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 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
