Basic Math Questions and Answers

Match the function with its features V Spe N The function has a vertical asymptote at x 0 and is increasing for x 0 The domain is R and the function is increasing for ER The function has no y intercept an x intercept at 1 0 and a point at 2 1 The range is y ER y 0 and the function is decreasing for ER 1 y 52 2 y log 3 y log x 4

When f x log x is transformed to g x 3 log x 4 which transformations do not occur Check all that apply a Reflection over the y axis b Vertical shift down 5 units c Horizontal compression by a factor of d Vertical stretch by a factor of 3 c Horizontal shift left 4 units

Determine the equation of the inverse of y log x 1 log7 b y log 7 a y Ocy 7 C y log r

Where is the vertical a x 1 b x 0 O c x 2 d x 2 asymptote of g x 3 log x 2 5

What is true about the function shown below Check all that apply 10 a The y intercept is at 0 1 b The x intercept is at 1 0 c The vertical asymptote is at x 0 d The horizontal asymptote is at y 0 e It is an exponential function of the form f x ab where 0 b 1 G K

Give a pair of alternate interior angles a pair of corresponding angles and a pair of alternate exterior angles a b 12 3 4 5 6 7 8 h a Alternate interior angles b Corresponding angles c Alternate exterior angles X and Z 0 2 and 2 and 0

A rectangular region is removed from another rectangular region to create the shaded region shown below Find the area of the shaded region Cm 4 cm 15 cm 9 cm

Questions 1 3 relate to two objects that start at x 0 at t 0 and move in one dimension independently of one another Graphs of the velocity of each object versus time are shown below Object A 2 v m mc 1 04 4 of 1 0 2 01 10 i Which object is farthest from the origin at t 2 seconds A A B B C they are in the same location at t 2 seconds D They are the same distance from the origin but in opposite directions 3 Which object is in its initial position A A B B C both A and B t sec Which object moves with constant non zero acceleration A A B B C both A and B D neither A nor B Velocity m s Object B v m ec 10 A 1 0 2 0 101 at t 2 seconds D neither A nor B 14 0 t sec Time s The graph above shows the velocity versus time for an object moving in a straight line At what time after t 0 does the object again pass through its initial position A 1 s B Between 1 and 2 s C 2 s D Be veen 2 and 3 s 5 A body moving in the positive x direction passes the origin at time t 0 Between t 0 and t 1 second the body has a constant speed of 24 meters per second At t 1 second the body is given a constant acceleration of 6 meters per second squared in the negative x direction The position x of the body at t 11 seconds is A 99m B 36m C 36 m E 99 m 6 A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v A d B 2d C 2d D 4d

A kite flying in the air has a 12 ft line attached to it Its line is pulled taut and casts an 11 ft shadow Find the height of the kite If necessary round your answer to the nearest tenth 12 11 1 2 P

Answer the questions about the polygons below Figure A Figure B Figure C Figure CO None Figure CO None Figure B O Figure CO None Figure A Figure B Which figure is a triangle Which figure is a heptagon O Figure A O Figure B Which figure is a quadrilateral O Figure A

Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression and all functions are of 8 onl 1 sec 8 sec 0 1 sec 8 sec 8

Question In APQR sin P sin Q 2 and p 15 Find the side length q H Select the correct answer below 09 1 O q 75 Oq 6 Oq 31 09 4 q 30

Give a pair of alternate exterior angles a pair of corresponding angles and a pair of alternate interior angles 18 7 3 4 1 2 S 9 h m a Alternate exterior angles b Corresponding angles c Alternate interior angles X 20 and 20 and 2 0 0 and 2

16 If a b which of the following must be true 1 a b II 2a 2b III b a A II only B I and II only C II and III only D I II and III

Find the missing side length Assume that all intersecting sides meet at right angles Be sure to include the correct unit in your answer 8 ft 13 ft 6 ft 5 ft 10 ft 00

