Project Maths

Paper 1

1. Algebra (Strand 4)

Multiplication and division of Polynomials(Linear, Quadratic & Cubic) Factor Theorem Solving linear equations with 2 and 3 unknowns Inequalities(Quadratic & Rational)

2. Complex Numbers(Strand 3)

Addition, multiplication, subtraction and division with complex numbers. Represent complex numbers on an Argand diagram and calculate the Modulus & Argument. Convert Complex numbers from rectangular form to polar form. Use De Moivre’s Theorem to calculate powers of complex numbers.

3. Number Patterns(Strand 2)

Arithmetic Sequences and Series Geometric Sequences and Series Financial Mathematics Proof by Induction Limits Logs and Indices

5. Calculus & Functions

Finding the period and range. If   y = asinbx+c  or  y = acosbx+c , Period = 2π/b     Range = [c-a,c+a] Recognise surjective, injective  and bijective functions and finding the inverse of a function. Graph functions of the form ax2+bx + c, abx , logarithmic, exponential and trigonometric Differentiate linear and quadratic functions from first principles Differentiate the following functions; polynomial, exponential, trigonometric, rational powers , inverse functions and logarithms Find the derivatives of sums, differences, products, quotients & compositions of functions Integrate functions of the form; xa, ax, sin ax and cos ax Determine areas of plane regions bounded by polynomial and exponential curves

Paper 2

6. Coordinate Geometry of the Line & Circle(Strand 2)

Use slopes to show that lines are parallel or perpendicular. Solve problems involving slopes of lines, the perpendicular distance from a point to a line and the angle between two lines. Divide a line segment internally in a given ratio m : n. Recognise that (x-h)2 + (y-k)2 = r2 represents the equation of a circle with centre (h, k) and radius r. Recognise that x2+y2+2gx+2fy+c = 0  represents the equation of a circle with centre (-g, -f )  and radius r = √(g2+f2-c) Solve problems involving a line and a circle.

7. Trigonometry(Strand 2)

Use trigonometry to solve problems in 2D & 3D. Solve problems involving the area of a sector and the arc length of a circle. Graph trigonometric functions sin x,cos x  and tan x. Solve trigonometric equations. Derive trigonometric formulae

8. Length, Area & Volume(Strand 3)

Investigate the nets of prisms, cylinders and cones. Solve problems involving the perimeter and area of discs, triangles, parallelograms and trapeziums. Solve problems involving surface area and volume of blocks, cylinders, cones, prism, spheres, hemispheres, and solids made from combinations of these. Use the trapezoidal rule to approximate area.

9. Probability and Statistics(Strand 1)

Finding, collecting and organising data. Representing data graphically and numerically. Draw the line of best and make predictions. Calculate the correlation coefficient using a calculator. r = 0………….…….……….None 0 < r ≤ 0.3……………….Weak 0.3 < r ≤ 0.7….….Moderate 0.7 < r < 1…………….….Strong r = 1……………….……….Perfect  · Addition Rule: P(A U B) = P(A) + P(B) − P(A n B) · Mutually Exclusive Events: P(A U B) = P(A) + P(B) · Multiplication Law: P(A n B) = P(A|B) × P(B) · Independent Events: P(A n B) = P(A) × P(B) Calculate Probabilities using the Normal Distribution tables and the Binomial Distribution. Calculate the margin of error Conduct 95% hypothesis test Make decisions based on the Empirical Rule. 68% of the data will fall within 1 standard deviation of the mean. 95% of the data will fall within 2 standard deviations of the mean. 99.7% of the data will fall within 3 standard deviations of the mean.