Mixed Topic Worksheet Grades 6/7: Day 021
- 1
Question 1. The highest common factor of 84 and n is 12
The lowest common multiple of 84 and n is 252
Work out the value of n.
You must show your working.Venn Diagram Method▶ Show worked answerHide worked answer
- M1: 84 × n = 12 × 252 (product of the two numbers equals product of HCF and LCM), or 84 = 2² × 3 × 7 and 252 = 2² × 3² × 7
- M1: n = dfrac12 × 25284, or n = 2² × 3²
- A1: 36
Answer: 36[3 marks] - 2
Question 2. Make x the subject of y = dfrac8x - 3
Rearranging Harder Equations▶ Show worked answerHide worked answer
- M1: y + 3 = dfrac8x
- M1: x(y + 3) = 8
- A1: x = dfrac8y + 3
Answer: x = dfrac8y + 3[3 marks] - 3
Question 3. A captain, a vice-captain and a goalkeeper are chosen from 9 players.
No player can have more than one of these jobs.
Work out the number of different ways the three jobs can be given out.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 9 choices for captain, then 8 for vice-captain
- M1: 9 × 8 × 7
- A1: 504
Answer: 504[3 marks] - 4
Question 4. Here is triangle ABC.
Tom says, "I can use the sine rule to work out the length x."
Is Tom correct?
You must give a reason for your answer.Finding Side Lengths Using the Sine Rule▶ Show worked answerHide worked answer
- B1: No
- B1: the angle given is not opposite either of the sides given (there is no side and its opposite angle)
Answer: No, because no side is given together with the angle opposite it[2 marks] - 5
Question 5. The line x = 3 meets the circle x² + y² = 58 at the points P and Q.
Work out the length of PQ.Sketching Circles▶ Show worked answerHide worked answer
- M1: substitutes x = 3: 9 + y² = 58
- M1: y² = 49, so y = 7 or y = -7
- A1: PQ = 7 - (-7) = 14
Answer: 14[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 021
- 1
Question 1. The highest common factor of 84 and n is 12
[3 marks]
The lowest common multiple of 84 and n is 252
Work out the value of n.
You must show your working.Venn Diagram Method▶ Show worked answerHide worked answer
- M1: 84 × n = 12 × 252 (product of the two numbers equals product of HCF and LCM), or 84 = 2² × 3 × 7 and 252 = 2² × 3² × 7
- M1: n = dfrac12 × 25284, or n = 2² × 3²
- A1: 36
Answer: 36 - 2
Question 2. Make x the subject of y = dfrac8x - 3
[3 marks]Rearranging Harder Equations▶ Show worked answerHide worked answer
- M1: y + 3 = dfrac8x
- M1: x(y + 3) = 8
- A1: x = dfrac8y + 3
Answer: x = dfrac8y + 3 - 3
Question 3. A captain, a vice-captain and a goalkeeper are chosen from 9 players.
[3 marks]
No player can have more than one of these jobs.
Work out the number of different ways the three jobs can be given out.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 9 choices for captain, then 8 for vice-captain
- M1: 9 × 8 × 7
- A1: 504
Answer: 504 - 4
Question 4. Here is triangle ABC.
[2 marks]
Tom says, "I can use the sine rule to work out the length x."
Is Tom correct?
You must give a reason for your answer.Finding Side Lengths Using the Sine Rule▶ Show worked answerHide worked answer
- B1: No
- B1: the angle given is not opposite either of the sides given (there is no side and its opposite angle)
Answer: No, because no side is given together with the angle opposite it - 5
Question 5. The line x = 3 meets the circle x² + y² = 58 at the points P and Q.
[3 marks]
Work out the length of PQ.Sketching Circles▶ Show worked answerHide worked answer
- M1: substitutes x = 3: 9 + y² = 58
- M1: y² = 49, so y = 7 or y = -7
- A1: PQ = 7 - (-7) = 14
Answer: 14
Mixed Topic Worksheet Grades 6/7: Day 021
- 1
Question 1. The highest common factor of 84 and n is 12
The lowest common multiple of 84 and n is 252
Work out the value of n.
You must show your working.Venn Diagram Method▶ Show worked answerHide worked answer
- M1: 84 × n = 12 × 252 (product of the two numbers equals product of HCF and LCM), or 84 = 2² × 3 × 7 and 252 = 2² × 3² × 7
- M1: n = dfrac12 × 25284, or n = 2² × 3²
- A1: 36
Answer: 36[3 marks] - 2
Question 2. Make x the subject of y = dfrac8x - 3
Rearranging Harder Equations▶ Show worked answerHide worked answer
- M1: y + 3 = dfrac8x
- M1: x(y + 3) = 8
- A1: x = dfrac8y + 3
Answer: x = dfrac8y + 3[3 marks] - 3
Question 3. A captain, a vice-captain and a goalkeeper are chosen from 9 players.
No player can have more than one of these jobs.
Work out the number of different ways the three jobs can be given out.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 9 choices for captain, then 8 for vice-captain
- M1: 9 × 8 × 7
- A1: 504
Answer: 504[3 marks] - 4
Question 4. Here is triangle ABC.
Tom says, "I can use the sine rule to work out the length x."
Is Tom correct?
You must give a reason for your answer.Finding Side Lengths Using the Sine Rule▶ Show worked answerHide worked answer
- B1: No
- B1: the angle given is not opposite either of the sides given (there is no side and its opposite angle)
Answer: No, because no side is given together with the angle opposite it[2 marks] - 5
Question 5. The line x = 3 meets the circle x² + y² = 58 at the points P and Q.
Work out the length of PQ.Sketching Circles▶ Show worked answerHide worked answer
- M1: substitutes x = 3: 9 + y² = 58
- M1: y² = 49, so y = 7 or y = -7
- A1: PQ = 7 - (-7) = 14
Answer: 14[3 marks]