Stage 8 - Q1 - 2 marks
Evaluate when \(x=-13\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q2 - 2 marks
Evaluate when \(x=-14\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q3 - 3 marks
Evaluate when \(x=-2\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q4 - 3 marks
Evaluate when \(x=-3\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q5 - 4 marks
A model uses \(C=7r+8h\), where C is cost in dollars. Find C when \(r=10\) and \(h=2\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q6 - 4 marks
A model uses \(C=2r+1h\), where C is cost in dollars. Find C when \(r=3\) and \(h=4\).
Hint
Substitute first, keeping brackets, then follow the order of operations.
Stage 8 - Q7 - 5 marks
Evaluate \(p^{2}-2\) \(pq+q^{2}\) when \(p=-3\) and \(q=2\). Then evaluate \((p-q)^{2}\) and compare.
Hint
Calculate each expression independently.
Stage 8 - Q8 - 5 marks
A pupil claims \(2x^{2}=(2x)^{2}\). Test \(x=-2\), 0, 3. Does the evidence support an identity?
Hint
Keep the position of each square separate from the multiplication.
Stage 8 - Q9 - 5 marks
Let \(E(x)=x^{3}+4x^{2}-2x\). Without evaluating both long expressions separately, find \(E(7)+E(-7)\).
Hint
Compare the signs of each term when x is replaced by -x.
Stage 8 - Q10 - 5 marks
Find every integer x between -3 and 3 for which \(x^{2}+2x=3\). Show how you know the list is complete.
Hint
The domain is small enough to test every allowed input.