Functions & Relations
Quadratics
Polynomials/
Binomial Theorem
Binomial Theorem
Sequences & Series/Binomial Theorem
Math SL
100
What is a relation?
An association between a set of inputs and outputs.
100
What is the product of the solutions to the following equation:
x2 - 9
x= -3, 3
100
What is the definition of a polynomial
An expression of the following form where a is a constant, n is a non-negative integer (whole number), and x is a variable:
100
Write down the formula for the following sequence:
2x2 + 4x4 + 16x8 ...
(2x2)(n-1)
100
A triangle has a side that is 3cm and a side that is √(2)cm Find the missing side
x = 3.61
200
What makes a function different than any other relation?
A function is a relation in which every input maps to one and only one output.
200
What is the sum squared of the solutions to the following equation:
x2 -3x + 4
x2 -3x + 4
(x-4)(x+1)
x= -1, 4
4 -1 = 3
32 = 9
200
What do the remainder and factor theorems state?
When f(x) is divided by some divisor (x-a), f(a) is equal to the remainder.
When f(a) =0, the remainder =0, therefore f(x) is divisible by (x-a), (x-a) is a factor of f(x).
200
Find the Sum of the first 27 terms of the Arithmetic Series... (100 + 94 + 88 + ...)
S27 = 594
200
A triangle has a side 2x and a side 6, find the missing side.
x = 2√(3)
300
What does an inverse function do?
It maps the range back to the domain. It reverses the function.
300
Solve the following inequality:
(x2 + 14x + 22) > 5x + 2
x2 + 14x - 5x + 22 - 2 > 0
x2 + 9x + 20 > 0
(x+5)(x+4)
x < -5 OR x > -4
300
Expand ((x/3) + 13)4 fully for the term independent of x.
28,561
300
Find the number of terms in the series
(120 + 116 + 112 + ... + 28)
n = 24
300
A (√(2), 0)
B (-√(2), 0)
C (0, -√(5))
Determine whether the triangle is equilateral, Isosceles, or scalene
Equilateral Triangle
400
What is the domain and range of the following function:
1 / √(x^2-1) = f(x)
Domain:
x is a member of all real values
x= -1 U (1,infinity)
Range:
The set of all real values
(0,infinity)
400
Find the values of 𝑘 for which the line 𝑦 + 2𝑥 = 𝑘 is tangent to the curve 𝑦 = 𝑥2 + 3
k = 2
400
Expand (x + 6)6 fully.
x6 + 36x5 + 540x4 + 4320x3 + 19440x2 + 46656x + 46656
400
(DAILY DOUBLE) A geometric series has the third term 1.2, and eighth term 291.6, find the common ratio and the value of S10
r = 3
S10 = 59048/15
400
What is the meaning of { n | n ≤ 3 or n > 6 }
n therefore n is less than or equal 3 or greater than 6
500
How, using composite functions, does on prove that 2 functions are each other's inverses?
By proving that their composite is equal to x.
x --> f(x)
f(x) --> x
500
Find the range of values of c for which the line 𝑦 = 𝑐𝑥 + 5 does not intersect the curve 2𝑥2 = 𝑥𝑦 + 3
c > 49/12
500
Expand (x + 1)((x/2) + 6)2 find the term for x3
1/4
500
In a geometric series, the sum of the first four terms is 10 times the sum of the first two terms. If r > 1, find the common ratio.
r = 3