Algebra Questions

X v ix Q Y 0 V yzo If u and v are in V is u v in V Why Find a specific vector u in V and a specific scalar c such that cu is not in V If u and v are in V is u v in V OA The vector u v may or may not be in V depending on the values of x and y OB The vector u v must be in V because V is a subset of the vector space R OC The vector u v must be in V because the x coordinate of u v is the sum of two negative numbers which must also be negative and the y coordinate of u v is the sum of nonnegative numbers which must also be nonn OD The vector u v is never in V because the entries of the vectors in V are scalars and not sums of scalars Find a specific vector u in V and a specific scalar c such that cu is not in V Choose the correct answer below 2 A U B u c u 2 2 D u 2 2 2 c 4 0 1 C c 1 c 4

A box of washing powder is 12 cm tall and contains 750 g of washing powder A similar box is 18 cm tall How much washing powder does it contain

There are two similar cylindrical drink cans The larger can is 15 cm high and contains 350 mL of drink If the smaller can is 9 cm high how much drink does it contain

46 A garden s length is 7 times its width It takes 66 meters of fence to enclose the garden Which equation best represents the perimeter of the garden in one variable 66 14w 66 2 7w 2w 66 21 2w EN English United States

48 The property demonstrated in the equation 10 9 1 10 9 10 1 is O distributive O commutative O associative ONeither side of the equation is equal to the other EN English United States

37 Considering the inequality 5x 4y 12 the shaded area of its graph is described by Oshaded below a solid line O shaded below a dashed line Oshaded above a dashed line Oshaded above a solid line

45 If triangle ABC is similar to triangle XYZ and side AB 16 when side XY 18 what is the length of side BC when side YZ 27 O24 O 10 3 O 22 O 15 2

39 If 9x 8 18 x O x 9 O O x O x 100 9 100 9 x 10 EN English United States 81 F CO

38 Identify the property demonstrated in the following equation 10 7 11 10 11 7 O Distributive Property 8 O Commutative Property O None Associative Property

35 The reciprocal ofis O 2 1000 O 0 10 10 there is none

29 Identify the solution of the inequality 2x 3 6 7 Ox 5 Ox 8 or x 5 Ox 8 O 8 x 5 2

32 Solve for a 6 09x 8 12 4 06x O x O O 30 O 45 x 1 10 x

31 Simplify 10 a 9 7a 25 266 b 12 4 O62a 236 15 54a 756 15 7a 756 6 E

27 Solve the linear system of equations using the substitution method y x 5 7x 2y 15 This question is weighted four times as heavily as the other questions In or partial credit for this question use the space provided to justify your an x 7 y 12 A x 3 y 18 l x 5 y 10 Ox 4 y 1

25 Solve the linear system of equations using the elimination or addition multiplication method 6x 2y 6 5x 5y 5 O 3 y 12 O 4 y 3 Ox 3 y 6 Ox 2 y 3

23 Find the length of the diagonal of a rectangle whose dimensions are 17m by 13m Approximate to the nearest hundredth O22 2926 O22 29 O21 4009 21 40 EN English United States

22 Solve for x 0 23x 4 2 0 55x 7 2 O O O 356 25 O 3 56 O 35 63 X

18 How many ml of 50 percent acid should be added to pure acid to make 40 ml of 90 percent acid O2 4 ml 8 8 ml 3 2 ml 8 ml X 4

21 Simplify completely 11 2 5 32 2 8 35 2 O 35 2 58 2 X O 58 2

19 The speed of a spaceship in orbit is about 11400 miles per hour How many feet per second does the spaceship travel 130 feet per second O7773 feet per second 16720 feet per second O 1003200 feet per second C

20 Solve the linear system of equations using the graphing method y 7x 12 y 3x 8 x 1 y 5 x 3 y 17 x 2 y 2 x 5 y 22 4

15 Solve for a 0 30 7a12a 4 O 0 74 O 0 19 0 86 0 23 12

17 Find y when x 53 if y varies inversely as x and y 108 when x 17 30 2 O 39 9 34 64 36 51 4

16 Given the formula M u5 solve for u Ou 54 Ou 2 M 5 u M 5 5 2M O 5 2 5M U 4

13 Two ordered pair that are solutions of the equation 3y 2x 8 are This question is weighted four times as heavily as the other questions In answer or show your work 2 4 3 5 O 1 2 2 5 1 0 3 3 5

12 Given two circles whose radii are 10 and 15 the ratio of their areas is This question is weighted four times as heavily as the other questions In or partial credit for this question use the space provided to justify your ans O4 to 6 O4 to 9 2 to 3 l

9 Solve for b Abh This question is weighte or partial credit for this qu O O C A Ah 2A A

5 Given two circles O and P with radii 7 in and 12 in respectively the ratio of the areas is Oin 12 O in 4 49 144 both of these choices are equivalent

6 Use properties of exponents to simplify and then write the answer in radical form 81 4 x y O 1 81zy O 3xy6 O 3 xy C 8 81 ru6 4

