Stage 8 - Q1 - 2 marks
Factorise fully.
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q2 - 2 marks
Expand.
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q3 - 3 marks
Evaluate when \(x=-5\).
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q4 - 3 marks
Add 3 to n, then multiply the whole result by 14.
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q5 - 4 marks
Find one inequality describing all values that satisfy both conditions.
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q6 - 4 marks
A number is multiplied by 12, then 6 is added. The result is 102. Form an equation and find the number.
Hint
Decide first whether the task asks for an expression, a value, a solution or a range.
Stage 8 - Q7 - 5 marks
Find k so that \(3(2x+k)-x=5x+21\) for all x.
Hint
The coefficient of x already matches.
Stage 8 - Q8 - 5 marks
Solve \(2(3x-4)-3(x+1)=10\), then check the result in the original equation.
Hint
Keep the negative sign attached to the second bracket.
Stage 8 - Q9 - 5 marks
Classify each equality as true for every x, true for one x or true for no x: \(2(x+3)=2x+6\); \(2(x+3)=3x+2\); \(2(x+3)=2x+1\).
Hint
Remove equal terms and examine what remains in each case.
Stage 8 - Q10 - 5 marks
A rectangle has sides \(x+2\) and \(3x-1\) cm, where x is an integer. Its perimeter is less than 34 cm and both sides are positive. Find all possible x and the corresponding areas.
Hint
Combine the geometric domain with the perimeter inequality.