50 Challenging Math Problems With Solutions Algebra 1, 2021

, 04 Jun 2021




Maths Solutions 4




Useful Formulas

Factoring Formulas

∎ + 2 =2+2+2

∎ − 2 =2−2+2

∎ 2−2 = + −

∎ 3−3 = − 2 + +2

∎ 3+3 = − 2 − +2




Quadratic Formulas

−± 2 −4
∎ If 2 + + =0 then =
2




Logarithmic Functions

∎ log = ⇒ = > 0, ≠ 1 & ≠ 0

∎ log = log − log > 0, ≠ 1, > 0 & ≠ 0

∎ log ∙ = log + log > 0, ≠ 1 & ∙ > 0

log
∎ log = > 0, ≠ 1, > 0, > 0 & ≠ 1
log

∎ ln = log ≠ 0 & = 𝑥𝑜 𝑥𝑜𝑜

∎ log = log10 ≠0

∎ log = ∙ log > 0, ≠ 1 & > 0

∎ log = log > 0, ≠ 1, > 0 & > 0



50 Math Problems With Solutions: Algebra 1

, 04 Jun 2021




Maths Solutions 5



Sequence & Series


∎ 1 = 1+1+1+1+........... =
=0

+1
∎ = 1 + 2 + 3 + 4 + ........... =
2
=0

+1 2+1
∎ 2 = 12 + 22 + 32 + 42 + . . . . . . . . . . . + 2 =
6
=0

2
+1
∎ 3 = 13 + 23 + 33 + 43 +........... + = 3

=0
2




Arithmetic Progression 𝑨

Let − First term & − common difference

∎ th term of an 𝐴, = + − 1

∎ Sum of terms of an 𝐴, = +
2

= 2+ −1
2




Geometric Progression 𝑨

Let − First term & − common ratio

∎ th term of an 𝐴, = −1

1− 1−
∎ Sum of terms of an 𝐴, =
1
∎ Sum of ∞ terms of an 𝐴, ∞ = , <1
−




50 Math Problems With Solutions: Algebra 1

, 04 Jun 2021




Maths Solutions 6



Exponential Series
1 2 3 4
∎ =1+ + + + +.........∞
1! 2! 3! 4!
2 3 4
∎ =1+ + + + + .........∞
1! 2! 3! 4!


+− 2 4 6
∎ =1+ + + +.........∞
2 2! 4! 6!
3
−− 5 7
∎ = + + + +.........∞
2 1! 3! 5! 7!

∞ ∞
1 1
∎ = = = 1, 2, 3. . . .
! −!
=0 =0

∞ 1 2 3 4
1
∎ = + + + + .........∞ = − 1
! 1! 2! 3! 4!
=1

∞ 2 3 4
1
∎ = + + +.........∞ = − 2
! 2! 3! 4!
=2


∞
1 2 3 4
∎ 1 = + + + + .........∞ = − 1
+ 1 ! 1! 2! 3! 4!
=0
∞
2 3 4
∎ 1 = + + +.........∞ = − 2
+ 2 ! 2! 3! 4!
=0


∞
1 1 1 1 + −1
∎ = + + +.........∞ =
2! 2! 4! 6! 2
=0

∞
1 1 1 1 1 − −1
∎ = + + + + .........∞ =
2−1! 1! 3! 5! 7! 2
=0




50 Math Problems With Solutions: Algebra 1