TSIA2 STUDY GUIDES MATH Exam
Questions and 100% Verified with correct
answers 2025
Adding with same denominator - Answer- (a/b)+c/b)=((a+c)/b)
Subtracting with same denominator - Answer- (a/b)-(c/b)=((a-c)/b)
Adding with different denominator - Answer- (a/b)+(c/d)=((ad)+(cb))/bd
Subtracting with different denominator - Answer- (a/b)-(c/d)=((ad)-(cb))/bd
Multiplying Factors - Answer- (a/b)*(c/d)=(a*c)/(b*d)
Dividing Factors - Answer- (a/b)/(c/d)=(ad)/(bc)
Factoring numbers - Answer- a(c/d)= a+(c/d)= (ad+c)/d
Intergers - Answer- {...,−3,−2,−1,0,1,2,3,...}
Real Numbers - Answer- All numbers that are on number line. Integers plus
fractions, decimals, and irrationals
PEMDAS - Answer- Parentheses, Exponents, Multiplication, Division, Addition,
Subtraction
,Percentages - Answer- part = (percent / 100) x whole
percent of change - Answer- ((New value - old value)/old value) X 100
Distance from A to B - Answer- √(x2 − x1)^2 + (y2 − y1)^2
Parallel and Perpendicular lines - Answer- Parallel lines have equal slopes.
Perpendicular lines (i.e., those that make a 90∘90° angle where they intersect) have
negative reciprocal slopes: 𝑚1m1 .𝑚2=−1m2=−1.Parallel Lines (l ∥∥ m)
Mid-point of the segment AB - Answer- M (𝑥1+𝑥2/2),(𝑦1+𝑦2/2)
Slope of the line - Answer- (𝑦2−𝑦1)/(𝑥2-𝑥1)=𝑟𝑖𝑠𝑒/𝑟𝑢𝑛
Point-slope form - Answer- y-y1=m(x-x1), where (x1,y1) is any point on the line
and m is the slope of the line
Slope-intercept form - Answer- y=mx+b, where m is the slope and b is the y-
intercept of the line.
Factoring - Answer- "FOIL"
(𝑥+𝑎)(𝑥+𝑏)(x+a)(x+b)=
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab
"Difference of Squares"
𝑎2−𝑏2=
(𝑎+𝑏)(𝑎−𝑏)a2−b2=
, (a+b)(a−b)𝑎2+2𝑎𝑏+𝑏2=
(𝑎+𝑏)(𝑎+𝑏)a2+2ab+b2=
(a+b)(a+b)𝑎2−2𝑎𝑏+𝑏2=
(𝑎−𝑏)(𝑎−𝑏)a2−2ab+b2=
(a−b)(a−b)
"Reverse FOIL"
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab=
(𝑥+𝑎)(𝑥+𝑏)
Pythagorean Theorem: - Answer- a²+b²=c²
Area of a triangles - Answer- A=1/2bh
The angles inside a triangle add up to ? - Answer- 180 degrees
equilateral triangle - Answer- These triangles have three equal sides, and all three
angles are 60∘
Isosceles - Answer- An isosceles triangle has two equal sides. The "base" angles
(the ones opposite the two sides) are equal (see the 45∘ triangle above).
Area of a Circle - Answer- A=π𝑟2
Circumference of a Circle - Answer- C =2π𝑟
Questions and 100% Verified with correct
answers 2025
Adding with same denominator - Answer- (a/b)+c/b)=((a+c)/b)
Subtracting with same denominator - Answer- (a/b)-(c/b)=((a-c)/b)
Adding with different denominator - Answer- (a/b)+(c/d)=((ad)+(cb))/bd
Subtracting with different denominator - Answer- (a/b)-(c/d)=((ad)-(cb))/bd
Multiplying Factors - Answer- (a/b)*(c/d)=(a*c)/(b*d)
Dividing Factors - Answer- (a/b)/(c/d)=(ad)/(bc)
Factoring numbers - Answer- a(c/d)= a+(c/d)= (ad+c)/d
Intergers - Answer- {...,−3,−2,−1,0,1,2,3,...}
Real Numbers - Answer- All numbers that are on number line. Integers plus
fractions, decimals, and irrationals
PEMDAS - Answer- Parentheses, Exponents, Multiplication, Division, Addition,
Subtraction
,Percentages - Answer- part = (percent / 100) x whole
percent of change - Answer- ((New value - old value)/old value) X 100
Distance from A to B - Answer- √(x2 − x1)^2 + (y2 − y1)^2
Parallel and Perpendicular lines - Answer- Parallel lines have equal slopes.
Perpendicular lines (i.e., those that make a 90∘90° angle where they intersect) have
negative reciprocal slopes: 𝑚1m1 .𝑚2=−1m2=−1.Parallel Lines (l ∥∥ m)
Mid-point of the segment AB - Answer- M (𝑥1+𝑥2/2),(𝑦1+𝑦2/2)
Slope of the line - Answer- (𝑦2−𝑦1)/(𝑥2-𝑥1)=𝑟𝑖𝑠𝑒/𝑟𝑢𝑛
Point-slope form - Answer- y-y1=m(x-x1), where (x1,y1) is any point on the line
and m is the slope of the line
Slope-intercept form - Answer- y=mx+b, where m is the slope and b is the y-
intercept of the line.
Factoring - Answer- "FOIL"
(𝑥+𝑎)(𝑥+𝑏)(x+a)(x+b)=
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab
"Difference of Squares"
𝑎2−𝑏2=
(𝑎+𝑏)(𝑎−𝑏)a2−b2=
, (a+b)(a−b)𝑎2+2𝑎𝑏+𝑏2=
(𝑎+𝑏)(𝑎+𝑏)a2+2ab+b2=
(a+b)(a+b)𝑎2−2𝑎𝑏+𝑏2=
(𝑎−𝑏)(𝑎−𝑏)a2−2ab+b2=
(a−b)(a−b)
"Reverse FOIL"
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab=
(𝑥+𝑎)(𝑥+𝑏)
Pythagorean Theorem: - Answer- a²+b²=c²
Area of a triangles - Answer- A=1/2bh
The angles inside a triangle add up to ? - Answer- 180 degrees
equilateral triangle - Answer- These triangles have three equal sides, and all three
angles are 60∘
Isosceles - Answer- An isosceles triangle has two equal sides. The "base" angles
(the ones opposite the two sides) are equal (see the 45∘ triangle above).
Area of a Circle - Answer- A=π𝑟2
Circumference of a Circle - Answer- C =2π𝑟
