HSC Maths Standard 2 free practice questions with answers

1. What is

Correct answer: A —

• Use a common denominator: 10.

• Subtract the tops over that denominator.

• Simplify:

• Why the other options are wrong:

• B ( wrong stage; the exact working above gives

• C (

• D (

2. Gym A charges a $5 joining fee plus $9 per visit. Gym B charges a $29 joining fee plus $1 per visit. For how many visits do the two gyms cost the same? [Break-even]

Correct answer: A — 3

• Cost at Gym A after m visits: 5 + 9m. Cost at Gym B: 29 + 1m.

• Set them equal: 5 + 9m = 29 + 1m.

• Collect m terms: 9m - 1m = 29 - 5, so 8m = 24.

• m = 24 ÷ 8 = 3 visits.

• Check: A costs 5 + 9×3 = 32; B costs 29 + 1×3 = 32.

• Why the other options are wrong:

• B (4): Check by putting m in both costs.

• C (

• D (24): Divide by the difference in the per-visit rates as well. 3 5 - 1 2 ? Give the answer in simplest form. [Fraction operations]

1 10 1 10 . 1 5 ): This is very close to the correct value, but it is the result of rounding or approximating at the 1 10 . 4 7 ): You cannot add the tops and bottoms separately. 3 10 ): Check which operation is asked. 17 5 ): The costs are EQUAL, so subtract the totals, not add.

3. A salesperson is paid a retainer of $600 per week plus 5% commission on sales above $20,000. In one week the salesperson sells goods worth $73,500. What is the total pay for the week? [Earning money]

Correct answer: C — $3,275

• Commission = 5% of $53,500 = $2,675.

• Total pay = retainer + commission = $600 + $2,675 = $3,275.

• Why the other options are wrong:

• A ($4,275): Commission is paid only on sales above $20,000.

• B ($2,675): Add the weekly retainer to the commission.

• D ($19,325): The commission is for the week; do not multiply it by 7.