Basic Math Questions and Answers

x 3x y dx e ydy 0 Begin by separating the variables Choose the correct answer below O A y 1 3y OB dx C dx dy x 3x y et y x et dy y 1 3y D The equation is already separated dy et ax An implicit solution in the form F x y C is C where C is an arbitrary constant Type an expression using x and y as the variables

problem dy x y 4 y 0 9 dx The solution is Type an implicit solution Type an equation using x and y as the variables

Solve the initial value problem dy y dx X 8xe y 1 8e 7 The solution is y x

tain the general solution to the equation dy y dx x 4x 1 The general solution is y x 4x 1 ignoring lost solutions if any

Obtain the general solution to the equation dr de rtan 0 9 sec 0 The general solution is r 0 ignoring lost solutions if any

b is proportional to a bis 63 when a a b 3 63 3 11 252

8 10 points Solve for r using log10 Write your answer as a ratio of two logs both base 10 7 hx

8888 1 ATT 1 2 3 4 5 6 7 8 9 10 11 12 M A D

8888 lo 1 2 3 4 5 6 7 8 9 10 11 12 M A D

7 5 cm 9 cm 15 cm 6 cm A pie the

and the surface area of each rectangular 5 6 cm 1 8 4 cm 6 cm

A piece of cake in the shape of a triangular prism is shown below Find the surface area of the cake 3 cm 8 cm 10 cm 6 cm

Find the surface area of each triangular prism 5 in 6 in 2 5 in 6 5 in

1 point The profit a company earns is the revenue the company makes minus the expense revenue the company makes in a month is represented by the equation R x 5 000 2x while the expenses of the company for the month are represented by the equation E x 15x 1 000 Which equation represents the profit the company earns during the month P x A P x 2x 15x 4 000 B P x 2x 15x 4 000 C P x 2x 15x 4 000 D P x 2x 15x 4 000

9 What new political party formed because of the fight over slavery in the mid 1800s2 OA Republican OB Democratic OC Whig OD Green

In order to solve the equation x Sx 6 x 31 9 a student graphs the equation f x x 5x 6 and g x x 31 9 as shown 2 B HE Ax 9 and x I tank What are the approximate solutions of the equation x 5x 6 x 3 97 6 8 and x Dandx 5 2 2 and 3 ins Wy 10

A school purchases new basketballs and soccer balls The school purchases at least 20 basketballs B and at least 30 soccer balls S and spends no more than 300 The table shows the price for each type of ball Basketball Price Soccer Ball Price 4 25 5 65 Which set of inequalities represents the scenario A B 20 S 30 4 25B 5 65S 300 B B2 20 S230 4 25B 5 65S 300 C B 20 S30 4 25B 5 65S 300 D B220 S2 30 4 25B 5 65S 300

8 9 29 In the second attempt the bird hit the pile of pigs at a height of 36 inches above the ground Determine how long it took for the bird to hit the pile of pigs by factoring and using the zero product property Remember you can only use the zero product property when the equation is equal to zero

Consider the function 46 HE Which equation represents g x A g x lx 21 3 B g x x 2 3 C g x x 21 3 SM S Ped 1943 gx

atio 180 degrees over Pi radians What is the algebraic proof Do not emphasize examples but proof re Functions TO he C e Conversion between Degrees and Radians Using the basic relationship w radians 180 1 To convert degrees to radians multiply degrees by Tradians 1802

A football coach is trying to decide When a team is ahead late in the game which strategy is better Play the regular defense Play a prevent defense that guards against long gains but makes short gains easier The coach reviews the outcomes of 100 games Regular defense Prevent defense Total Win 41 32 73 Loss 9 18 27 Total 50 50 100 Compare the probability of winning when playing regular defense with the probability of winning when playing prevent defense Draw a conclusion based on your results A P win regular 0 82 P win prevent 0 64 Conclusion You are more likely to win by playing regular defense B P win regular 0 82 P win prevent 0 64 Conclusion You are more likely to win by playing prevent defense C P win regular 0 33 P win prevent 0 67 Conclusion You are more likely to win by playing prevent defense D P win regular 0 33 B P win prevent 0 67 Conclusion You are more likely to win by playing regular defense

3 Describe the difference between surface area and volume using a real world application You must make it clear that you understand the difference betwee surface area and volume For the toolbar press ALT F10 PC or ALT FN F10 Mac

A Name of shape B C 1 Plane Geometry 2 Prism 3 Cylinder 4 Oblique Prism 5 Oblique Cylinder D 1 Fill in the blanks with the vocabulary words above 6 Base 7 Base edge 8 Lateral Face 9 Lateral edge 10 Parallel Planes 11 Axis of Cylinder A B C D Name of shape D The volume of cylinder A is of cylinder B is compares to Cylinder B by A The volume Therefore Cylinder A B C A 3 Cylinder B 6 Base C 8 Lateral Face D 2 Prism E 7 Base Edge F 9 Lateral Edge

