Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8

Solve: 16 = 4 + 3(x + 2)

The graph of the function f is shown in the xy-plane above, where y =f  . Which of the following functions could define f ?

Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.

At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?

f(x) =2^x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?

In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?

Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.

The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?

Which of the following is equivalent to  ?

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

Note:
As the equation   is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.

The scatterplot above gives the tree diameter plotted against age for 26 trees of a single species. The growth factor of this species is closest to that of which of the following species of tree?

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
According to the information in the table, what is the approximate age of an American elm tree with a diameter of 12 inches?

y=x² - a
In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?

In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)