Mixed Topic Worksheet Grades 8/9: Day 098
- 1
Question 1. Ravi writes √200 = 2√50 and says that this is the simplest form of √200. Is Ravi correct? Give a reason for your answer.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √50 = √25 × 2 = 5√2
- A1: Not correct, as 2√50 = 10√2
Answer: No. 2√50 = 10√2, because 50 has the square factor 25[2 marks] - 2
Question 2. A triangle has base 14 cm, to the nearest cm, and perpendicular height 8.6 cm, to 1 decimal place. Work out the lower bound of its area.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the lower bound of base and of height
- M1: frac12 × 13.5 × 8.55
- A1: 57.7125 cm²
Answer: 57.7125 cm²[3 marks] - 3
Question 3. Three houses next to each other on one side of a road have consecutive positive integers as their numbers. Anna multiplies the lowest house number by the highest house number. Prove algebraically that Anna's result is 1 less than the square of the middle house number.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (n - 1)(n + 1)
- M1: n² - 1
- C1: n² - 1 is 1 less than the square of the middle number n
Answer: n² - 1, one less than n²[3 marks] - 4
Question 4. Solve 2x² + 6x - 3 = 0 by completing the square. Give your solutions to 2 decimal places.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2≤ft(x + frac32)² - frac92 - 3 = 0
- M1: ≤ft(x + frac32)² = 15/4
- A1: x = 0.44 or x = -3.44
Answer: x = 0.44 or x = -3.44[3 marks] - 5
Question 5. Solve the simultaneous equations
y = x + 2
xy = 3 [4]Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: substitute: x(x + 2) = 3
- M1: x² + 2x - 3 = 0 so (x + 3)(x - 1) = 0
- A1: x = 1 and x = -3
- A1: y = 3 and y = -1 paired correctly
Answer: x = 1, y = 3 or x = -3, y = -1[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 098
- 1
Question 1. Ravi writes √200 = 2√50 and says that this is the simplest form of √200. Is Ravi correct? Give a reason for your answer.
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: √50 = √25 × 2 = 5√2
- A1: Not correct, as 2√50 = 10√2
Answer: No. 2√50 = 10√2, because 50 has the square factor 25 - 2
Question 2. A triangle has base 14 cm, to the nearest cm, and perpendicular height 8.6 cm, to 1 decimal place. Work out the lower bound of its area.
[3 marks]Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the lower bound of base and of height
- M1: frac12 × 13.5 × 8.55
- A1: 57.7125 cm²
Answer: 57.7125 cm² - 3
Question 3. Three houses next to each other on one side of a road have consecutive positive integers as their numbers. Anna multiplies the lowest house number by the highest house number. Prove algebraically that Anna's result is 1 less than the square of the middle house number.
[3 marks]Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (n - 1)(n + 1)
- M1: n² - 1
- C1: n² - 1 is 1 less than the square of the middle number n
Answer: n² - 1, one less than n² - 4
Question 4. Solve 2x² + 6x - 3 = 0 by completing the square. Give your solutions to 2 decimal places.
[3 marks]Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2≤ft(x + frac32)² - frac92 - 3 = 0
- M1: ≤ft(x + frac32)² = 15/4
- A1: x = 0.44 or x = -3.44
Answer: x = 0.44 or x = -3.44 - 5
Question 5. Solve the simultaneous equations
[4 marks]
y = x + 2
xy = 3 [4]Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: substitute: x(x + 2) = 3
- M1: x² + 2x - 3 = 0 so (x + 3)(x - 1) = 0
- A1: x = 1 and x = -3
- A1: y = 3 and y = -1 paired correctly
Answer: x = 1, y = 3 or x = -3, y = -1
Mixed Topic Worksheet Grades 8/9: Day 098
- 1
Question 1. Ravi writes √200 = 2√50 and says that this is the simplest form of √200. Is Ravi correct? Give a reason for your answer.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √50 = √25 × 2 = 5√2
- A1: Not correct, as 2√50 = 10√2
Answer: No. 2√50 = 10√2, because 50 has the square factor 25[2 marks] - 2
Question 2. A triangle has base 14 cm, to the nearest cm, and perpendicular height 8.6 cm, to 1 decimal place. Work out the lower bound of its area.
Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: use the lower bound of base and of height
- M1: frac12 × 13.5 × 8.55
- A1: 57.7125 cm²
Answer: 57.7125 cm²[3 marks] - 3
Question 3. Three houses next to each other on one side of a road have consecutive positive integers as their numbers. Anna multiplies the lowest house number by the highest house number. Prove algebraically that Anna's result is 1 less than the square of the middle house number.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: (n - 1)(n + 1)
- M1: n² - 1
- C1: n² - 1 is 1 less than the square of the middle number n
Answer: n² - 1, one less than n²[3 marks] - 4
Question 4. Solve 2x² + 6x - 3 = 0 by completing the square. Give your solutions to 2 decimal places.
Solving Quadratics by Completing the Square (a > 1)▶ Show worked answerHide worked answer
- M1: 2≤ft(x + frac32)² - frac92 - 3 = 0
- M1: ≤ft(x + frac32)² = 15/4
- A1: x = 0.44 or x = -3.44
Answer: x = 0.44 or x = -3.44[3 marks] - 5
Question 5. Solve the simultaneous equations
y = x + 2
xy = 3 [4]Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: substitute: x(x + 2) = 3
- M1: x² + 2x - 3 = 0 so (x + 3)(x - 1) = 0
- A1: x = 1 and x = -3
- A1: y = 3 and y = -1 paired correctly
Answer: x = 1, y = 3 or x = -3, y = -1[4 marks]