Maths

Algebra 1 Semester 1 Final Exam

1) (…, -3, -2, -1, 0, 1, 2, 3,)

2) (a ) ×c=a× (b×c) is an associative property of multiplication

3) 4x+20-3x-6=14

4)

5) (x2y3)2*(x3y) 3= ( ) × ( )

            =x4y6*x9y3=x13y9

1.256097 rounded off to the nearest thousandth is 1.256

7) 36/48 into percentage =36/48*100=75%

8) First step in evaluating  is 6-4

9) 1 oz=28.3495 g

22 oz=22*28.3495=623.69 g=624 g

10) (x-4) (x+7) =0

x-4=0; x=4 or x+7=0; x=-7

11) 3(x-2) =3x(x-2); (x-2) cancels out on both sides hence we are left with 3=3x. dividing through by 3; x=1

12) 5x+y=-23; when x is 0, y=-23 and when y=0, x=-23/5

13) Cannot be determined

14) Graph D

15) Find (f⁰g) (4) when f(x) =4x+5 and g(x) =4x2-5x-3

Evaluate (f (g)) by substituting in the value of g into f

4(4x2-5x-3) +5=16x2-20x-12+5

=16x2-20x-7

16) A

17) B

18) Graph C

19) Graph of g(x) =|x|+3 is C

20) Graph A

21) Inverse of the function -8-5x=  (B)

Algebra 2 Semester 1 Final Exam

1) A: 14x-4

2) B. transitive axiom

3) A. x=-2

4)

5) A. Always

6)

7) x>3

8) |x-8| ; |x| ; Number line D

9) A. I

10) C; y=3/2x-8

11) A.

12) Graph of the equation 5x+2.5y=20 is (A), the coefficients of x and y are 4 and 8 respectively

13) Equation of the line

x/1.5+y/-3=1; -2x+y=-3

            y=2x-3 (B)

14) Parallel Lines

15) Fundamental Theorem of Arithmetic

16) C. 6y+3+2y=5

17) A. Add the 2 equations together to eliminate y

18) B. 2x=8

19) D. (3, 1)

Geometry Semester 1 Final Exam

1.)

2.) GFC

3.) AC

4.) 6 planes

5.) Postulate

6.) b.

7.) <MRQ

8.) <PRN

9.) d. 154⁰

10.) c. congruent angles

11.) b. Perpendicular

12.) Lines l and m must be parallel

13.) a. All quadrilaterals are squares

Algebra 2 Semester 2 Final Exam

Q1: x2=10x-24

x2-10x+24=0

x2-4x-6x+24=0

x(x-4)-6(x-4) =0

x-6=0   or x-4=0

x=6                   x=4

The solution is thus (4, 6)

Q2: x2=49

In this case it problem is solved using the first identity equation

x2-49=0

x2-7x+7x-49=0

x(x-7) +7(x-7) =0

X-7=0; x=7

Q3: 2n2=-10n+7

2n2+10n+7=0

The quadratic formula is

= = =

Q4: x2+x+4=0

= =

Q5: Completing square method

z2+16z+44=0

z2+16z=-44

z2+ 16z+ (16*1/2)2=-44+ (16*1/2)2

z2+82=-44+64

Z+8= ; z= =

Q14: SAS similarity: The ratio between two sides is the same as the ratio between another two sides and the included angle angles are equal

Q15: Reflection in the line y=x since there is change in the places of the x-coordinate and y-coordinate

Q16: The length WZ is determined from the ratio of any known two sides of the two parallelograms

XW /EF =6 in/2 in=3

The length of WZ=length EH*3 (the ratio)

            =3*3 in=9 in

Q17: Inductive and deductive arguments make different claims about their conclusion: In a deductive argument, the premises are a guarantee to the truth of the conclusion while in an inductive argument; the premises are anticipated only to be very strong that should they be true then the conclusion is true

Q18: Certain

Q20: If Marie does not have soccer practice, and then it is not Tuesday

Q21: If we cannot go hiking, then there is lighting

Algebra 2 Semester 2

(6) s2+3s-4=0

D=b2-4ac; 9-(-4) =13; Two rational solutions

(7) t2+8t+16=0

D=b2-4ac; 64-64=0: One rational solution

(8) 4y2=6y-7; 4y2-6y+7=0

D=b2-4ac; 36-112=-76: Two no rational complex solutions

(9) : C

(10)

(11)

(12) =1 since

(13) Express in terms of natural log

(14) Conic section represented by the equation x2+6x+4y2=9; Ellipse

(15) Conic section represented by the equation x2+6x+4y2+12y=9; Circle

(16) Conic section represented by the equation x2+6x+4y2-18y=9; Circle

(17) Conic section represented by the equation x2+6x-4y=9; Hyperbola

(18) Center of a circle x2+y2+4x-8y+10=0; (-2, 4)

(19) Foci of the hyperbola 16x2-9y2=144

            (16x2/144)- ( 9y2/144)=1; (x2/9)-( y2/16)=1

            a=3, b=4 and since c2=a2+b2, c=5; the foci is thus (5, 0) and (-5, 0)

Algebra 2

(1) -4x+1;

(2) 14x-13

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10) x-7

(11) 10x (x+10)

(12) (x-7) (x+11)

(13) Graph B; The coefficient of f(x) =0 when x=0

(14)

(15)

(16)

(17) no real number; 2x+3=2, x=-1.5

(18)

(19) Asymptotes of

Find the point at which the expression is undefined; x=-3

Vertical asymptotes occur at the points of infinite discontinuity; x=-3; Horizontal asymptotes: y=-10

(20) Removable discontinuity at x=2

(21)

(22) 2

(23)

(24)

(25)

(26)

(27) 

References

Aziz, T.A., Pramudiani, P. and Purnomo, Y.W., 2018, January. Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views. In Journal of Physics: Conference Series (Vol. 948, No. 1, p. 012043). IOP Publishing

Jones, S.R., 2018. Prototype images in mathematics education: the case of the graphical representation of the definite integral. Educational Studies in Mathematics97(3), pp.215-234

Kodosky, J.L., Andrade, H.A., Odom, B.K., Butler, C.P., MacCleery, B.C., Nagle, J.C., Monroe, J.M. and Barp, A.M., National Instruments Corp, 2018. Graphical development and deployment of parallel floating-point math functionality on a system with heterogeneous hardware components. U.S. Patent 9,904,523

Schnetz, O., 2018. Numbers and functions in quantum field theory. Physical Review D97(8), p.085018

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