2 Match each of the volume formulas given Column A with the correct description of the geometric shapes Column B whose volume is given by that formula Column A a V Bh b V lwh c V m h d V s Match a b c and d WITH e f g and h Column B e Cylinders f All prisms and cylinders Cubes h Rectangular Prism I length of a base wwwidth of a base r radius of a base Ae 8 9

4 Angela is having a contractor pour a concrete driveway When completed the driveway will be foot 3 inches deep Based on the diagram shown what volume of concrete will be needed note the driveway is 3 squares by 1 5 squares on the diagram A 8 438 ft B 14 ft C 2 813 ft D 703 ft OA B OC 6 5 2 Driveway House 23 4587 Scale 1 unit 25 feet

8 A soda can has a radius of 3 cm and a height of 12 cm as shown Which sets of measurements for a new radius and height could be used to make a cylinder with a volume that is 8 times greater than this can of soda OO ABC OB A h 24 cm r 6 cm B h 96 cm r 24 cm C h 48 cm r 12 cm D h 12 r 8 cm 3mm

6 A section of concrete drainage pipe is shown How much concrete is needed to create this section of the pipe O A D 3 A 24543 7 cm 3 B 3927 0 cm 3 C 35342 9 cm D 8835 7 cm 50 cm 20 cm 25 cm

5 Marc wants to buy a fish tank that will fit on a bookshelf He wants to find the volume of the fish tank so he can buy the appropriate amount of fish Marc found a tank that is 3 5 feet tall and has a width twice its length Which of the following formulas gives the volume V in terms of the fish tank s length 00 A B C A V 7x 2 2 B V x 3 5x C V 2x 3 5 D V 2x

14 A sphere has a radius of 7 inches What is the volume Round to the nearest tenth 0000 H E 1436 8 in F 1578 2 in G 205 3 in H 615 8 in

The area of a rectangle is 45ft 2 and the length of the rectangle is 1ft more than double the width Find the dimensions of the rectangle

Ahmad had 8 9 acres of land He planted 4 5 of this land with corm How many acres did he plant with corn Write your answer in simplest form

7 A cylinder with a height of 10 in and a diameter of 10 in If Ted has 1000 square inches of wrapping paper and he wraps the whole cylinder how much wrapping paper will he have left Round to the nearest tenth

Find the area of the shaded region in the figure Use the button and round to the nearest tenth Use the formula A or A 0 7854d N 6

Find the total surface area of the cone Use the button and round to the nearest whole number Use T 2 r r h or the formula T rs r 4 5 ft SORTIRE DAL FEMEINESRE THETIMETIME IHRE FONTANERALISERE 4 ft

A ramp that is being constructed must be 42 inches long and reach a ledge that is 21 inches tall How far is the base of the ramp from base of the ledge A 21 in C 21 5 3 7 21 21 3 42 in 00

x 4 6 use binomial theorem to expand Simplify

3 A sequence is defined recursively by a 4 a2 5 ak 1 2ak ak 1 Find the first 5 terms

10 Find the sum of the geometric sequence that satisfies the stated conditions a 2 r 3 n 8

8 A bicycle rider coasts downhill traveling 4 feet the first second In each succeeding second the rider travels 5 feet further than the preceding second If the rider reaches the bottom of the hill in 11 seconds find the total distance traveled

6 Find the nth term the 5th term and the 10th term of the arithmetic sequence 4 9 14 19

2 Find the first 5 terms of the recursively defined infinite sequence a 10 ak 1 1 ak

Solve the initial value problem dy 4x x 3 dx x 1 y 1 Y 1 5 The solution is Type an implicit solution Type an equation using x and y as the variables

x 3x y4 dx ex y dy 0 Begin by separating the variables Choose the correct answer below OA dx OB 43 C 1 3y x 3x y ets dx ET 4 dy 8 ets o y 1 3y4 OD The equation is already separated An implicit solution in the form F x y C is C where C is an arbitrary constant Type an expression using x and y as the variables x4 e s dx

y is inversely proportional to x When x 2 y 24 X y 2 24 6 1 5483870968

to a b is proportional bis 320 when a 8 a b 8 320 15 720

n is proportional to m n is 14 when m 49 m n 49 14 144 500

y is proportional to x y is 24 when x 6 X y 6 24 8 0 40

9 q is proportional to p3 qis 250 when p 5 P 9 5 250 6 0 686

Use Goal Seek function and solve the following y 5x 2x 3x 6

2 c Refer to diagram in Figure Q4c find the radius and the circumference of the given circle AB diameter A 26 Figure Q4c C 6 B 4 Marks