Stage 8 - Q1 - 2 marks
Find the mean of the two decimals.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q2 - 2 marks
Find the mean of the two decimals.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q3 - 3 marks
Two circle values have mean 3.3. One is 3. Find the other.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q4 - 3 marks
Two circle values have mean 4.5. One is 4.1. Find the other.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q5 - 4 marks
Each square is the mean of its two joined circles. Fill all five squares.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q6 - 4 marks
Each square is the mean of its two joined circles. Fill all five squares.
Hint
Twice a square value is the sum of the connected circle values.
Stage 8 - Q7 - 5 marks
Two joined circle values have mean 3.25. One circle is increased by 0.6 while the other is unchanged. Find the new mean.
Hint
Only one of the two values changes.
Stage 8 - Q8 - 5 marks
The top, left and right circles have values w, x, y. The upper-left, upper-right and centre squares are 2.1, 2.7 and 3.2. Find w, x, y.
Hint
Use three pair sums to isolate a circle value.
Stage 8 - Q9 - 5 marks
Can a mean diamond have upper-left square 1.2, upper-right 1.6, lower-left 2.0 and lower-right 2.5? Justify without guessing the circles.
Hint
Compare the difference between the two top means with the difference between the two bottom means.
Stage 8 - Q10 - 5 marks
The five squares, in order upper-left, upper-right, centre, lower-left, lower-right, are a, \(a+g\), \(a+2g\), \(a+3g\), \(a+4g\). Find expressions for the top, left, right and bottom circle values and verify all five means.
Hint
Double each mean to turn the diagram into equations for pair sums.