Mixed Topic Worksheet Grades 6/7: Day 093
- 1
Question 1. Here is a cone with base diameter 12 cm and slant height 11 cm.
Work out the total surface area of the cone.
Give your answer in terms of π.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 6 × 11 + π × 6²
- A1: 102π
Answer: 102π cm²[2 marks] - 2
Question 2. Simplify fully dfrac6x+153
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: divides each term of the numerator by 3 (2x or 5)
- A1: 2x+5
Answer: 2x+5[2 marks] - 3
Question 3. The diagram shows a right-angled triangle. Use a square number to work out an estimate for x, to the nearest whole number.
Estimating Roots▶ Show worked answerHide worked answer
- M1: 7² + 12²
- M1: 14² = 196 is the nearest square number to 193
- A1: 14
Answer: 14[3 marks] - 4
Question 4. A code has 3 digits.
Each digit is chosen from 1 to 9.
Digits can be used more than once.
A code is chosen at random.
Work out the probability that all 3 digits in the code are different.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 9 × 9 × 9 codes altogether
- M1: 9 × 8 × 7 codes with different digits
- A1: dfrac5681
Answer: dfrac5681[3 marks] - 5
Question 5. n is a positive integer.
Prove that (2n + 3)² - (2n + 1)² is a multiple of 8Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: 4n² + 12n + 9 or 4n² + 4n + 1
- M1: 4n² + 12n + 9 - (4n² + 4n + 1)
- A1: 8n + 8
- C1: 8(n + 1), which is a multiple of 8
Answer: 8n + 8 = 8(n + 1), a multiple of 8[4 marks]
Mixed Topic Worksheet Grades 6/7: Day 093
- 1
Question 1. Here is a cone with base diameter 12 cm and slant height 11 cm.
[2 marks]
Work out the total surface area of the cone.
Give your answer in terms of π.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 6 × 11 + π × 6²
- A1: 102π
Answer: 102π cm² - 2
Question 2. Simplify fully dfrac6x+153
[2 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: divides each term of the numerator by 3 (2x or 5)
- A1: 2x+5
Answer: 2x+5 - 3
Question 3. The diagram shows a right-angled triangle. Use a square number to work out an estimate for x, to the nearest whole number.
[3 marks]Estimating Roots▶ Show worked answerHide worked answer
- M1: 7² + 12²
- M1: 14² = 196 is the nearest square number to 193
- A1: 14
Answer: 14 - 4
Question 4. A code has 3 digits.
[3 marks]
Each digit is chosen from 1 to 9.
Digits can be used more than once.
A code is chosen at random.
Work out the probability that all 3 digits in the code are different.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 9 × 9 × 9 codes altogether
- M1: 9 × 8 × 7 codes with different digits
- A1: dfrac5681
Answer: dfrac5681 - 5
Question 5. n is a positive integer.
[4 marks]
Prove that (2n + 3)² - (2n + 1)² is a multiple of 8Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: 4n² + 12n + 9 or 4n² + 4n + 1
- M1: 4n² + 12n + 9 - (4n² + 4n + 1)
- A1: 8n + 8
- C1: 8(n + 1), which is a multiple of 8
Answer: 8n + 8 = 8(n + 1), a multiple of 8
Mixed Topic Worksheet Grades 6/7: Day 093
- 1
Question 1. Here is a cone with base diameter 12 cm and slant height 11 cm.
Work out the total surface area of the cone.
Give your answer in terms of π.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 6 × 11 + π × 6²
- A1: 102π
Answer: 102π cm²[2 marks] - 2
Question 2. Simplify fully dfrac6x+153
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: divides each term of the numerator by 3 (2x or 5)
- A1: 2x+5
Answer: 2x+5[2 marks] - 3
Question 3. The diagram shows a right-angled triangle. Use a square number to work out an estimate for x, to the nearest whole number.
Estimating Roots▶ Show worked answerHide worked answer
- M1: 7² + 12²
- M1: 14² = 196 is the nearest square number to 193
- A1: 14
Answer: 14[3 marks] - 4
Question 4. A code has 3 digits.
Each digit is chosen from 1 to 9.
Digits can be used more than once.
A code is chosen at random.
Work out the probability that all 3 digits in the code are different.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 9 × 9 × 9 codes altogether
- M1: 9 × 8 × 7 codes with different digits
- A1: dfrac5681
Answer: dfrac5681[3 marks] - 5
Question 5. n is a positive integer.
Prove that (2n + 3)² - (2n + 1)² is a multiple of 8Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: 4n² + 12n + 9 or 4n² + 4n + 1
- M1: 4n² + 12n + 9 - (4n² + 4n + 1)
- A1: 8n + 8
- C1: 8(n + 1), which is a multiple of 8
Answer: 8n + 8 = 8(n + 1), a multiple of 8[4 marks]