IB Math HL Final Review Part 1

Differential Equations

100

The integrating factor m=e^{integral (p(x))dx} is the key to solving these differential equations.

What are first order linear?

200

It is the test to determine whether an Euler's Method approximation is above or below the actual value.

What is the second derivative test?

300

The function that is the solution to this differential equation: p^' = kp(m-p)

What is a logistics function?

400

Is a line that joins neighboring points with the same gradient, much like contour lines on a map joins neighboring points with the same heights.

What is an isocline?

500

It is the key step from differential calculus used in simplifying one side of a first order linear differential equation into: the integrating factor x the function or m(x) y(x).

What is the product rule?

Pre-Calculus

100

This is the resulting transformation of f(-x).

What is horizontal reflection?

200

These are the three different scenarios involving discriminant and roots.

What are: 1) b2 - 4ac < 0 - 0 roots 2) b2 - 4ac = 0 - 1 root 3) b2 - 4ac > 0 - 2 roots

300

a₁(1-rⁿ )/(1 - r)

What sum of a finite geometric series?

400

Solve for x:  

2 - log₃ (x+7) = log_1/3 (2x)

What is 7/17?

500

Given that tan (A+B) = (tan A + tan B)/(1- tanAtanB) and tan(1/5) + tan(1/8)= tan (1/p).  Find p.

What is 3?

Complex Numbers

100

The magnitude of a complex number.

What is the modulus?

200

Daily Double

What are powers of i

300

(rcisx)ⁿ = rⁿ (cos nx + i sin nx)

What is De Moivre's Theorem?

400

The process where you multiply the radii and add the angles of complex numbers.

What is multiplying complex numbers in polar form?

500

Given that z= cos x + i sin x.  Find 

Re ( z - 1)/(z + 1)

What is 0?

Vectors Basic

100

This happens when two vectors are perpendicular.

When is the scalar product (dot product) equal to zero?

200

(a*b)/(|a||b|)

What is the cosine of theta?

300

To find this in vectors, you multiply the ones that match and add all of those products together.

What is the dot product? (scalar product)

400

i, j and k hat are special versions of this family of vectors.

What are unit vectors?

500

The method of using a determinant to find the volume of a tetrahedrom formed by points A(1,-1,1) B(1,1,0) C(-1,1,-1) and D(1,1,1)

What is the triple scalar product divided by 2..

Statistics & Probability

100

When this happens, the denominators on a tree diagram decrease from left to right.

What is "without replacement?"

200

If 1 is the 0th row, this is the 4th row of Pascal's triangle.

What is 1, 4, 6, 4, 1?

300

This tool measures the average of the squared deviations of each data value from the mean.

What is the Variance?

400

View Image in Doc.

What are Mutually Exclusive Events?

500

Two events A and B are such that P(A and B) = 0.7 and P(A|B')=0.6

Find P(B) = 

What is 1/4?