Resources

Resources

Find Coordinate on Unit Circle

Identify the part of the circle given the equation.

\newline

11

x^{2}+(y+3)^{2}=81

\newline

\square

\newline

\square

\newline

\square

(answer in terms of pi)

Use Green's theorem to find the work done by the force

\mathbf{F}(x,y)=x(x+y)+x^{2})

in moving a particle from the origin along the

x

(5,0)

, then along the line segment to

(0,5)

, and then back to the origin along the

y

1

\newline

\newline

\newline

9

16

4

021

\newline

Use Green's theorem to find the work done by the force

\left.F(x, y)=x(x+y)+x^{2}\right)

in moving a particle from the origin along the

x-a

(5,0)

, then along the line segment to

(0,5)

, and then beac to the ongin along the

y

\newline

\square

\newline

3

\newline

1

\newline

Find the length of an arc whose central angle measures

\newline

90^\circ

that is on a circle whose diameter is

20

\newline

2\pi

\newline

4\pi

\newline

5\pi

\newline

10\pi

A\left(\frac{1}{x} , 1 \leq x \leq 5\right)

8

left endpoint rectangles. What is that sigma notation to show the sum of the areas of the rectangles.

A

passes through the points

(4,9)

(12,23)

B

passes through the points

(0,2)

(-8,-12)

. Which statement is true?

\newline

\newline

A

intersects line

B

at exactly one point.

\newline

A

does not intersect line

B

\newline

A

B

What is the image of a circle with equation

(x + 2)^2 + (y - 2)^2=1

when it is rotated through

\frac{\pi}{6}

about the origin?

\newline

(x + (\sqrt{3} + 1))^2 + (y - ( \sqrt{3} - 1))^2 = 1

\newline

(x - ( \sqrt{3} + 1))^2 + (y + (\sqrt{3} - 1))^2 = 1

\newline

(x + (\sqrt{3} - 1))^2 + (y - ( \sqrt{3} + 1))^2 = 1

\newline

(x - (\sqrt{3} - 1))^2 + (y + (\sqrt{3} + 1))^2 = 1

6

9

Find the centre of mass of the uniform triangular plate enclosed by the lines

y= \pm \frac{1}{2} x

x=4

The graph of quadratic function is shown on the grid.

\newline

Based on the graph, which statement appears to be true?

\newline

k

x

(-1,0)

\newline

k

y

10

\newline

The minimum point on the graph of

k

(3,16)

\newline

The axis of symmetry of the graph of

k

y=3

\newline

1

If the center of a circle is

(4,2)

and a point on the circle is

(12,6)

, what is the radius?

FCPS Managed Bookmarks

\newline

\newline

\newline

\newline

8

-Fitness Tracker

\newline

\newline

\newline

\newline

\newline

10

. Find the solution(s) of

3 x^{2}-20 x+12=0

. Give your answer to three decimal places. If there is more than one solution, write all the solutions on the same line, separated by commas.

\newline

x=\text { Enter your next step here }

\newline

\stackrel{+\infty}{x+}

\quad \overline{\pi \infty} \quad a^{b} \quad \frac{a}{b}

\newline

\newline

\newline

(b) A person at the top of a lighthouse,

T B

, sees two ships,

S_{1}

S_{2}

, approaching the coast as illustrated in the diagram below. The angles of depression are

12^{\circ}

20^{\circ}

respectively. The ships are

110 \mathrm{~m}

\newline

(i) Complete the diagram below by inserting the angles of depression and the distance between the ships.

\newline

1

\newline

(ii) Determine, to the nearest metre,

\newline

a) the distance,

T S_{2}

, between the top of the lighthouse and Ship

2

1

A B C

has vertices as shown. Using the formula

A=\frac{1}{2} b h

, what is the area of the triangle?

\newline

\newline

\newline

1

(0,4)

inside or autside the circle of radius \& with centre at

(-3,1)

\newline

2

. Determine y so that

(0, y)

shall be on the circle of radius

4

(-3,1)

\newline

3

. If ane end of a line whose length is

13

arits is the point

(4,8)

and the ordinate of the other end is

3

. What is its abscissa?

\checkmark 1

\newline

2

\newline

3

\newline

4

\newline

5

\newline

6

\newline

7

\newline

8

\newline

9

\newline

10

\newline

The flgure below has a point marked with a large dot.

\newline

First, translate the figure

5

\newline

Then, glve the coordinates of the marked point in the original figure and the final figure.

