Knowledge of mathematics is the pedestal of all sciences

### Introduction

The language-mathematics can trigger mathematical trauma. Mathematical trauma can have serious consequences for students who are affected. They may reject mathematics as something they are not able to do. This can also affect their belief in themselves as been capable to solve some mathematical problems.

Lange and Meaney(2011) describe mathematical trauma as:'being deprived of opportunities for expression, interpretation and agency in relation to mathematics, and hence positioned as passive receivers of superficial mathematical knowledge amounts'. This trauma may seem easy to dismiss but, more research provides evidence that some students experience real distressing trauma while studying mathematics. With us, you will find great algebra tutoring online for your kids anytime; when they are studying or working on homework, before class or after practice. We strive to help students with quality online calculus tutoring. Struggling students find our sessions rewarding as it helps them bridge the learning gap they suffer while in the brick-and-mortar classroom.

### Key Learning Outcomes and Skills

- To help the student build a better understanding of mathematics.
- Effective ways to teach students to visualize the mathematical system through online calculus tutoring..
- How to support students to develop interest in mathematics through our algebra tutoring online.
- Algebra tutor will advocate strategies to help students deal with being stuck by themselves, so they develop personal strategies for getting 'unstuck'.
- Calculus tutor will help the student build an understanding of continuity, limit, integration and differentiation in application of calculus.
- To help the student build the use of mathematical thinking skills in problem solving.
- Algebra tutor will help students build a basic knowledge of algebraic expressions.

### Quick reference symbols and expressions

##### Useful Symbols

- = is equal to
- ≈ is approximately equal to
- ≠ is not equal to
- > is greater than
- ≡ is identical to
- ≥ is greater than or equal to
- < is less than
- n! factorial n=1x2x3x…xn
- ≤ is less than or equal to
- |k| Modulus of k, i.e size of k irrespective of sign
- ∞ infinity
- ∑ Summation

#### Useful mathematical expressions

##### Laws of Mathematics

- Trigonometrical identities
- Standard Curves

sin (A + B) = sin A cos B + cos A sin B

sin (A - B) = sin A cos B – cos A sin B

cos (A + B) = cos A cos B – sin A sin B

cos (A - B) = cos A cos B + sin A sin B

2sin A cos B = sin(A+ B) + sin(A - B)

2cos A sin B = sin(A+ B) – sin(A - B)

2cos A cos B = cos(A+ B) + cos(A - B)

2sin A sin B = cos(A - B) - cos (A + B

##### Angles having the same trigonometrical ratios:

(i) Same sine: θ and (1800 -θ)

(ii) Same cosine: θand (3600 – θ), i.e. (-θ)

(iii) Same tangent: θand (1800 + θ)

##### Association laws – for addition and multiplication

(i) a+(b+c)=(a+b)+c

(ii) a(bc)=(ab)c

##### Commutative laws-for addition and multiplication

(i) a+b=b + a

(ii) ab = ba

##### Distributive laws-for multiplication and division

(i) a(b + c) =ab + ac

(ii) (b+c)/a=b/c + c/a (provided a≠0)

##### Circle

(i) Centre at origin, radius r: x2 + y2 = r2

(ii) Parametric equations; x:rcosθ,y=rsin θ