Free Printable MATH1015 Revision Session

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MATH1015 Revision Session

Total questions: 27

Worksheet time: 14mins

Name

Class

Date

If we have two complex numbers such that a = 2 + i and b = -3 - 2i, find a + b

-1 - i

-1 - 2i

-5 - i

-1 + i

a = 2cis(30)

b = 3cis(20)

Find a x b

7cis(60)

4cis(10)

6cis(50)

5cis(40)

Convert the following to polar form:

2 + i

√5cis(26.57)

5cis(26.57)

√5cis(153.43)

5cis(153.43)

What is the centre and radius of the following complex region:

|z + 4| > 3

Center: (0,0) Radius: 4

Center: (-3,0) Radius: 2

Center: (-4,0) Radius: 3

Center: (-5,0) Radius: 5

Draw the following complex region:

Im(z) < 2

y > 2

Area above line y = 2

x < 2

Area below line x = 2

y < 2

Area below line y = 2

x > 2

Area above line y = 2

Find the dot/scalar product between:

[1, 2, 1] and [3, 6, 8]

Find the unit vector of:

[2, 1, 3]

[0.5, 0.5, 0.5]

$\left[\frac{2}{14},\frac{1}{14},\frac{4}{14}\right]$

[0, 1, 0]

$\left[\frac{2}{\sqrt{14}},\frac{1}{\sqrt{14}},\frac{4}{\sqrt{14}}\right]$

Find the cross product between:

[0, 1, 1] and [2, 1, 0]

[-1, 2, -2]

[1, 0, 2]

[1, 2, -2]

[1, 2, 2]

Find the angle between:

[3, 1, 2] and [-2, 2, 2]

180 degrees

45 degrees

90 degrees

60 degrees

10.

What does the cross product of two vectors actually represent?

A vector that lies in the same plane as the two vectors.

A scalar value representing the length of the vectors.

A vector perpendicular to the plane of the two vectors, with magnitude equal to the area of the parallelogram they form.

The sum of the two vectors represented as a single vector.

11.

Find the vector projection of a on b

a = [1, 3] and b = -2i + 2j

[1, -1]

[0, 0]

[2, 6]

[-1, 1]

12.

Find 3A if:

A = [2 3 -6]

[0, 0, 0]

[1, 2, -3]

[4, 6, -12]

[6, 9, -18]

13.

Find the transpose of the following matrix:

[2 4 6

3 2 5

9 1 8]

[[2, 3, 9],

[4, 2, 1],

[6, 5, 8]]

[[6, 5, 8],

[2, 3, 9],

[4, 2, 1]]

[[2, 4, 6],

[3, 2, 5],

[9, 1, 8]]

[[4, 3, 1],

[2, 6, 5],

[9, 8, 2]]

14.

Find the inverse of the following matrix:

-1 2

-1 4

[1, -0.5],

[2, -1]

[-1, 0],

[2, 1]

[[-2, 1],

[0.5, -0.5]]

[0, 2],

[-1, 1]

15.

Find vector in the same direction as c but with a length of 4 units.

𝒄 = [2, −2, 1]

$\left[\frac{8}{3},-\frac{8}{3},\frac{4}{3}\right]$

[4, -4, 2]

$\left[\frac{8}{3},\frac{8}{3},\frac{4}{3}\right]$

[8, -8, 4]

16.

Multiply the following matrices:

[2 1 [4 6

3 5] and 2 3]

[[6, 9],

[14, 18]]

[[8, 12],

[20, 24]]

[[10, 15],

[26, 33]]

[[12, 18],

[30, 36]]

17.

Find the determinant of the following matrix:

[3 4

6 8]

-1

18.

What does it mean when the determinant of a matrix is 0?

The matrix has a unique solution.

The matrix is orthogonal and has an inverse.

The matrix is diagonal and has a determinant of 1.

The matrix is singular and does not have an inverse.

19.

How many solutions does the following system of linear equations have?

[1 0 2| 1

0 2 3| 2

0 0 0| 0]

Two solutions

Exactly one solution

No solutions

Infinitely many solutions

20.

If a matrix A is 6 × 4 and the product AB is 6 × 8, what is the order (dimensions) of B?

8 × 6

4 × 8

4 × 6

6 × 4

21.

Find C² if C=

[1 2

-2 1]

[[2, 5],

[3, 4]]

[[0, 1],

[1, 0]]

[[1, 2],

[2, 1]]

[[-3, 4],

[-4, -3]]

22.

Consider the following systems of equations,

3x₁ + x₂ = 11

−2x₁ + 3x₂ = −22

Using Cramer’s Rule determine the value of x₁

23.

Find the magnitude of the following vector in R⁶

[-2, 3, 0, -5, -7, 7]

$3\sqrt{34}$

$2\sqrt{34}$

$\sqrt{34}$

$-2\sqrt{34}$

24.

Given the plane, (𝑥 + 2) + 4(𝑦 − 2) − 2𝑧 = 0

Does the point (2, 1, 0) lie on the plane?

Yes

25.

Find the vector equation of the line passing through the points (−4,0,2) and (−1,3,5)

r(t) = (-4, 0, 2) + t(2, 2, 2)

r(t) = (-1, 3, 5) + t(3, 0, 3)

r(t) = (-4, 0, 2) + t(1, 1, 1)

r(t) = (-4, 0, 2) + t(3, 3, 3)

26.

Are the following pair of lines parallel, perpendicular or skew?

−8x − 6y + 2z = 1

z = 4x + 3y

Perpindicular

Parallel

Intersecting

Skew

27.

Find the angle between the two planes:

x + y + z = 0 and x + 2y + 3z = 1

22.21 degrees

-22.21 degrees

157.79 degrees

-157.79 degrees

100 %

MATH1015 Revision Session

Total questions: 27

Worksheet time: 14mins

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