Stage 8 - Q1 - 2 marks
Combine the two conditions.
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q2 - 2 marks
Combine the two conditions.
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q3 - 3 marks
How many integer solutions are there?
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q4 - 3 marks
How many integer solutions are there?
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q5 - 4 marks
Find one inequality describing all values that satisfy both conditions.
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q6 - 4 marks
Find one inequality describing all values that satisfy both conditions.
Hint
Use the stricter lower and upper conditions, then test the boundary integers.
Stage 8 - Q7 - 5 marks
Find all integers satisfying both \(-2.5<x\leq 4.5\) and \(1\leq x<6\).
Hint
Find the overlap before listing integers.
Stage 8 - Q8 - 5 marks
A pupil reverses \(-3\leq x<5\) as \(5\leq x<-3\). Correct the statement and explain the change in sign direction.
Hint
Read the original inequality aloud before reversing the order.
Stage 8 - Q9 - 5 marks
The smallest integer in \(a<x<8\) is 3, and a is an integer. Find a, count the integer solutions and find their sum.
Hint
Use the strict endpoints to locate the first and last integers.
Stage 8 - Q10 - 5 marks
Find all integer pairs(a, b) with \(a<b\) such that \(a<x\leq b\) has exactly six integer solutions and the sum of those integers is 15.
Hint
Write the six consecutive integers in terms of the lower endpoint.