Algebra Questions

Y Y 168 In a shop the price of a jacket is 168 more expensive than a T shirt If the total price of 2 T shirts and a jacket is 528 find the total price of a T shirt and a jacket 6 marks

10 A piece of wire of length 178 cm is cut into two parts The first part is bent into a square and the second part is bent into an equilateral triangle If the length of a side of the square is 6 cm longer than that of the 6 marks equilateral triangle Find the lengths of the two parts of the wire cut out

Find a subset of the vectors v 02 03 7 1 v 3 V V3 H That forms a basis for the subspace of R spanned by these vecto b Express each vector not in the basis as a linear combination of the basis vectors 5 Marks

Solve the formula H JW for the variable W w w W 1 2 OW HI

Lorene plans to make several open topped boxes in which to carry plants The boxes are mac 5 in squares from each corner The length of the original piece of cardboard is 10 in more tha dimensions of the original piece of cardboard x 10 The dimensions of the original piece of cardboard are 5 in in by 5 in in

Let S p x E P p 1 p 2 a Show that S is a subspace of P b Find a basis and the dimension of S c Find the coordinates of the vector p x 5x 15x 7 relative to the basis found part b 0 Determine whether the following statement is true or false Justify your answer with a proof or a counterexample a The planes x y 2z 5 and x y z 1 2 3 1 1 2 s 3 0 7 t are perpendicular b If A is a matrix such that A is symmetric then A is symmetric c If u v w is a basis of a vector space V then u u v w u 2v 2w is also a basis of V

R If f x ax 4 and gkx x 3x a 2f 3g 1 7 then find the vala 1 9

One factor of the function fix x 9 20x 12 is x 6 Describe how to find the x intercepts and the yintercept of the graph of fox without using technology Show your work and include all intercepts in your answer

Is x 5 a factor of f x x 4x 3x 7 Explain your reasoning

02 05 HC The functions f x x 4 2 and g x x 2 2 have been rewritten using the completing the square method Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning

03 04 HC The function f x x 7x 7x 15 has zeros located at 5 3 1 Verify the zeros of f x and explain how you verified them Describe the end behavior of the function

How does the graph of f x x 2 4 6 compare to the parent function g x x

Show all work to solve 3x 5x 2 0

POSSIBLE POINTS 2 The rectangular area of the new school courtyard is represented by the expression 25m 16 Which expression represents the length and width of the courtyard A B C D 5m 4 5m 4 5m 4 25m 4 m 4 cannot determine 4 1 2 2 Tw 4 5 N

Which of the following leading terms would make the expression a perfect square trinomial 156xy 169y A B C D 36x2 81x 25x 49x

POSSIBLE POINTS 2 Match each polynomial from the first column with a factoring technique in the second column If none of the techniques can be used to factor the polynomial choose none 49x 100y 64a 48ab 96 a 3a 2a 6 144m 25m Factor out GCF Perfect Square Trinomial Difference of Squares Factor by Grouping None 1 of E

8 There are some questions in a quiz 3 marks will be awarded for each correct answer and 2 marks will be deducted for each wrong or blank answer It is given that Karen answered all questions and she scored 40 marks in the quiz If Karen got 12 more correct answers than wrong answers find the total number of questions in the quiz 5 morka

10 AB BA EN AB BA 45 A 5 B 6 min A C 7 The right D 8 answer is E 9

Find 5 solutions to the equation y 3x 1 X 2 1 0 1 2 Y

Solve the compound inequality and give your answer in interval notation 3 10x 1 6 15x 21 AND 3x 1 3x 23

Solve the compound inequality and give your answer in interval notation 3x6 12 OR 3x 8 7

Solve and graph the compound inequality 1 x 1 5 Select the correct choice below and if necessary fill in the answer box to complete your choice O A The solution set in interval notation is O B There is no solution

Describe the shape of the data summarized in the histograms below 15 H P

35 x 2 2

3 x 2

Function A and Function B are linear functions 4 Function A Function B y 3x 3 X 9 6 2 3 3 y 1 Which statements are true Select all that apply The slope of Function A is greater than the slope of Function B The slope of Function A is less than the slope of Function B The y intercept of Function A is greater than the y intercept of Function B The y intercept of Function is log

