Free Year 11 Vectors Quiz — 10 Questions, Instant Results

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Vectors in Year 11 Specialist Mathematics

Here is the ground the questions cover. In Units 1 and 2 vectors are introduced in two dimensions: components, magnitude, addition, scalar multiplication and the scalar product.

The items are tagged to the VCE study design for Year 11, so a score here reflects the standard a Year 11 class is working to, not a generic online level.

Mistakes we see most often in vectors

A wrong answer is more useful than a right one if you know why it happened. In sessions with Year 11 students, these are the patterns our tutors see most:

• The scalar product is treated as a vector.
• Resolutes are found in the wrong direction.
• Direction is dropped when finding a magnitude.

Each of these is fixable in a session or two once it has been named, which is why the results panel below shows the correct answer and an explanation rather than just a score.

Ways to build vectors at Year 11

If the quiz shows a gap, more of the same worksheets rarely fixes it. Try these instead:

1. Prove geometric results with vectors.
2. Use the CAS for three-dimensional calculations.
3. Draw every vector problem before calculating.

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 the 10 questions are chosen

The 10 questions are drawn from 11 eligible items on vectors in our Year 11 Specialist Mathematics bank, all at the easy and at-level tiers. The selection is fixed for this address so a shared link shows the same quiz; press New set of questions or add ?seed= to the address for a different mix. Options are shuffled, no two questions share a stem, and the answer key is fetched from our server only after you submit, so it is not hidden in the page.

Use this page to answer one question well: is vectors secure at Year 11 level? For the broader picture across every topic and every difficulty tier, the free Skills Check takes about fifteen minutes and produces a report a tutor walks you through.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 71273 · New set of questions →

Question 1

Vectors

Two vectors are perpendicular when their dot product is?

0 −1 1 their magnitudes

Question 2

Vectors

Find (5, 3) − (2, 1).

(2, 3) (3, 2) (3, 4) (7, 4)

Question 3

Vectors

The unit vector in the direction of (3, 4) is?

(1/3, 1/4) (3/5, 4/5) (3, 4) (4/5, 3/5)

Question 4

Vectors

Vectors **u** and **v** satisfy |**u**| = 5, |**v**| = 3, and **u**·**v** = 12. What is the angle between **u** and **v**, correct to the nearest degree?

67° 53° 37° 23°

Question 5

Vectors

Vector **a** = 2**i** + **j** and **b** = −**i** + 3**j**. Find the vector projection of **b** onto **a**.

(4/5)**i** + (2/5)**j** (2/5)**i** + (1/5)**j** (1/5)**i** + (3/5)**j** (−2/5)**i** + (−1/5)**j**

Question 6

Vectors

Add the vectors (1, 2) + (3, 4).

(2, 2) (3, 8) (4, 8) (4, 6)

Question 7

Vectors

The magnitude of the vector (3, 4) is?

√7 7 12 5

Question 8

Vectors

Let **a** = **i** + 2**j** and **b** = 3**i** − **j**. Find the value of the scalar λ such that (**a** + λ**b**) is perpendicular to **b**.

λ = 1/2 λ = −1/10 λ = 1/10 λ = −1/2

Question 9

Vectors

The dot product (1, 2)·(3, 4) is?

7 24 (3, 8) 11

Question 10

Vectors

The magnitude of (5, 12) is?

13 √17 17 60

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

Other Specialist Mathematics topics for Year 11

Mixed Year 11 Specialist Mathematics quiz (all topics) →

Vectors in other year levels

Year 12 Vectors

All 3,261 free practice questions, Prep to Year 12 →