Mixed Topic Worksheet Grades 6/7: Day 087
- 1
Question 1. Two straight rails are drawn on a map grid.
Rail mathbfA has equation y = 3x - 4
Rail mathbfB is parallel to rail mathbfA and passes through the point (2, 9)
The point S is on rail mathbfB where x = 5
Work out the y-coordinate of S.Properties of Parallel Lines▶ Show worked answerHide worked answer
- M1: gradient of B = 3 and 9 = 3 × 2 + c
- M1: y = 3x + 3 and x = 5 substituted
- A1: 18
Answer: 18[3 marks] - 2
Question 2. Simplify fully dfrac10y-2515
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac5(2y-5)15
- A1: dfrac2y-53
Answer: dfrac2y-53[2 marks] - 3
Question 3. Here are 9 numbers.
14 22 35 41 46 52 60 68 74
Work out the range of the numbers.Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: 74 - 14
- A1: 60
Answer: 60[2 marks] - 4
Question 4. Prove algebraically that the square of any odd number is odd.
Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: (2n + 1)² = 4n² + 2n + 2n + 1
- A1: 4n² + 4n + 1 = 2(2n² + 2n) + 1
- C1: 1 more than a multiple of 2, so it is odd
Answer: 2(2n² + 2n) + 1[3 marks] - 5
Question 5. Express dfrac√5 + 10√5 in the form a + b√5 where a and b are integers.
Rationalising Denominators of the Form √a▶ Show worked answerHide worked answer
- M1: dfrac(√5 + 10) × √55
- M1: dfrac5 + 10√55
- A1: 1 + 2√5
Answer: 1 + 2√5[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 087
- 1
Question 1. Two straight rails are drawn on a map grid.
[3 marks]
Rail mathbfA has equation y = 3x - 4
Rail mathbfB is parallel to rail mathbfA and passes through the point (2, 9)
The point S is on rail mathbfB where x = 5
Work out the y-coordinate of S.Properties of Parallel Lines▶ Show worked answerHide worked answer
- M1: gradient of B = 3 and 9 = 3 × 2 + c
- M1: y = 3x + 3 and x = 5 substituted
- A1: 18
Answer: 18 - 2
Question 2. Simplify fully dfrac10y-2515
[2 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac5(2y-5)15
- A1: dfrac2y-53
Answer: dfrac2y-53 - 3
Question 3. Here are 9 numbers.
[2 marks]
14 22 35 41 46 52 60 68 74
Work out the range of the numbers.Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: 74 - 14
- A1: 60
Answer: 60 - 4
Question 4. Prove algebraically that the square of any odd number is odd.
[3 marks]Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: (2n + 1)² = 4n² + 2n + 2n + 1
- A1: 4n² + 4n + 1 = 2(2n² + 2n) + 1
- C1: 1 more than a multiple of 2, so it is odd
Answer: 2(2n² + 2n) + 1 - 5
Question 5. Express dfrac√5 + 10√5 in the form a + b√5 where a and b are integers.
[3 marks]Rationalising Denominators of the Form √a▶ Show worked answerHide worked answer
- M1: dfrac(√5 + 10) × √55
- M1: dfrac5 + 10√55
- A1: 1 + 2√5
Answer: 1 + 2√5
Mixed Topic Worksheet Grades 6/7: Day 087
- 1
Question 1. Two straight rails are drawn on a map grid.
Rail mathbfA has equation y = 3x - 4
Rail mathbfB is parallel to rail mathbfA and passes through the point (2, 9)
The point S is on rail mathbfB where x = 5
Work out the y-coordinate of S.Properties of Parallel Lines▶ Show worked answerHide worked answer
- M1: gradient of B = 3 and 9 = 3 × 2 + c
- M1: y = 3x + 3 and x = 5 substituted
- A1: 18
Answer: 18[3 marks] - 2
Question 2. Simplify fully dfrac10y-2515
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: dfrac5(2y-5)15
- A1: dfrac2y-53
Answer: dfrac2y-53[2 marks] - 3
Question 3. Here are 9 numbers.
14 22 35 41 46 52 60 68 74
Work out the range of the numbers.Benefits of IQR & Range▶ Show worked answerHide worked answer
- M1: 74 - 14
- A1: 60
Answer: 60[2 marks] - 4
Question 4. Prove algebraically that the square of any odd number is odd.
Proof with Odd Numbers▶ Show worked answerHide worked answer
- M1: (2n + 1)² = 4n² + 2n + 2n + 1
- A1: 4n² + 4n + 1 = 2(2n² + 2n) + 1
- C1: 1 more than a multiple of 2, so it is odd
Answer: 2(2n² + 2n) + 1[3 marks] - 5
Question 5. Express dfrac√5 + 10√5 in the form a + b√5 where a and b are integers.
Rationalising Denominators of the Form √a▶ Show worked answerHide worked answer
- M1: dfrac(√5 + 10) × √55
- M1: dfrac5 + 10√55
- A1: 1 + 2√5
Answer: 1 + 2√5[3 marks]