5 The foot bottom of a ladder is placed 1 5 m from a wall The ladder makes a 70 angle with the level ground Find the length of the ladder le X 1 5 m at about 40 m from the

5 Given the points A 3 0 1 and B 2 1 0 a Find the point Con the YZ plane i e the plane spanned by j and k such the points A B and Care collinear b Find the distance between the origin and the line passing through the points A and B c Determine whether the points A and Bare on the same side of the plane 7x y z 1 6 a If u 0 1 1 and v p 4 p then find the parameter p such that the angle between vectors u and v is 3 b Show that if u and v are vectors in R such that u vand u v have the same length then u and v are orthogonal c If u v and w are vectors in R then prove the identity 6u vxw u 3w 2v

8 20 3

1 3

Solve the triangle if possible A 97 a 16 3 in b 18 7 in GEREN If possible identify the equation below that uses the law of sines to find angle B Select the correct choice below fill in the answer boxes to complete your choice Type integers or decimals A There is a solution to the triangle and angle B can be found using the equation lo 16 3 sin B B There is a solution to the triangle and angle B can be found using the equation OC There is a solution to the triangle and angle B can be found using the equation OD There is a solution to the triangle and angle B can be found using the equation E Angle B cannot be found since there are no possible solutions for this triangle sin sin 265 69 sin 16 3 10 265 69 sin sin B sin B sin B

You generally don t need a personal identification number PIN to access your bank account using the ATM O False True

2 1 Rewrite 53 without using exponents 2 3 5 2 Solve 5 x 13 4 53 V5 x 13 4 13 4 10 70 7 IDK 3 Solve x 7 3 0 16 3 x 7 3 0 8 91 4 51 1 H4 4 Let p 3 91 and q 4 5i Write each expression in the form a bi b p q a p q 3 91 4 51 MO 7 4 H c p q 91 4 57 E 12 451 J

Select all expressions that are equivalent to 16 a C 3 16 2 b 16 163 d 32

4 Let p 7 31 and q 2 9i Write each expression in the form a bi a p q b p q

3 Solve Show work a x 1 3 h

5 Explain why 3x 2 4 1 has no real solution

a Solve the equation 4x 1 6 1 Show work

X 15 x 16 3 Select one O a 15 16 b All real numbers Oc No solution O d 1 3

or the function f x x 4x 45 solve f x 20 elect one a All real numbers b 9 5 Oc No solution Od 9 5 00

Write an equation for a function that has the given characteristics The shape of y x but shifted left 7 units and up 6 units Select one x 71 6 O a y O b y x 71 6 O c y O d y x 71 6 x 7 6

For the piecewise function find g 2 x 3 for x 2 4 x for x 2 g x Select one O a g 2 2 O b g 2 5 O c g 2 1 O d g 2 6

Find a polynomial function of degree 3 with real coefficients that has the given zeros 1 2 5 Find the coefficient of the squared term f x x x 7x 10 Select one a 4 O b 6 O c 6 d 4

Given f x 2x 3 g x 5x 1 find gof x Select one O a 50x 20x 5 O b 10x 8 O c 10x 14 O d 10x 4

Find the f x 5x 3 difference quotient Select one O a 5h O b not possible O c 5 O d 5x 3 f x h f x h

Simplify 2x 5 5 s Z 3 Select one O a a 2x 0 10 215 O b 2y2515 25 O c 2z 5 25 25 O d 2x 51528

Solve for m t 3m 3w Select one O a t W O b 3t 3w O c t 9w O d t 3w 3

Find the equation for a circle whose endpoints are 5 2 and 4 1 Write the equation in standard form Select one O a O b O c O d x 2 12 R v 12 2 x x 12 2 v 1 22 10 x I 2 12 2 2 2 1 X 1 2 12 0 92 100 221 2 1 2 2 10 10

Write the interval notation for x 1 6 x 6 Select one O a 6 U 6 O b 6 U 6 O c 6 6 O d 6 6

Express the following invertible matrix A as a product of elementary matrices You can resize a matrix when appropriate by clicking and dragging the bottom right corner of the matrix A 0 2 1 2 Number of Matrices 1 Jagal