Area Questions and Answers

An engineer is designing a parabolic reflector The area of aperture A is equivalent to times the square of the diameter D If the engineer wants the area of aperture to be at least 15 square feet which of the following inequalities could be used to determine the diameter OA 15 D 4 OB 15 VD O C 15 OD 15 TD

Scientists are examining a substance that has a half life of 10 years The table represents the amount in grams of the substance after x half life cycles X g x 2 750 3 375 4 187 5 5 93 75 6 46 875 What is the average rate of change over the interval 4 6 Round to the nearest hundredth if necessary A 140 62 grams per half life cycle B 70 31 grams per half life cycle C 35 16 grams per half life cycle D 23 44 grams per half life cycle

D 45 24 E What is the area of the shaded sector O 24T O 45T O 72 O 576

Indicate which property is illustrated in Step 3 A commutative B distributive C associative D arithmetic fact Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 5x 1 12x 4 5x 1 12x 4 5x 1 12x 4 5x 12x 1 4 5x 12x 1 4 5 12 x 1 4 17x 5

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet The yard has 3 sprinkler heads that each cover a circular area with no overlap What is the approximate total area that will be watered O 1963 5 ft O 1963 5 ft O 5890 5 ft O 5890 5 ft

25 A plane is steering at S83 E at an air speed of 550km h The wind is from N70 E at 85km h Find the ground velocity of the plane to 1 decimal and include a proper diagram 5 Marks

In the following figure the smaller triangle is the image of the larger triangle under a dilation centered at point O Find the scale factor and the length of x and y as pictured scale factor Tyne an integer or a simplified fraction Z 18 The numbers and letters represent the leng the sides of the triangles

10 One card is randomly drawn from a deck of 52 cards What is the probability of getting a Jack or a King 3 pts

Determine if the following scenarios are mutually exclusive or overlapping Explain your reasoning 2 pts each 7 You are taking a multiple choice test Event A is you choose the correct answer Event B is you choose D as the answer 8 You survey students in your school about what grade they are Event A is the person is a senior Event B is the person is a junior

4 Explain the difference between experimental and theoretical probability Give an example of each 4 pts

O is the center of the regular dodecagon below Find its perimeter Round to the nearest tenth if necessary 20 0

Write an equation for the translation of y 26 x 0 and y 4 27 x 2 and y 3 TEM 29 Construction The weight Pin pounds that a beam can safely carry is inversely that has the given asymptotes See 28 x 4 and y 8 See

3 7A The image shows a quadrilateral inscribed in a circle Select ALL true statements a The arc from B to D passing through C measures 70 degrees b The arc from A to C passing through D measures 200 degrees c Angle BCD measures 140 degrees d The sum of the measures of the arcs from A to C one passing through B and the other passing through D is 360 degrees e Angle CDA measures 80 degrees f Angle CDA measures 100 degrees A D 70 100 B C

Find the area of the shaded sector Round your answer to the nearest tenth 10cm 90 10cm 8

n circle O the length of radius OL is 6 cm and the length of arc LM is 6 3 cm The measure of angle MON is 75 6 cm 75 6 3 cm N M Rounded to the nearest tenth of a centimeter what is the length of arc LMN O 7 9 cm O 10 2 cm 12 6 cm O 14 2 cm

An arc on a circle measures 250 Within which range is the radian measure of the central angle OO to I radians Oto radians Oto 3 radians 2 O 3T to 2 radians 2

In circle U below VT 90 inches N T 104 U V What is the length of arc ZV inches

3 State each of the following for the equation y 3 sin 2x zt Amplitude Midline Phase Shift Five key points in one period

Can you develop a strategy to establish the area formula of a circle

4 Jack is planting a triangular rose garden The lengths of the sides of the plot are 6 feet 7 5 feet and 10 feet Find the area of the garden to the nearest tenth of a square foot out

What is the surface area of this rectangula pyramid 4 mm 7 mm 4 mm

5 Write an equation and solve to find the volume of the cylinder T3X2 18 r 3 cm h 2 cm

The image shows a circle with center 4 6 and radius 10 units Select all points that lie on the circle Select all that apply 4 12 6 6 4 6 13 10 4 16 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 6 5 4 3 2 O 2 5 6 T 4 6 1 2 3 4 5 6 7 8 9 101112131415161

The areas of two similar octagons are 112 in 2 and 63 in 2 What is the ratio larger to smaller of their perime Input answer as larger smaller

18 A month of the year and number from 1 40 is chosen at random What is the probability that the month begins with the letter A and the number is a perfect square 19 A coin is tossed four times What is the probability of getting tails each time

35 A bag contains three different colored marbles red blue and green Of these some are solid and some are striped If one of the marbles is chosen at random find each probability Red Blue Green Striped 6 15 12 Solid 10 8 9 a P green b P solid or blue c P striped green d P not blue solid

21 A card is chosen from a standard deck not replaced then another is chosen What is the probability that both cards are spades 22 A letter from the word BOOKKEEPER is chosen at random not replaced then another letter is chosen What is the probability of choosing a K then an E

Use for questions 11 and 12 Of the 125 students enrolled at a dance studio 96 take ballet and 50 take jazz Of those that take ballet 28 also take jazz 11 Draw a Venn diagram to represent this information Ballet Jazz 96 28 50 125 13 If a point is placed at random on AE 12 If a dance student is chosen at random find each probability Give each answer as a fraction in simplest form a P ballet or jazz b P ballet but not jazz c P neither ballet nor jazz 14 A shuttle bus arrives at a hotel every 40 146 96 49

