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Math Tutor Online(Higher Math paper 1)
Description
I will Cover the following Topics described as above:
1. Quadratics (• carry out the process of completing the square for a quadratic polynomial ax 2 + bx + c, and use this form, e.g. to locate the vertex of the graph of y = ax 2 + bx + c or to sketch the graph; • find the discriminant of a quadratic polynomial ax 2 + bx + c and use the discriminant, e.g. to determine the number of real roots of the equation ax 2 + bx + c = 0; • solve quadratic quations, and linear and quadratic inequalities, in one unknown; • solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic; • recognise and solve equations in x which are quadratic in some function of x, e.g. x 4 – 5x 2 + 4 = 0.)
2. Functions (• understand the terms function, domain, range, one-one function, inverse function and composition of functions; • identify the range of a given function in simple cases, and find the composition of two given functions; • determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases; • illustrate in graphical terms the relation between a one-one function and its inverse.)
3. Coordinate Geometry (• find the length, gradient and mid-point of a line segment, given the coordinates of the end-points; • find the equation of a straight line given sufficient information (e.g. the coordinates of two points on it, or one point on it and its gradient); • understand and use the relationships between the gradients of parallel and perpendicular lines; • interpret and use linear equations, particularly the forms y = mx + c and y – y1 = m(x – x1); • understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations (including, in simple cases, the correspondence between a line being tangent to a curve and a repeated root of an equation).)
4. Trignometry (• sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and using either degrees or radians); • use the exact values of the sine, cosine and tangent of 30°, 45°, 60°, and related angles, e.g. cos 150° = – 2 1 3 ; • use the notations sin−1 x, cos−1 x, tan−1 x to denote the principal values of the inverse trigonometric relations; • use the identities cos sin i i ≡ tan θ and sin2 θ + cos2 θ ≡ 1; • find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included).)
5. Vectors (• use standard notations for vectors, i.e. y x , xi + yj, z y x , xi + yj + zk, AB , a; • carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms; • use unit vectors, displacement vectors and position vectors; • calculate the magnitude of a vector and the scalar product of two vectors; • use the scalar product to determine the angle between two directions and to solve problems concerning perpendicularity of vectors.)
6. Series (• use the expansion of (a + b) n , where n is a positive integer (knowledge of the greatest term and properties of the coefficients are not required, but the notations r n and n! should be known); • recognise arithmetic and geometric progressions; • use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions; • use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression)
Cafetalk's cancellation policy
Before request is confirmed (fixed)
- Cancellation possible at any time without charge.
After request is confirmed (fixed)
- More than 24 hours before lesson start time.→ Cancellation is possible at any time.
- Less than 24 hours before lesson start time.→ The tutor may take a cancellation fee.
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No-Show→ The tutor may take a cancellation fee.
(Please check with the tutor for details.)
Lessons by this tutor
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Math Tutor online(Grade 1-12)
Grade 1 to 12 , ANY OF THE TOPICS LISTED BELOW : 1.Numbers 2. ALgebra60min 1,200PHas Trial
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