In the figure below I m Find x 55 60

Pea plant reproduction can be simulated with coin tossing The equally likely outcomes of heads and tails are used to simulate the transfer of equally likely genes R and r from two Rr pea plants red flowered because R is dominant bu carrying both red and white genes Two coins heads representing R and tails have been tossed 50 times for the simulation Using the color interpretation hh red ht th red and tt white gives the sequence of flower colors in offspring shown below red red red white red red red red red red red red white red red red red red red red red red red white red white red red red red red white white red white white red red red red red white red red white red red white white white Use the given sequence of flower colors to approximate the probability that five successive offspring all will have red flowers

A kite flying in the air has an 11 ft line attached to it Its line is pulled taut and casts a 9 ft shadow Find the height of the kite If necessary round your answer to the nearest tenth 11 5 X S

5 5 15 feet Part I State the equation that relates arc length to central angle 2 points Part II Find the angle 0 in radians 2 points Part III Convert your answer from Part II to degrees and write it to the neare hundredth of a degree 2 points

For the following right triangle find the side length x 35 12 X

The quadrilaterals JKLM and PQRS are similar Find the length x of RS M xXx 11 3 L J 5 6 K S 5 4 x R 5 P 9 10 8 Q

In the figure below m3 111 Find mZ1 m42 and m 24 4 3 1 2 m 21 m 22 m 24 0

Are the triangles below acute obtuse or right Triangle A 55 75 Acute Obtuse O Right 50 40 Triangle B 10 Acute Obtuse Right 30 55 Triangle C Acute Obtuse Right 35 50 Triangle D Acute Obtuse Right 80 50

In the figure below m42 39 Find m41 m43 and m44 T st 3 m 41 m 23 O C m 4

Are the triangles below acute obtuse or right 35 Triangle A Acute Obtuse O Right 55 50 80 Triangle B Acute Obtuse Right 50 60 Acute Obtuse Right Triangle C 60 60 30 Acute O Obtuse Right Triangle D 110 40

ur departments of a company need to order the following amounts of the same products Memo epartment Paper Tape Binders Pens Pads 1 11 3 4 5 7 2 7 4 4 8 7 1 2 4 3 4 aper pe nders emo ads ens 4 0 4 1 e unit price in dollars of each product is given below for two suppliers Supplier A Supplier B 4 5 1 1 4 4 3 4 1 0 4 11 6 a Use matrix multiplication to get a matrix showing the comparative costs for each department for the products from the two suppliers A B Dept TIL Dept 2 Dept 3 Dept 4 b Find the total cost over all departments to buy products from each supplier From which supplier should the company make the purchase O A The total cost for supplier A is and the total cost for supplier B is should make the purchase from supplier B OB The total cost for supplier A is and the total cost for supplier B is should make the purchase from supplier A so the company so the company

A soccer goal is 12 yards wide Suppose a goalie is standing on her line in the center of her goal as a striker from the opposing team moves the ball towards her The near post angle x is formed by rays extending from the ball to the near post and the goalie Similarly the far post angle is formed by rays extending from the ball to the far post and the goalie See the figure a Determine the near post angle and the far post angle when the striker is 28 yards from the near post and 32 yards from the far post b How far is the goalie from the ball c To cover the near post the goalie moves toward the near post in order to make the near post angle and the far post angle equal How far toward her near post does the goalie need to move a Near post B Goalie Far Do

Find the perimeter of the following polygon Be sure to include the correct unit in your answer 18 in 12 in 12 in 11 in X f

5 4 3 Amplitude Period 8 7 Midline V 6 5 4 3 1 2 Based on the graph above determine the amplitude midline and period of the functia 6

Find a counter example to show that the following statement is fa real numbers x and y x y x y

nd the perimeter of the following polygon Be sure to include the correct unit in your answer 11 cm 15 cm 12 cm 11 cm 0 mm km X

Use a sketch to find the exact value of the following expression cos tan 1 3 O A Which of the following triangles can be used to find the exact value of the given expression Ay Ve r 3 X X y 2 B Ay Ve 0 r 3 x 2 y Part 1 of 2 Q O C Ay Ve 0 x 3 X y 2 Points U of 1 O D Ve x 2 X y 3 Do Q

