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) =4x^{2}-5x-3

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

4(4x^{2}-5x-3) +5=16x^{2}-20x-12+5

=16x^{2}-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:** x^{2}=10x-24

x^{2}-10x+24=0

x^{2}-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:** x^{2}=49

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

x^{2}-49=0

x^{2}-7x+7x-49=0

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

X-7=0; **x=7**

**Q3:** 2n^{2}=-10n+7

2n^{2}+10n+7=0

The quadratic formula is

= = =

**Q4:** x^{2}+x+4=0

= =

**Q5:** Completing square method

z^{2}+16z+44=0

z^{2}+16z=-44

z^{2}+ 16z+ (16*1/2)^{2}=-44+ (16*1/2)^{2}

z^{2}+8^{2}=-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)** s^{2}+3s-4=0

D=b^{2}-4ac; 9-(-4) =13; Two rational solutions

**(7)** t^{2}+8t+16=0

D=b^{2}-4ac; 64-64=0: One rational solution

**(8)** 4y^{2}=6y-7; 4y^{2}-6y+7=0

D=b^{2}-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 x^{2}+6x+4y^{2}=9; Ellipse

**(15)** Conic section represented by the equation x^{2}+6x+4y^{2}+12y=9; Circle

**(16)** Conic section represented by the equation x^{2}+6x+4y^{2}-18y=9; Circle

**(17)** Conic section represented by the equation x^{2}+6x-4y=9; Hyperbola

**(18)** Center of a circle x^{2}+y^{2}+4x-8y+10=0; (-2, 4)

**(19)** Foci of the hyperbola 16x^{2}-9y^{2}=144

(16x^{2}/144)- ( 9y^{2}/144)=1; (x^{2}/9)-( y^{2}/16)=1

a=3, b=4 and since c^{2}=a^{2}+b^{2}, 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 Mathematics*, *97*(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 D*, *97*(8), p.085018