Math 4

Vectors

100

Which of the following groups are vector quantities?

A. Velocity, Displacement, Energy

B. Momentum, Acceleration, Work

C. Weight, Momentum, Displacement

D. Power, Force, Acceleration

C

200

What are 4 Examples of Vectors

Some examples of vector quantities include force, velocity, acceleration, displacement, and momentum.

300

Which of the following are vector quantities? 

i.The velocity of a frisbee

ii.The width of a crater made by an asteroid

iii.The speed of a car on the highway

iv.The displacement of a billiard ball after it is struck by the cue ball

A. i only

B. i and ii

C. ii and iii

D. i and iv

D

400

Steve is driving in his car to take care of some errands. The first errand has him driving to a location 2 km East and 6 km North of his starting location. Once he completes that errand, he drives to the second one which is 4 km East and 2 km South of the first errand. What is the magnitude of the vector that describes how far the car has traveled from its starting point, rounded to the nearest km?

A. 6 km

B. 7 km

C. 8 km 

D. 10 km

E. 14 km

B

500

A Physics teacher, Susan, drove to her high school which is located 15km East from her house. After school, she drove to her children's elementary school which is 10 km South from her high school. Then, she drove to a grocery store, located 15km West from the elementary school. Finally, she drove back to home with her kids and several grocery bags. Choose a true statement from the following:

A. The total distance she traveled from her house to elementary school is 18 km.

B. The magnitude of the displacement vector from the high school to the grocery store is 25 km.

C. The magnitude of the displacement vector for the whole trip is 50 km.

D. The magnitude of the displacement vector from her house to the grocery store is 10 km.

D

Trigonometry

100

What's the formula for a right triangle?

a^2+b^2=c^2

200

Find X

2.69

300

Find the lengths of all sides of the right triangle below if its area is 400.

2x = 40

x=20

H= 20 √(5)

400

The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle.

x = 10

 H = 10 √(2)

500

Find x and H in the pictures.

x=8.1

H=13

System of Equations

100

SOLVE

3x−y=13

3y−2x=−4

x = 5

y = 2

200

SOLVE

2x−y=−5

y=1−3x

 x = 1

 y = -2

300

Two of the following systems of equations have solution (1;3). Find them out by checking.
a) x+y=5

2x−y=7

b) 2x+y=5

x−y=2

c) 3x+y=6

4x−3y=−5

d) x−1/1=y−3

x−y=−2

e) (9x+4y)/3(−5x−11)/2=13−y

13x−7y=−8

C and E

400

SOLVE

3x+4(x−3)=3(2y−3)−3y

3y+2(x−4)=5(y+2)−28

(-4; 1)

500

Are the systems equivalent(check if solutions of the both systems are the same):
4x+5y=11

x−y=5
and
4x−5y=11

2x+y=9

No

Matrices

100

Whats order to you list a Matrix definition?

Row/Column

Column/Row

Row/Column

200

Whats the dimensions of the matrics

[2 −2 0 1 1]

[0 1 3 0 3]

[1 −1 1 0 1]

[1 1 1 1 1]

4,5

300

Solve the following system of equations, using matrix inversion method:

2x1 + 3x2 + 3x3 = 5,

x1 – 2x2 + x3 = -4,

3x1 – x2 – 2x3 = 3

The matrix form of the system is AX = B,where

So, the solution is ( x1 = 1, x2 = 2, x3 = −1)

400

So, the solution is ( x1 = 1, x2 = 2, x3 = −1)

So, the solution is (x1 = 2, x2 = - 1,  x3 = 4).

500

Solve the following system of linear equations, using matrix inversion method:

5x + 2 y = 3, 3x + 2 y = 5

The matrix form of the system is AX = B , where 

(x = −1, y = 4)

Inverses

100

find g−1(x)
g(x)=12x+7

y=(1/2)x+7

200

find h^−1(x) 

h(x)=5−9x  

y=5−9x

300

A=5√(2x+11)

Find A^-1

y=5√(2x+11)

400

 find f^−1(x)
f(x)=(4x)/(5−x)

y=(4x)/(5−x)

500

h(x)=(1+2x)/(7+x) find h−1(x)

y=(1+2x)/(7+x)