Free Year 12 Algebra Quiz — 10 Questions, Instant Results

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Algebra at Year 12: what the curriculum expects

In Units 3 and 4 the algebra topic covers solving equations involving exponentials, logarithms and circular functions, literal equations, simultaneous equations with parameters and algebraic manipulation in show-that questions.

This topic sits inside the VCE study design for Year 12 Mathematical Methods; the questions stay at the easy and at-level tiers so the result is a fair check of the foundations.

Common algebra misconceptions tutors see

The distractors in this quiz are built from real misconceptions rather than random wrong numbers, so a specific wrong answer usually points to a specific gap. The ones we see most at Year 12:

• Exact values are replaced by decimals.
• Logarithm laws are misapplied to sums and differences.
• Solutions to trigonometric equations are found for one period only.

None of these is a sign of low ability. Each is a reasonable idea that worked in an earlier year and needs replacing, which is exactly what a good explanation, or a tutor, does.

Practising algebra with a Year 12 student

The habits that move algebra from shaky to secure at Year 12:

1. Practise log and index laws with a mixed daily set.
2. Solve trig equations over a given domain and list all solutions.
3. Solve literal equations from the formula sheet.

At VCE, practise by hand for Exam 1 and with the CAS for Exam 2, use past papers under time and mark against the examiners' reports. Fix the errors the same week.

How this algebra quiz works

We keep 12 algebra questions for Year 12 that meet our standard, at the easy and at-level tiers, and this page serves 10 of them at a time. The default set is stable, so a teacher or parent can share the link; a fresh set is one click away. Marking happens on our server so the answer key cannot be read from the page.

A single-topic quiz is more precise than a mixed one: if the score here is low, the gap is in algebra, not somewhere in Year 12 Mathematical Methods generally. It is still short, though, and it cannot show how a student copes with the stretch and challenge questions that decide a top result. That is what the free Skills Check adds.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 81656 · New set of questions →

Question 1

Algebra

Factorise: x² + 5x + 6.

(x + 2)(x + 3) (x + 1)(x + 6) (x + 5)(x + 1) (x − 2)(x − 3)

Question 2

Algebra

Solve x² + x − 6 = 0.

x = 1 or 6 x = −2 or 3 x = 3 or 2 x = 2 or −3

Question 3

Algebra

Simplify: log(a) + log(b).

log(ab) log(a) log(b) log(a+b) log(a/b)

Question 4

Algebra

The polynomial P(x) = x³ + px² + qx + 6 has roots α, β, and γ. Given that α + β + γ = −2 and αβ + αγ + βγ = −5, what are the values of p and q?

p = 2, q = −5 p = −2, q = −5 p = −2, q = 5 p = 2, q = 5

Question 5

Algebra

The equation x⁴ − 5x² + 4 = 0 is to be solved. How many real solutions does it have, and what are they?

Two real solutions: x = ±√5 No real solutions Four real solutions: x = ±1, x = ±2 Two real solutions: x = 1, x = 2

Question 6

Algebra

The function f(x) = ln(x − 1) + ln(3 − x) is defined on its natural domain. On this domain, f is concave down everywhere. What is the x-value at which f attains its maximum?

x = √3 x = 1.5 x = e x = 2

Question 7

Algebra

Evaluate 8^(−1/3).

1/2 −2 1/8 2

Question 8

Algebra

Solve: 2ˣ = 16.

x = 8 x = 2 x = 4 x = 32

Question 9

Algebra

For the function f(x) = 2ˣ − 2⁻ˣ, which statement is TRUE?

f is odd only for integer values of x f is neither odd nor even because it involves two exponential terms f is an even function because the exponents are symmetric f is an odd function because f(−x) = −f(x) for all x

Question 10

Algebra

Solve log₃(x) = 2.

x = 5 x = 9 x = 8 x = 6

Mark my answers →

Your result

0 / 10

Take the free full Skills Check →   Try another set

How to read a score out of 10

9 or 10 out of 10

The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.

7 or 8 out of 10

Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.

5 or 6 out of 10

Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.

4 or fewer out of 10

Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

What to do with the result

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

Frequently asked questions

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