Mixed Topic Worksheet Grades 8/9: Day 095
- 1
Question 1. Simplify fully 4√90
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √90 = 3√10
- A1: 12√10
Answer: 12√10[2 marks] - 2
Question 2. y is inversely proportional to √x. When x=25, y=4. Work out y when x=16.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y=dfrack√x, k=20
- A1: y=dfrac204=5
Answer: 5[2 marks] - 3
Question 3. Prove that the product of any three consecutive integers is a multiple of 6.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- B1: at least one of the three is even, so the product is even
- B1: exactly one of the three is a multiple of 3, so the product is a multiple of 3
- C1: a multiple of 2 and of 3 is a multiple of 6
Answer: It is a multiple of 2 and of 3, so a multiple of 6[3 marks] - 4
Question 4. Priya simplifies dfracx²+xx-3÷dfracxx²-9 and gets (x+1)(x+3). Is Priya correct? You must show your working.
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfracx²+xx-3×dfracx²-9x
- M2: x(x+1) and (x-3)(x+3), cancels x and (x-3)
- A1: (x+1)(x+3), so Priya is correct
Answer: Yes, Priya is correct[4 marks] - 5
Question 5. Jess solves x²-5x-14 > 0.
(x-7)(x+2) > 0, x = 7 or x = -2, -2 < x < 7
Work out the correct solution.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: test x = 0: -14, which is not greater than 0
- A1: x < -2 or x > 7
Answer: x < -2 or x > 7[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 095
- 1
Question 1. Simplify fully 4√90
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: √90 = 3√10
- A1: 12√10
Answer: 12√10 - 2
Question 2. y is inversely proportional to √x. When x=25, y=4. Work out y when x=16.
[2 marks]Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y=dfrack√x, k=20
- A1: y=dfrac204=5
Answer: 5 - 3
Question 3. Prove that the product of any three consecutive integers is a multiple of 6.
[3 marks]Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- B1: at least one of the three is even, so the product is even
- B1: exactly one of the three is a multiple of 3, so the product is a multiple of 3
- C1: a multiple of 2 and of 3 is a multiple of 6
Answer: It is a multiple of 2 and of 3, so a multiple of 6 - 4
Question 4. Priya simplifies dfracx²+xx-3÷dfracxx²-9 and gets (x+1)(x+3). Is Priya correct? You must show your working.
[4 marks]Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfracx²+xx-3×dfracx²-9x
- M2: x(x+1) and (x-3)(x+3), cancels x and (x-3)
- A1: (x+1)(x+3), so Priya is correct
Answer: Yes, Priya is correct - 5
Question 5. Jess solves x²-5x-14 > 0.
[2 marks]
(x-7)(x+2) > 0, x = 7 or x = -2, -2 < x < 7
Work out the correct solution.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: test x = 0: -14, which is not greater than 0
- A1: x < -2 or x > 7
Answer: x < -2 or x > 7
Mixed Topic Worksheet Grades 8/9: Day 095
- 1
Question 1. Simplify fully 4√90
Simplifying Surds▶ Show worked answerHide worked answer
- M1: √90 = 3√10
- A1: 12√10
Answer: 12√10[2 marks] - 2
Question 2. y is inversely proportional to √x. When x=25, y=4. Work out y when x=16.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y=dfrack√x, k=20
- A1: y=dfrac204=5
Answer: 5[2 marks] - 3
Question 3. Prove that the product of any three consecutive integers is a multiple of 6.
Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- B1: at least one of the three is even, so the product is even
- B1: exactly one of the three is a multiple of 3, so the product is a multiple of 3
- C1: a multiple of 2 and of 3 is a multiple of 6
Answer: It is a multiple of 2 and of 3, so a multiple of 6[3 marks] - 4
Question 4. Priya simplifies dfracx²+xx-3÷dfracxx²-9 and gets (x+1)(x+3). Is Priya correct? You must show your working.
Multiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfracx²+xx-3×dfracx²-9x
- M2: x(x+1) and (x-3)(x+3), cancels x and (x-3)
- A1: (x+1)(x+3), so Priya is correct
Answer: Yes, Priya is correct[4 marks] - 5
Question 5. Jess solves x²-5x-14 > 0.
(x-7)(x+2) > 0, x = 7 or x = -2, -2 < x < 7
Work out the correct solution.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: test x = 0: -14, which is not greater than 0
- A1: x < -2 or x > 7
Answer: x < -2 or x > 7[2 marks]