Maths Final Exam Study Material with Solved Assignments and Essays

This study material includes solved assignments, essays, and dissertation for Algebra 1, Algebra 2, and Geometry Semester 1 and 2 Final Exam. It covers topics such as associative property of multiplication, quadratic equations and functions, conic sections, logarithms, and more. The material is available in PDF format and can be downloaded from Desklib.

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Algebra 1 Semester 1 Final Exam
1) (…, -3, -2, -1, 0, 1, 2, 3,)
2) (a× b) ×c=a× (b×c) is an associative property of multiplication
3) 4x+20-3x-6=14
4) x(5−3) y(2−6) z
= x2 z
y4
5) (x2y3)2*(x3y) 3= ( x2.2 y3.2) × (x3.3 y3
)
=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 {6 [2 ( 6−4 ) ] } ÷ 4 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= −x
5 + 8
5 (B)
Algebra 2 Semester 1 Final Exam
1) A: 14x-4
2) B. transitive axiom
3) A. x=-2

4) y= m+d
x
5) A. Always
6) 1 ≤d ←3
7) x>3
8) |x-8|≥ 4; |x| ≥ 4 +8 ≥12; Number line D
9) A. I
10) C; y=3/2x-8
11) A. −1
5
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.) DB
↔
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 n=−b ± √ b2 −4 ac
2 a
=−10 ± √102−4∗2∗−7
4 =−10 ± 44
4 ={−10+ √ 11
2 , −10−√ 11
2 }

Q4: x2+x+4=0
x=−b ± √ b2−4 ac
2 a =−1± √12−4∗1∗4
2 ={−1+i √ 15
2 , −1−i√ 15
2 }
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
2
√ ( z+ 8 ) 2=√ 20
Z+8= ± √ 20; z=± √20−8={−8+ 2 √5 ,−8−2 √5 }
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)log b ( q2 + y3 ): C
(10) log 4 3
log4 x
(11) log [ 1
1000 ]=log10 0.001=−3

(12) ln e=1 since e1=e
(13) Express in terms of natural log e5 x=2
{ ln2
5 }
(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) e4 f 6
(4) v6
2

(5) 9 z8
y8
(6) x2 y +2 x y2 +6 x +4
(7) x2 y −2 x y2
(8) n2 −5 n+5
(9) 2 x7 −2 x −2
(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) 4 (c +2)(c+3)
3(c−3)( c+5)
(15) (a+b)12
16
(16) 8
15 ;implies that there are15 parts
(17) no real number; 2x+3=2, x=-1.5
(18) ∅
(19) Asymptotes of y= 1
8 x +24 −10

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) 1
5
(22) 2
(23) 2 √ 11
(24) −4 x12 y6
(25) 8 √ 2
(26) 3−2 √ 3 z
(27) 5 √ 33
3

References
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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