Q1
A student is simplifying 3(x + 8) - 2(5x - 7). What should the expression become after removing brackets and collecting like terms?
Checks: negative bracket expansion
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Q2
The area of a rectangle is represented by 10p2 - p - 3. Write this area as a product of two linear factors.
Checks: quadratic factorisation with non-unit leading coefficient
Q3
Solve 3(4y - 5) + 2(y + 6) = 6y + 25.
Checks: equation balance after expansion
Q4
Simplify (x + 4)/(x2 - 16) + 3/(x + 4) and state excluded values of x.
Checks: algebraic fractions and restrictions
Q5
A workshop charges a fixed booking fee of $18 plus $6 per student. The total charge is $162. How many students attended?
Checks: forming equations from word statements
Q6
A tile pattern has 6 tiles in Figure 1. Each new figure uses 5 more tiles than the previous figure. Find a formula for the number of tiles in Figure n.
Checks: linear pattern recognition
Q7
A student writes (x - 5)2 = x2 - 25. Explain the mistake and give the correct expansion.
Checks: binomial square misconception
Q8
The product of two positive odd integers that differ by 2 is 255. Find the two integers.
Checks: quadratic equation in context