The new dolphin tank at the city aquarium is in the shape of a rectangular prism It is 29 yd long by 12 yd wide by 5 yd deep To make the tank livable for t dolphins the aquarium workers treat the water using bags of salt The amount of water a bag of salt can treat is known in cubic feet a Find the volume of water in the tank in cubic feet Use the table of conversion facts as needed 3 ft b To make the tank livable for the dolphins a bag of salt must be added for each 19 4 ft of water The aquarium doesn t have any salt on hand and the salt can only be purchased in whole bags How many bags of salt must be purchased to treat the water bags c If each bag of salt costs 4 85 how much must the aquarium pay for salt to treat all the water in the new dolphin tank Conversion facts for length 1 foot ft 12 inches in 3 feet ft 1 yard yd 1 yard yd 36 inches in

1 Show all work neatly and in an organized manner to get full points a Find an angle less than 360 degrees co terminal with i 760 ii 5 23 b B 4000 miles 8 The distance between two cities on the Earth can be calculated using the arc length formula s r0 where r is the radius of the Earth 4000 miles and 0 is the difference in latitudes in radians Choose any two cities in the same time zone Google their latitu and calculate the distance between them Then use Google Maps or such a tool to check your answer Show your results

ind the perimeter of the following polygon Be sure to include the correct unit in your answer 7 cm 10 cm 10 cm 16 cm 17 cm 7 mm km X

Approximate the definite integrals of the following functions Given the definite integral of S e x 1 dx n 6 use Trapezoidal Rule What is the value of 2f x3 2 1234545634789 1 5678902345566

Linda built a compost bin in the shape of a rectangular prism The bin is 60 in long 48 in wide and 24 in deep After the compost cycle is complete the bin be full of potting soil that Linda can sell at a farmer s market The potting soil will be packaged in bags The amount of soil each bag can hold is known in cub feet a Find the volume of the compost bin in cubic feet Use the table of conversion facts as needed 3 ft b Linda is going to put the potting soil in bags Each bag holds 0 35 ft of the soil She is going to bag up as much soil as possible but she won t partially fill any bags How many whole bags will she fill bags c The bags will sell for 5 29 each If Linda sells all the bags how much money I will she collect Conversion facts for length 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 yard yd 36 inches in

A kitchen has a tabletop that is a rectangle 36 in long and 24 in wide Lucy is an interior designer and wants to cover the tabletop in small tiles She knows the area each bag of tiles covers but only in square centimeters a Find the area of the tabletop in square centimeters Do not round intermediate computations and round your final answer to two decimal places Use the table of conversion facts as needed 2 cm b The designer wants to cover the tabletop with tiles She doesn t have any to begin with and she can t buy partial 2 bags of tiles Each bag of tiles covers 495 cm How many whole bags of tiles does the designer need to buy to completely cover the tabletop bags c If each bag of tiles costs 4 51 how much will she need to spend on tile Write your answer to the nearest cent Conversion facts for length 2 54 centimeters cm 1 inch in 1 foot ft 30 48 centimeters cm 1 yard yd 0 91 meters m 1 mile mi 1 61 kilometers km Note that means is approximately equal For this problem treat as if it were

A farmer has farmland that is a rectangle 3 km long and 2 5 km wide He wants to completely cover the farmland in dirt He knows the area each truckload of dirt covers but only in square miles a Find the area of the farmland in square miles Do not round intermediate computations and round your final answer to two decimal places Use the table of conversion facts as needed 2 mi b The farmer wants to cover his farmland with dirt He doesn t have any to begin with and he can t buy partial truckloads of dirt Each truckload of dirt covers 0 8 mi How many whole truckloads of dirt does the farmer need to buy to completely cover his farmland truckloads c If each truckload of dirt costs 65 18 how much will he need to spend on dirt Write your answer to the nearest cent Conversion facts for length 1 inch in 1 foot ft 1 yard yd 1 mile mi 1 61 kilometers km Note that means is approximately equal t For this problem treat as if it were B 2 54 centimeters cm 30 48 centimeters cm 0 91 meters m

