Exam-Style Problems

Stage 9 - Q1 - 2 marks

19007

Evaluate when \(x=-9\).

\[3 x + 1\]

Hint

Multiply before adding.

Stage 9 - Q2 - 2 marks

19008

Evaluate when \(x=-10\).

\[x^{2} - 1\]

Hint

Use brackets around a negative value being squared.

Stage 9 - Q3 - 3 marks

19009

Evaluate when \(x=-2\).

\[7 x^{2} + 1\]

Hint

The coefficient is outside the square.

Stage 9 - Q4 - 3 marks

19010

Evaluate exactly when \(x=-3\).

\[\frac{9x}{2}\]

Hint

Write an exact fraction if the result is not an integer.

Stage 9 - Q5 - 4 marks

19011

Evaluate when \(x=-4\) and \(y=2\).

\[x^{2} - 3 y\]

Hint

Keep the two substitutions distinct.

Stage 9 - Q6 - 4 marks

19012

Evaluate when \(x=-5\) and \(y=3\).

\[x^{2} - 5 y\]

Hint

Keep the two substitutions distinct.

Stage 9 - Q7 - 5 marks

19013

Evaluate when \(x=-6\).

\[(x - 3)^{3}\]

Hint

Follow the brackets before the power.

Stage 9 - Q8 - 5 marks

19014

A learner evaluates \(9x^2\) at \(x=-7\) as \(3969\). Explain and correct the error.

Hint

Compare the position of the brackets.

Stage 9 - Q9 - 5 marks

19015

The expression \(ax+4\) equals \(-20\) when \(x=-8\). Find a.

Hint

The unknown is the coefficient, not the input value.

Stage 9 - Q10 - 3 marks

19016

Choose distinct a and b from {\(-3\), \(-2\), \(-1\), 1, 2, 3}. Find the largest possible value and all ordered pairs that achieve it.

\[a^2-2ab+b^2\]

Hint

Try values of opposite signs, then explain why no larger difference is possible.