Number & Algebra &
Functions
Functions
Consider the sequence 11, 15, 19, 23, ...
a) Find the 101st term of the sequence.
b) Find the sum of the first 101 terms.
c) Find the sum of the first 20 terms.
a) 411
b) 21311
c) 980
Let A(2,-3,5) and B(-1,1,5). Find
a) the distance between A and B.
b) the coordinates of the midpoint M of A̅B̅
a) 5
b)(½, -1,5)
A school basketball coach kept a record of the number games played (x) and the number of points scored (y) for seven basketball games.
Player || Games (x) || Points (y) ||
Ali 3 9
Mateo 4 10
Jerry 4 20
Poom 4 16
Ayo 5 20
Chen 6 29
Jimmy 10 43
Calculate the correlation coefficient and describe the correlation.
r=0.957
strong, positive, linear correlation
Find the derivative of f(x)=5x(x2-1).
f'(x)=15x2-5
What is Daniel's favorite soccer team?
Millonarios
Let f(x)=(3x-6)/(x+2).
Write down the equations of the asymptotes and the x- and y-intercepts.
x=-2, y=3, (0,-3), (2,0)
O is the center of the circle which has a radius of 10 cm. The size of ∠AOB is 1.5 rad.
a) Find the lengths of the minor arc AB and of the major arc AB.
b) Find the areas of the minor sector AOB and the major sector AOB.
a) Minor arc: 15, Major arc: 20π-15 or approx. 47.8
b) Minor sector: 75, Major sector: 100π-75 or approx 239.16
Phil grows tomato plants in his garden. He records the number of tomatoes on each plant and presents his data using this table:
Tomatoes || 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 ||
Freq. || 2 | 4 | 4 | 6 | 10 | 15 | 4 | 5 ||
What is the median number of tomatoes?
7
Find the equation of the line tangent to f(x)=3x2-2 at the point where x=1.
y-1=6(x-1) or y=6x-5
What is Daniel's middle name?
Andrés
The quadratic equation 4x2+4kx+9=0, k>0 has exactly one solution for x.
Find the value of k.
k=3
For triangle △ABC, AB = 7 cm, BC = 9 cm and m∠ABC = 120°. Find AC and m∠BAC.
AC ≈ 13.9 or √‾̅1̅9̅3̅
m∠BAC ≈ 34.1°.
In a group of 50 people, 29 like eating fish (F) and 38 like eating chips (C) and 9 people like neither fish nor chips.
Find the probability that a person chosen at random from the group likes both fish and chips.
26/50 or 13/25
Calculate ∫-44 |x| dx
How many years did Daniel live in the U.S.
10
Find the sum of the series
1 + 2/5 + 4/25 + 8/125 + ...
and
1 - 2/5 + 4/25 - 8/125 + ...
5/3
5/7
Given that sinθ = ½, cosθ = -√‾̅3̅ /2 and 0°<θ<360°.
a) Find the value of θ.
b) Write down the exact value of tanθ.
θ = 150°
tanθ = -1/√‾̅3̅ = -√‾̅3̅ /3
A fair coin is tossed five times. Calculate the probability of obtaining at least one head.
P(x≥1)=0.96875≈0.969
Find the indefinite integral
∫(3x²+7x)⁵(6x+7)dx
1/6 · (3x²+7x)⁶+C
Daniel started working at the age of 17 in the U.S. What company gave him his first job?
Universal Studios
Find the term in x7 in the expansion of (1-x)10.
-120x7
The function f is defined by f(x)=30sin3xcos3x, 0 ≤ x ≤ π/3.
a) Write down an expression for f(x) in the form asin6x, where a is an integer.
b) Find the period of f.
c) Solve f(x) = 0, giving your answers in terms of π.
a) 15sin(6x)
b) 2π/6 or π/3
c) x=0, π/6, π/3
The heights of a group of students are normally distributed with mean of 160 cm and a standard deviation of 20 cm. In this group of students, 11.9% have heights less than d cm. Find the value of d.
d≈136
The cost per item, in euros, to produce x items is C(x)=x³-3x²-9x+30. Find the number of items that must be produced to minimize the cost per item.
3 items
Daniel likes to name his things. What was the name of his first car?
Ocho Cinco