For questions 7 10 give each answer as a fraction simplest form decimal and percent 7 If a letter in the word MATHEMATICIAN is chosen at random what is the probability of choosing a vowel 9 If a card is selected at random from a standard deck what is the probability that it is a face card or an 8 8 A number from 1 30 is chosen at random What is the probability that the number is a two digit number and prime 10 If a card is selected at random from a standard deck what is the probability that it is an ace or a red card

ndow elf Custom drapes are being fitted for a large circular window It is difficult to get these measurements but the window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame If the brace is extended upward it would go through the center of the shelf and the circle What is the diameter of the window Diameter feet

When a population grows past the ecosystem s carrying capacity what happens to the population OA The population starts to die off to return to carrying capacity OB Continues to grow OC The population grows then finds a new carrying capacity OD The population will go extinct due to lack of resources

Find the lateral and total surface area for the figure round to the nearest tenth if necessary 23 4 LA SA

number Area of smaller parallelogram 6 ft 4 The area of the larger parallelogram is Round to the nearest whole number as needed 00 2 ft 6 ft

The figure below is a square Find the length of side a to the nearest tenth V10

D 50 A 58 B E C What is the measure of angle AOC O 42 66 O 79

70 S R What is the measure of arc QSR

Use the information given in the diagram to prove that m Z JGI b a where a and b represent the degree measures of arcs FH and Jl G F a H J Angles JHI and GJH are inscribed angles We have that mZJHI band mZGJH a by the 2 Angle Because the JHI is an exterior angle of triangle measure of an exterior angle is equal to the sum of the measures of the remote interior angles mZJHI m JGI mZGJH By the 1 16 mZJGI a Using the subtraction property mZJGI b a Therefore m JGI b a by the distributive property

Which of these pairs of events are independent You remove a blue glove from a drawer without looking and do not replace it then remove another blue glove without looking You reach into a basket and draw a name for a prize return the name into the basket and then draw a second time for another prize Your CD player has a random mode that chooses songs randomly and plays each song once before repeating While listening to the CD player in random mode you hear track 5 first and then hear track 3 second You choose a member of the basketball team to be the center You choose a different member to be a forward None of the other answers are correct

Which of these pairs of events are dependent You flip a coin and get tails You flip it a second time and get heads You pull your friend s name out of a hat that holds 20 different names replace the name then draw out your friend s name again You spin a spinner divided into five equal parts and is numbered 1 5 You get a 3 on the first spin and then spin again and get a 2 on the second spin You remove a black sock from a drawer without looking and without replacing it then remove another black sock without looking None of the other answers are correct

At a school carnival one of the booths has 12 plastic ducks floating in a tub of water Each duck has either a zero one or two printed on the bottom indicating the number of prize tickets you receive if you select that duck Six of the ducks have a zero on the bottom three of them have a one printed on the bottom and three of them have a two printed on the bottom If you randomly select a duck and then randomly select another duck without returning the first to the tub what is the probability that you will receive four prize tickets O 1 16 22 0

Suppose that the origin on a computer screen is in the lower left corner of the screen A target moves along a straight line at a constant speed from po 670 460 to point B 470 320 in 2 sec Part 1 of 2 a Write parametric equations to represent the target s path as a function of the time in sec after the target leaves its initial position The parametric equations are x 670 1001 and y 460 70t for 0 t 2 Part 1 2 Part 2 of 2 b Where is the target located 1 4 sec after motion starts The location of the target 1 4 sec after motion starts is

Find the area of the figure Sides meet at right angles 6 m 2 m 3 m 3 m 2 m 3 m 6 m m

Find the area of the figure 15 cm 15 cm 11 17 cm 8 cm

6 10 06 Review In circle K above the area of sector JKL 94 etermine m JKL to the nearest tenth of a degree A 94 in K O

78 Name 2 At Pizza Pie Heaven a large pizza has a 16 in diameter and is cut into 8 equal slices Per What is the approximate length of the arc formed by the crust of one slice Be sure to show your work

2 What is the approximate length of the red arc Round your answer to the tenth place Type your answer U 4 1 point What is the area of the shaded section round you answer to the nearest centimeter 140 110 S 5 cm R T

NAME Perimeter Problems page 2 of 2 3 Jacob and his dad are going to make a rabbit pen in the backyard They have 16 feet of fencing Help Jacob draw some plans Sketch and label at least 4 different rectangles with a perimeter of 16 centimeters on the centimeter grid paper below Write an equation under each sketch to show that the perimeter is actually 16 centimeters Put a star beside the sketch you think would be best for a rabbit pen 20 Op H

A bag contains eight red marbles and four blue marbles You randomly pick a marble and then pick a second marble without returning the marbles to the bag The first marble is red and the second marble is blue Determine if this scenario involves independent or dependent events O Independent Events

Inscribed angle theorem The measure of an inscribed angle is measure of its intercepted arc The Case 1 is one side of the angle Case 2 The center of the circle lies the angle The Case 3 the the circle lies within the angle of

19 A plaza is to be constructed in a city redevelopment area The shaded area shown represents the proposed plaza Determine Zy in the diagram below to the nearest hundredth degree 204 0 m 62 00 m RADIUS 1620 m