
Question 1. The diagram shows an equilateral triangle with sides of length 12.6 cm.
Work out the height h of the triangle.
Use trigonometry.
Give your answer to 1 decimal place.Finding the Height of an Equilateral Triangle▶ Show worked answerHide worked answer
- M1: h = 12.6 × sin 60°
- A1: 10.9
Answer: 10.9 cm[2 marks] - 2
Question 2. The diagram shows triangle PQR.
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 1/2 × 9.5 × 7 × sin 65^°
- A1: 30.1
Answer: 30.1 cm²[2 marks] - 3
Question 3. A rectangle has area (2x²+10x) m² and length 2x m.
Work out an expression for the perimeter of the rectangle, in metres.Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: width =dfrac2x²+10x2x
- A1: x+5
- M1: perimeter =2×(2x+x+5)
- A1: 6x+10
Answer: (6x+10) m[4 marks] - 4
Question 4. The length of a rectangle is 1 cm more than twice its width
The area of the rectangle is 45 cm²
Work out the width of the rectangle.Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: let the width be w cm: w(2w + 1) = 45
- M1: 2w² + w - 45 = 0 and factorise (2w - 9)(w + 5) = 0
- M1: 2w - 9 = 0 or w + 5 = 0
- A1: w = 4.5 (w = -5 rejected as a width cannot be negative)
Answer: 4.5 cm[4 marks] - 5
Question 5. Five different digits are chosen from 1, 2, 3, 4, 5, 6, 7, 8 and 9.
The five digits are used to make a 5-digit number.
No digit can be used more than once.
Work out the number of these 5-digit numbers that are odd and greater than 50000.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5 ways to fill the three middle digits
- M1: first digit odd (5, 7 or 9) gives 3 × 4 × (7 × 6 × 5) = 2520 numbers
- M1: first digit even (6 or 8) gives 2 × 5 × (7 × 6 × 5) = 2100 numbers
- M1: 2520 + 2100
- A1: 4620
Answer: 4620[5 marks]
Mixed Topic Worksheet Grades 6/7: Day 078
- 1
Question 1. The diagram shows an equilateral triangle with sides of length 12.6 cm.
[2 marks]
Work out the height h of the triangle.
Use trigonometry.
Give your answer to 1 decimal place.Finding the Height of an Equilateral Triangle▶ Show worked answerHide worked answer
- M1: h = 12.6 × sin 60°
- A1: 10.9
Answer: 10.9 cm - 2
Question 2. The diagram shows triangle PQR.
[2 marks]
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 1/2 × 9.5 × 7 × sin 65^°
- A1: 30.1
Answer: 30.1 cm² - 3
Question 3. A rectangle has area (2x²+10x) m² and length 2x m.
[4 marks]
Work out an expression for the perimeter of the rectangle, in metres.Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: width =dfrac2x²+10x2x
- A1: x+5
- M1: perimeter =2×(2x+x+5)
- A1: 6x+10
Answer: (6x+10) m - 4
Question 4. The length of a rectangle is 1 cm more than twice its width
[4 marks]
The area of the rectangle is 45 cm²
Work out the width of the rectangle.Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: let the width be w cm: w(2w + 1) = 45
- M1: 2w² + w - 45 = 0 and factorise (2w - 9)(w + 5) = 0
- M1: 2w - 9 = 0 or w + 5 = 0
- A1: w = 4.5 (w = -5 rejected as a width cannot be negative)
Answer: 4.5 cm - 5
Question 5. Five different digits are chosen from 1, 2, 3, 4, 5, 6, 7, 8 and 9.
[5 marks]
The five digits are used to make a 5-digit number.
No digit can be used more than once.
Work out the number of these 5-digit numbers that are odd and greater than 50000.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5 ways to fill the three middle digits
- M1: first digit odd (5, 7 or 9) gives 3 × 4 × (7 × 6 × 5) = 2520 numbers
- M1: first digit even (6 or 8) gives 2 × 5 × (7 × 6 × 5) = 2100 numbers
- M1: 2520 + 2100
- A1: 4620
Answer: 4620
Mixed Topic Worksheet Grades 6/7: Day 078
- 1
Question 1. The diagram shows an equilateral triangle with sides of length 12.6 cm.
Work out the height h of the triangle.
Use trigonometry.
Give your answer to 1 decimal place.Finding the Height of an Equilateral Triangle▶ Show worked answerHide worked answer
- M1: h = 12.6 × sin 60°
- A1: 10.9
Answer: 10.9 cm[2 marks] - 2
Question 2. The diagram shows triangle PQR.
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: 1/2 × 9.5 × 7 × sin 65^°
- A1: 30.1
Answer: 30.1 cm²[2 marks] - 3
Question 3. A rectangle has area (2x²+10x) m² and length 2x m.
Work out an expression for the perimeter of the rectangle, in metres.Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: width =dfrac2x²+10x2x
- A1: x+5
- M1: perimeter =2×(2x+x+5)
- A1: 6x+10
Answer: (6x+10) m[4 marks] - 4
Question 4. The length of a rectangle is 1 cm more than twice its width
The area of the rectangle is 45 cm²
Work out the width of the rectangle.Solving Quadratics by Factorising (a > 1)▶ Show worked answerHide worked answer
- M1: let the width be w cm: w(2w + 1) = 45
- M1: 2w² + w - 45 = 0 and factorise (2w - 9)(w + 5) = 0
- M1: 2w - 9 = 0 or w + 5 = 0
- A1: w = 4.5 (w = -5 rejected as a width cannot be negative)
Answer: 4.5 cm[4 marks] - 5
Question 5. Five different digits are chosen from 1, 2, 3, 4, 5, 6, 7, 8 and 9.
The five digits are used to make a 5-digit number.
No digit can be used more than once.
Work out the number of these 5-digit numbers that are odd and greater than 50000.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5 ways to fill the three middle digits
- M1: first digit odd (5, 7 or 9) gives 3 × 4 × (7 × 6 × 5) = 2520 numbers
- M1: first digit even (6 or 8) gives 2 × 5 × (7 × 6 × 5) = 2100 numbers
- M1: 2520 + 2100
- A1: 4620
Answer: 4620[5 marks]