Stage 8 - Q1 - 2 marks
List all integer values of x.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q2 - 2 marks
List all integer values of x.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q3 - 3 marks
Write the inequality shown on the number line.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q4 - 3 marks
Write the inequality shown on the number line.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q5 - 4 marks
A temperature must be above -2°C and at most 2°C. Write one inequality for T and list the permitted integer temperatures.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q6 - 4 marks
A temperature must be above -6°C and at most 0°C. Write one inequality for T and list the permitted integer temperatures.
Hint
Check each boundary sign before listing or drawing possible values.
Stage 8 - Q7 - 5 marks
Which of -1.5,-1, 0, 2, 2.5 satisfy \(-1<x\leq 2\)? Explain the boundary decisions.
Hint
Test each value against both conditions.
Stage 8 - Q8 - 5 marks
A value is recorded to exactly two decimal places and satisfies \(1.24\leq x<1.30\). List every possible recorded value.
Hint
Use the recording precision as the step size.
Stage 8 - Q9 - 5 marks
Give an interval containing infinitely many real numbers but no integers. Explain both claims.
Hint
Place both endpoints between two consecutive integers, or exclude those two integers.
Stage 8 - Q10 - 5 marks
An interval has integer endpoints and contains exactly the integers -2,-1, 0, 1, 2. Find four different ways to write such an interval, one for each choice of open or closed endpoints.
Hint
Treat the left and right endpoints separately.