Mixed Topic Worksheet Grades 6/7: Day 099
- 1
Question 1. The diagram shows the graph of y = x² - 4
Write down the solutions of x² - 4 = 0Identifying the Roots of a Quadratic from a Graph▶ Show worked answerHide worked answer
- M1: the graph crosses the x-axis at (-2, 0) and (2, 0)
- A1: x = -2 and x = 2
Answer: x = -2 and x = 2[2 marks] - 2
Question 2. Class A has a median mark of 62 and an interquartile range of 8. Class B has a median mark of 60 and an interquartile range of 15. Which class has more consistent marks? Give a reason.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: Class A
- B1: smaller IQR means the middle half of the marks is closer together
Answer: Class A, as its IQR (8) is smaller than Class B's (15)[2 marks] - 3
Question 3. Zoe says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 48 for all integer values of n. Luis says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 24 for all integer values of n. Only one of them is correct. Who is correct? You must show your working.
Proof with Multiples▶ Show worked answerHide worked answer
- M1: 3(4n² + 20n + 25) - 3(4n² + 4n + 1)
- M1: 48n + 72 = 24(2n + 3)
- C1: 2n + 3 is always odd, so 24(2n + 3) is never a multiple of 48
- C1: Luis is correct
Answer: Luis: the expression is 24(2n + 3) and 2n + 3 is odd[4 marks] - 4
Question 4. A parallelogram has sides of 15 cm and 9 cm. The angle between these sides is 30°. Work out the area of the parallelogram.
Finding the Area of a Parallelogram▶ Show worked answerHide worked answer
- M1: 15 × 9 × sin 30°
- A1: 67.5 cm²
Answer: 67.5 cm²[2 marks] - 5
Question 5. A solid pyramid has a square base of side 20 cm and height 30 cm. A smaller pyramid of height 12 cm is cut off the top parallel to the base. Work out the volume of the frustum left.
Volume of Frustums▶ Show worked answerHide worked answer
- M1: small side 20 × 12 ÷ 30 = 8
- M1: 1/3 × 20² × 30 and 1/3 × 8² × 12
- M1: 4000 - 256
- A1: 3744
Answer: 3744[4 marks]
Mixed Topic Worksheet Grades 6/7: Day 099
- 1
Question 1. The diagram shows the graph of y = x² - 4
[2 marks]
Write down the solutions of x² - 4 = 0Identifying the Roots of a Quadratic from a Graph▶ Show worked answerHide worked answer
- M1: the graph crosses the x-axis at (-2, 0) and (2, 0)
- A1: x = -2 and x = 2
Answer: x = -2 and x = 2 - 2
Question 2. Class A has a median mark of 62 and an interquartile range of 8. Class B has a median mark of 60 and an interquartile range of 15. Which class has more consistent marks? Give a reason.
[2 marks]Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: Class A
- B1: smaller IQR means the middle half of the marks is closer together
Answer: Class A, as its IQR (8) is smaller than Class B's (15) - 3
Question 3. Zoe says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 48 for all integer values of n. Luis says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 24 for all integer values of n. Only one of them is correct. Who is correct? You must show your working.
[4 marks]Proof with Multiples▶ Show worked answerHide worked answer
- M1: 3(4n² + 20n + 25) - 3(4n² + 4n + 1)
- M1: 48n + 72 = 24(2n + 3)
- C1: 2n + 3 is always odd, so 24(2n + 3) is never a multiple of 48
- C1: Luis is correct
Answer: Luis: the expression is 24(2n + 3) and 2n + 3 is odd - 4
Question 4. A parallelogram has sides of 15 cm and 9 cm. The angle between these sides is 30°. Work out the area of the parallelogram.
[2 marks]Finding the Area of a Parallelogram▶ Show worked answerHide worked answer
- M1: 15 × 9 × sin 30°
- A1: 67.5 cm²
Answer: 67.5 cm² - 5
Question 5. A solid pyramid has a square base of side 20 cm and height 30 cm. A smaller pyramid of height 12 cm is cut off the top parallel to the base. Work out the volume of the frustum left.
[4 marks]Volume of Frustums▶ Show worked answerHide worked answer
- M1: small side 20 × 12 ÷ 30 = 8
- M1: 1/3 × 20² × 30 and 1/3 × 8² × 12
- M1: 4000 - 256
- A1: 3744
Answer: 3744
Mixed Topic Worksheet Grades 6/7: Day 099
- 1
Question 1. The diagram shows the graph of y = x² - 4
Write down the solutions of x² - 4 = 0Identifying the Roots of a Quadratic from a Graph▶ Show worked answerHide worked answer
- M1: the graph crosses the x-axis at (-2, 0) and (2, 0)
- A1: x = -2 and x = 2
Answer: x = -2 and x = 2[2 marks] - 2
Question 2. Class A has a median mark of 62 and an interquartile range of 8. Class B has a median mark of 60 and an interquartile range of 15. Which class has more consistent marks? Give a reason.
Benefits of IQR & Range▶ Show worked answerHide worked answer
- B1: Class A
- B1: smaller IQR means the middle half of the marks is closer together
Answer: Class A, as its IQR (8) is smaller than Class B's (15)[2 marks] - 3
Question 3. Zoe says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 48 for all integer values of n. Luis says that 3(2n + 5)² - 3(2n + 1)² is a multiple of 24 for all integer values of n. Only one of them is correct. Who is correct? You must show your working.
Proof with Multiples▶ Show worked answerHide worked answer
- M1: 3(4n² + 20n + 25) - 3(4n² + 4n + 1)
- M1: 48n + 72 = 24(2n + 3)
- C1: 2n + 3 is always odd, so 24(2n + 3) is never a multiple of 48
- C1: Luis is correct
Answer: Luis: the expression is 24(2n + 3) and 2n + 3 is odd[4 marks] - 4
Question 4. A parallelogram has sides of 15 cm and 9 cm. The angle between these sides is 30°. Work out the area of the parallelogram.
Finding the Area of a Parallelogram▶ Show worked answerHide worked answer
- M1: 15 × 9 × sin 30°
- A1: 67.5 cm²
Answer: 67.5 cm²[2 marks] - 5
Question 5. A solid pyramid has a square base of side 20 cm and height 30 cm. A smaller pyramid of height 12 cm is cut off the top parallel to the base. Work out the volume of the frustum left.
Volume of Frustums▶ Show worked answerHide worked answer
- M1: small side 20 × 12 ÷ 30 = 8
- M1: 1/3 × 20² × 30 and 1/3 × 8² × 12
- M1: 4000 - 256
- A1: 3744
Answer: 3744[4 marks]