\newline

Point in original figure: (

\square, \square

\newline

Point in final figure:

\square

\newline

\newline

2024

McGraw Hill LLC

Consider the right triangle where

a=2

\alpha=

43^{\circ}

. Find an approximate value, rounded to

3

decimal places, of each of the following. Give the angle in degrees.

\newline

Note: Triangle may not be drawn to scale.

\newline

b=\square \text { i }

\newline

\newline

c=

\newline

\square

\newline

\beta=

\newline

\square

\circ

\newline

\newline

ABCD

is relected across the

\newline

x-axis, what are the resulting coordinates of point

\newline

A

\newline

A

\newline

(1,-3)

\newline

B

\newline

(-3,1)

\newline

C

\newline

(\beta-1)

\newline

D

\newline

(3,-1)

\newline

A

0

\newline

A

1

4

. CTRCULAR MEASURE

\newline

The diagram shows a circle with centre

A

r

C A D

B A E

are perpendicular to each other. A larger circle has centre

B

and passes through

C

D

\newline

(i) Show that the radius of the larger circle is

r \sqrt{ } 2

\newline

\newline

(ii) Find the area of the shaded region in terms of

r

\newline

6

Identify the center and radius.

(X-8)^2+y^2=12

7

A rectangular patio is represented by the vertices

(4,8),(-6,8),(-6,-5)

(4,-5)

, where each unit represents a foot.

\newline

What is the area of the patio?

\newline

24

\newline

32

\newline

48

\newline

130

: A circle is graphed on a coordinate grid with its center at

(-4,7)

. The circle will be translated

p

units to the right and

v

units down. Which rule describes the center of the new circle after this translation?

\newline

(x, y) \rightarrow(-4+p, 7+v) \quad(x, y) \rightarrow(-4+p, 7-v)

\newline

1

\newline

2

\newline

(x, y) \rightarrow(-4-p, 7-v) \quad(x, y) \rightarrow(-4-p, 7+v)

\newline

3

\newline

4

2 \mathrm{~cm}

x

-4 \leq x \leq 4

\newline

2 \mathrm{~cm}

y

\quad-4 \leq y \leq 6

\newline

y=\frac{1}{2} x+1

\newline

\begin{tabular}{|c|c|c|c|c|}

\newline

x

-4

-2

0

4

\newline

y

-1

0

1

3

\newline

\newline

Find the area of the figure. I understand that the units may be hard to enter, so l've included them for you.

\newline

What is the area of the square?

\newline

\mathrm{m}^{2}

\newline

What is the area of the

\newline

\square

\mathrm{m}^{2}

\newline

What is the area of the entire figure?

\square

\mathrm{m}^{2}

ed arc or angle measure(s).

\newline

2

11

. Find m \overparen{B C}=

\qquad

2

Circles, Surface Area, Volume

\newline

\newline

Surface Area of a Pri

\newline

The surface area

S

of an lateral faces.

\newline

S=a r

\newline

13.5 \mathrm{in}

A=\left(\begin{array}{cc}4 & 2 \\ -1 & 3\end{array}\right), B=\left(\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right)

C

\mathrm{C}=\mathrm{AB}

\operatorname{det} \mathrm{C}=\ldots

\newline

8

\newline

18

\newline

12

\newline

22

\newline

15

\vec{u} = (-10,7)

\newline

Find the direction angle of

\vec{u}

. Enter your answer as an angle in degrees between

\newline

0^{\circ}

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=\square^{\circ}

Find all angles,

0^{\circ} \leq \theta<360^{\circ}

, that satisfy the equation below, to the nearest tenth of a degree.

\newline

8 \cos ^{2} \theta+6 \cos \theta-2=-3

find the points on the parabola

2x+y^2=0

closest to the point

(-3,0)

\newline

\newline

\newline

DeltaMath Sudent Applicat

\newline

\newline

\newline

\newline

\newline

E

\overline{C D}

\overline{E A} . \overline{A B}

E

A

A C=26

E A=16

E C

. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click

\vec{u}=(-10,7)

\newline

Find the direction angle of

\vec{u}

\newline

Enter your answer as an angle in degrees between

0^{\circ}

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=

\newline

\square

1

\newline

7

2

\newline

Create a function table to sketch the graph of each line.

\newline

1

y=-2 x+3

\newline

2

y

\newline

Evaluate each function for the given value.

