Mixed Topic Worksheet Grades 6/7: Day 004
- 1
Question 1. Four of five numbers are
3 8 11 5
The mean of the five numbers is 9
Work out the missing number.Reverse Mean from a List▶ Show worked answerHide worked answer
- M1: 5 x 9 = 45
- M1: 45 - (3 + 8 + 11 + 5)
- A1: 18
Answer: 18[3 marks] - 2
Question 2. Write down the whole number that is closest to the cube root of 30
Estimating Roots▶ Show worked answerHide worked answer
- M1: 3³ = 27 and 4³ = 64 with 30 nearer to 27
- A1: 3
Answer: 3[2 marks] - 3
Question 3. A shape is reflected in the line y = 3
Work out the image of the point (4, 7) and describe the invariant points.Invariant Points▶ Show worked answerHide worked answer
- M1: (4, 7) is 4 above y = 3
- A1: image (4, -1)
- B1: every point on the line y = 3 is invariant
Answer: image (4, -1); the invariant points are all the points on the line y = 3[3 marks] - 4
Question 4. 7 runners take part in a race.
There are no tied places.
The runners who finish first, second and third win medals.
Work out the number of different ways the 3 medals can be won.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5
- A1: 210
Answer: 210[2 marks] - 5
Question 5. x_n+1 = sqrt[3]dfrac60x_n + 3
x_0 = 3
Work out x_1, x_2 and x_3
Give your answers correct to 3 decimal places.Iteration Equations▶ Show worked answerHide worked answer
- M1: x_1 = sqrt[3]dfrac603 + 3
- A1: x_1 = 2.844 and x_2 = 2.888
- A1: x_3 = 2.875
Answer: x_1 = 2.844, x_2 = 2.888, x_3 = 2.875[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 004
- 1
Question 1. Four of five numbers are
[3 marks]
3 8 11 5
The mean of the five numbers is 9
Work out the missing number.Reverse Mean from a List▶ Show worked answerHide worked answer
- M1: 5 x 9 = 45
- M1: 45 - (3 + 8 + 11 + 5)
- A1: 18
Answer: 18 - 2
Question 2. Write down the whole number that is closest to the cube root of 30
[2 marks]Estimating Roots▶ Show worked answerHide worked answer
- M1: 3³ = 27 and 4³ = 64 with 30 nearer to 27
- A1: 3
Answer: 3 - 3
Question 3. A shape is reflected in the line y = 3
[3 marks]
Work out the image of the point (4, 7) and describe the invariant points.Invariant Points▶ Show worked answerHide worked answer
- M1: (4, 7) is 4 above y = 3
- A1: image (4, -1)
- B1: every point on the line y = 3 is invariant
Answer: image (4, -1); the invariant points are all the points on the line y = 3 - 4
Question 4. 7 runners take part in a race.
[2 marks]
There are no tied places.
The runners who finish first, second and third win medals.
Work out the number of different ways the 3 medals can be won.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5
- A1: 210
Answer: 210 - 5
Question 5. x_n+1 = sqrt[3]dfrac60x_n + 3
[3 marks]
x_0 = 3
Work out x_1, x_2 and x_3
Give your answers correct to 3 decimal places.Iteration Equations▶ Show worked answerHide worked answer
- M1: x_1 = sqrt[3]dfrac603 + 3
- A1: x_1 = 2.844 and x_2 = 2.888
- A1: x_3 = 2.875
Answer: x_1 = 2.844, x_2 = 2.888, x_3 = 2.875
Mixed Topic Worksheet Grades 6/7: Day 004
- 1
Question 1. Four of five numbers are
3 8 11 5
The mean of the five numbers is 9
Work out the missing number.Reverse Mean from a List▶ Show worked answerHide worked answer
- M1: 5 x 9 = 45
- M1: 45 - (3 + 8 + 11 + 5)
- A1: 18
Answer: 18[3 marks] - 2
Question 2. Write down the whole number that is closest to the cube root of 30
Estimating Roots▶ Show worked answerHide worked answer
- M1: 3³ = 27 and 4³ = 64 with 30 nearer to 27
- A1: 3
Answer: 3[2 marks] - 3
Question 3. A shape is reflected in the line y = 3
Work out the image of the point (4, 7) and describe the invariant points.Invariant Points▶ Show worked answerHide worked answer
- M1: (4, 7) is 4 above y = 3
- A1: image (4, -1)
- B1: every point on the line y = 3 is invariant
Answer: image (4, -1); the invariant points are all the points on the line y = 3[3 marks] - 4
Question 4. 7 runners take part in a race.
There are no tied places.
The runners who finish first, second and third win medals.
Work out the number of different ways the 3 medals can be won.Combinations Problem Solving▶ Show worked answerHide worked answer
- M1: 7 × 6 × 5
- A1: 210
Answer: 210[2 marks] - 5
Question 5. x_n+1 = sqrt[3]dfrac60x_n + 3
x_0 = 3
Work out x_1, x_2 and x_3
Give your answers correct to 3 decimal places.Iteration Equations▶ Show worked answerHide worked answer
- M1: x_1 = sqrt[3]dfrac603 + 3
- A1: x_1 = 2.844 and x_2 = 2.888
- A1: x_3 = 2.875
Answer: x_1 = 2.844, x_2 = 2.888, x_3 = 2.875[3 marks]