A kitchen has a tabletop that is a rectangle 61 cm long and 46 cm wide Jenny is an interior designer and wants to cover the tabletop in small tiles She knows the area each bag of tiles covers but only in square inches a Find the area of the tabletop in square inches Do not round intermediate computations and round your final answer to two decimal places Use the table of conversion facts as needed 2 b The designer wants to cover the tabletop with tiles She doesn t have any to begin with and she can t buy partial bags of tiles Each bag of tiles covers 65 in How many whole bags of tiles does the designer need to buy to completely cover the tabletop bags c If each bag of tiles costs 3 27 how much will she need to spend on tile Write your answer to the nearest cent Conversion facts for length 1 inch in 2 54 centimeters cm 1 foot ft 30 48 centimeters cm 0 91 meters m 1 yard yd 1 mile mi 1 61 kilometers km Note that means is approximately equal t For this problem treat as if it were

Tom s rectangular flower bed measures 121 cm long and 89 cm wide He wants to cover the flower bed in mulch He knows the area each bag of mulch covers but only in square feet a Find the area of Tom s flower bed in square feet Do not round intermediate computations and round your final answer to two decimal places Use the table of conversion facts as needed 2 ft b Tom wants to cover his flower bed with mulch He doesn t have any to begin with and he can t buy partial bags of 2 mulch Each bag of mulch covers 1 7 ft How many whole bags of mulch does Tom need to buy to completely cover his flower bed bags c If each bag of mulch costs 3 47 how much will he need to spend on mulch Write your answer to the nearest cent Conversion facts for length 1 inch in 1 foot ft 1 yard yd 0 91 meters m 1 mile mi 1 61 kilometers km Note that means is approximately equal to For this problem treat as if it were 1 2 2 54 centimeters cm 30 48 centimeters cm

The pentagons ABCDE and JKLMN are similar Find the length x of KL A 3 E 2 B 5 4 C D J 1 8 N 1 2 K 3 X L 1 8 M

2 yd deep To haul away all of the dirt from the hole a dump truck will take trips to a nearby landfill The crew knows the amount of dirt the t trip in cubic feet a Find the volume of dirt that will be hauled away in cubic feet Use the table of conversion facts as needed 3 ft b Each trip the truck can haul away 290 ft of dirt To save gas the crew wants to take as few trips as necessary to haul all of the dirt away Since all of the dirt needs to be hauled away the crew might have to take a partial load for one trip How many trips are needed to haul away all of the dirt Count each trip it makes the same even if the truck isn t full trips c If it costs 1075 for each trip that the truck makes how much will it cost to haul away all the dirt S Conversion facts for length 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 yard yd 36 inches in

A rectangular field is 350 meters long and 300 meters wide What is the area of the field in square kilometers Do not round your answer km 2 X Conversion facts for length 1000 millimeters mm 1 meter m 100 centimeters cm 1 meter m 10 decimeters dm 1 meter m 1 decameter dam 10 meters m 1 hectometer hm 100 meters m 1 kilometer km 1000 meters m

Over what interval s is the graph of the rational function decreasing 4 2 y 4 2 A E IN a x 2 2 x 1 b 2 x 4 c 2 x x4 dx1 x 4

k A reciprocal of a quadratic function has the form f x x r x s kER k0 The graph is shown as below If r 1 s 2 and the minimu value of f x is 0 8 over the interval 1 x 2 Determine the value of k rounded to one decimal place Show your work by attaching a file IN SI This graph is not to be scaled A

3 What is true about the function f x 6x 5 as XX Oa f x 0 from below Ob b f x O c f x c d f x 0 from above

Match the graph with its function 1 2 M N 0

At a factory a worker measures liquid using a beaker that has a volume of 54 7 mL Find how many cubic decimeters of water will completely fill the beaker Use the table of conversion facts as needed 3 dm Conversion facts for volume and capacity 1 cubic centimeter cm 1 milliliter mL 1 cubic decimeter dm 1 liter L 1 cubic meter m 1 kiloliter KL

A fish tank has a volume of 768 L Find how many cubic centimeters of water it would take to completely fill the fish tank Use the table of conversion facts as needed cm 3 X S Conversion facts for volume and capacit 1 milliliter mL 1 cubic centimeter cm 1 cubic decimeter dm 1 liter L 1 cubic meter m 1 kiloliter KL