\newline

3

f(x)=3 x

f(3)

\newline

4

\newline

\newline

1

\newline

5

\newline

What is the surface area of the pyramid above? *Don't forget your units. Ex:

\mathrm{cm}

\mathrm{cm}^{\wedge} 2

\newline

\square

\newline

\newline

100 \%

\newline

07

13

\newline

\newline

If a cubic centimetre is enlarged by a scale factor of

3

, what is the new volume?

\mathrm{cm}^{3}

\newline

\frac{d y}{d x}+y x=-x^{3}

2

\newline

\qquad

130

\newline

1

\newline

6

\newline

\begin{tabular}{|l|l|l|l|l|}

\newline

\hline Polynomlal & Coefficients & Degree & Varlable & Constant \\

\newline

5 x^{2}-8 x+2

\newline

-6 x-7

\newline

-10 x^{2}+3 x

\newline

\newline

6

4

\newline

Here is a unit circle where

\angle Q P R

has a measure of

\frac{\pi}{12}

R \approx(0.97,0.26)

\newline

1

Q P T

\frac{11 \pi}{12}

radians. What are the approximate coordinates

Circle Geometry Assizment s

\newline

Wing cliogram to answer quastions

8

\newline

find the measure of angle

b

The diagram shows the top view of a building WXYZ. OWX and OZY are sectors of a circle with centre

O

. Find the area of the top surface of the building.

\newline

\newline

\newline

\newline

\newline

96

\newline

\newline

Two points are plotted on a coordinate plane. Point

A

(0,5)

B

(\mathbf{0},-\mathbf{5})

. What is the distance, in units, from point

A

B

\newline

P=\left(x, \frac{2}{3}\right)

lies on the unit circle shown below. What is the value of

x

in simplest form?

\newline

(Note: the figure is not drawn to scale)

Directions: Find the following arc measures.

\newline

1

\newline

\begin{array}{r} m \overparen{J L}= \\ m \widehat{J M L}= \end{array}

\newline

\qquad

\newline

m J M L=

\qquad

SERIE SUR LES ISOMETRIES DU PLAN

\newline

QUESTIONS DE COURS:

\newline

\newline

\overrightarrow{1}

un vecteur du plan,

O

un point fixe et

\theta

un nombre réel. Monirer que la composée de la translation de vecteur

\vec{U}

et de la rotation de centre

O

d

\theta

est une rotation d'angle

\theta

; puis construire son centre.

\newline

2

\vec{u}=(4,-2)

\newline

Find the direction angle of

\vec{u}

. Enter your answer as an angle in degrees between

0^{\circ}

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=\square^{\circ}

6

\newline

\newline

\bar{W}

\overline{X Y}

are chords of circle

O

that intersect at point

Z

m \overline{X W}=98^{\circ}

\mathrm{m} \angle \mathrm{VZY}=64^{\circ}

\newline

m \angle W Y

O gráfico de uma funçăo trigonométrica é mostrado ababo. Ele tem um ponto máximo em

(1,2 ; 5,5)

e uma amplitude de

3

5

\newline

Qual é a equaç̉̉o da linha média da funçăo?

Find the radius of a circle in which the central angle,

\alpha

, intercepts an arc of the given length

\newline

\alpha=60^{\circ}, \mathrm{s}=95 \text { in }

\newline

\square

\newline

(Round to the nearest hundredth as needed.)

Use Lagrange multipliers to find the points on the given surface

y^{2}=16+xz

that are closest to the origin.

\newline

(\text{smaller } y\text{-value}) \quad(x,y,z)=(\square)

(\text{larger } y\text{-value}) \quad(x,y,z)=(\square)

\newline

Jika rata-rata dari

5

7, 5, 2y, -17, 3y+2

x

y

x=

Diketahui matriks

\mathrm{A}=\left(\begin{array}{cc}-1 & 2 \\ 3 & 2\end{array}\right), \mathrm{C}=\left(\begin{array}{cc}-2 & 16 \\ -10 & 16\end{array}\right)

\mathrm{I}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)

\mathrm{A}^{2} . \mathrm{B}=\mathrm{C} . \mathrm{I}

\mathrm{B}=\ldots

\newline

\left(\begin{array}{cc}0 & -1 \\ 2 & 1\end{array}\right)

\newline

\left(\begin{array}{cc}0 & -2 \\ -1 & 1\end{array}\right)

\newline

\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right)

\newline

\left(\begin{array}{cc}0 & -2 \\ -1 & 0\end{array}\right) \quad

\left(\begin{array}{cc}0 & 2 \\ -1 & 1\end{array}\right)