1 Greg is going into business selling homemade blankets The supplies for each blanket cost him 3 00 and he wants to earn at least 17 00 for each blanket to compensate for his time If P 17n3n represents Greg s profit as a function of the number of blankets sold what is the domain of the function O all positive real numbers O all positive integers O all rational numbers

2 Solve the linear systems of equations using the elimination or addition multiplication method 11x 11y 66 14x 7y 0 O x 3 y 5 x 3 y 7 x 2 y 5 x 2 y 4

Write the sentence as an equation in two variables Then graph the equation he y value is five more than three times the x value DA y 3x 5 G OB y 3x 5 GITS O C y 3x 5 Q O D y 3x 5

notation x 110 x OA 0 10 U 11 00 0 OC 10 11 12 2 4 6 4 0 8 10 4 8 12 12 OB 00 11 U 10 00 12 OD 11 10 12 8 4 4 8 8 12 12

mic expressions without using a calculator 1 2 1 2 S X Inx Iny 1 2 lnx IN In y ression as mu P

e figure shows the graphs of the cost and revenue functions for a company that manufactures and sell hat is the profit when 974 binoculars are produced 3500 2500 1500 500 R x 3x Break even Point 750 2250 A 2 396 B 5 396 C 3 448 D 448 C x 1500 x 200 400 500 000 Binoculars Produced and Sold GELE

Find the vertical asymptotes if any of the graph of the rational function x 4 x 16 h x OA x 4 x 4 OB X 4 OC x 4

A B C D 56 22 5 To 2 13 13 To 2

Darren purchased 250 000 in 364 day T bills 315 days before maturity to yield 2 86 After holding it for 120 days Darren sold the T bill for a yield of 3 25 a How much did Darren pay for the T bills b For how much did Darren sell the T bills c What rate of return per annum did Darren realize on the investment

15 The marginal revenue per unit is MR 0 6x 12 dollars The total revenue from the sale of 80 units is a 2880 b 2100 c 1800 d 1230

With the data provided in the following table it is requested a Calculate the marginal product b Calculate the average product c In a graph plane total product marginal product and average product d Interpret each of the terms graphed e Based on the results explain the theory and function of production Marginal Product Work units 0 1 2 3 4 5 Total product 0 2 000 3 000 3 500 3 800 3 900 Average Product

Solve the problem below You must solve each part completely and correctly and show all your work to get the indicated points for that part Let T R R be the linear transformation given by T X1 X2 X3 x1 x2 X2 X3 X3 a Find the standard matrix of T 2 points b Show that this matrix is invertible and find its inverse 1 point c Explain why T is an invertible linear transformation and find the standard matrix of T 1 point d Find T x x2 X3 2 points

A survey was conducted to determine who was the best bad guy in the Star Wars franchise Darth Vader Emperor Palpatine of General Grievous The rankings are shown in the preference table below Use pairwise comparison to determine who was the best bad guy among the three candidates Rankings 1st 2nd 3rd Total Votes O General Grievous Emperor Palpatine Darth Vader Vader Palpatine Grievous 206 Palpatine Grievous Vader 415 Grievous Vader Palpatine 124

a Find the binomial expansion of 1 3 x in ascending powers of x up to and including the x term simplifying each term 4 mark 2 mark 97 97 1000 e Substitute x into the binomial expansion in part a and hence obtain an approximation 3 mar 1 100 to 97 Give your answer to 5 decimal places b Show that when x 1 100 the exact value of 1 3x is

and rises 3500 vertical feet above the surrounding plain A cable car is to be installed that will travel from a point 810 ft from the base of the mountain to the top Find the shortest length of cable needed Your answer is ft 3 pts 1 Details To estimate the height of a building two students find the angle of elevation from a point at ground level down the street from the building to the top of the building is 31 From a point that is 200 feet closer to the building the angle of elevation at ground level to the top of the building is 51 If we assume that the street is level use this information to estimate the height of the building Question 21

Write down the first four terms of the given sequence an 1 1 3m

There are 14 more sophomores than juniors in an 8 AM algebra class If there are 92 students in this class find the number of sophomores and the number OA 53 sophomores 39 juniors OB 39 sophomores 53 juniors OC 92 sophomores 78 juniors OD 106 sophomores 78 juniors SEXCES

The logistic growth function f t nearest whole number OA 382 butterflies OB 182 butterflies OC 282 butterflies OD 11 200 butterflies 800 0 15 1 15e describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat after 14 month GELER

If o 3 are acute angles such that sin a and cos 3 calculate cos a 3 If your answer is a fraction type it using the symbol For example if the answer is write 3pi 2

Vrite the given sentences as a system of inequalities in two variables Then gr ne system The sum of the x variable and the y variable is no more than 5 The y variable ess than the difference between the square of the x variable and 2 Complete the system of inequalities in two variables first sentence 18 second sentence Type inequalities Simplify your answer

5 Consider the sequence an defined by the recursion for n 3 4 5 an an 1 1 4 An 2 a Calculate h such that an h 1 fulfills the recursive definition 1 b What is the limit of the sequence an if it exists