SAT Functions Perfect Score
To get a perfect score on SAT Math, you need to:
- Get every single problem correct.
- Have complete mastery of all of the SAT skills
- Remember the Tips and use them
- Figure out your common mistakes and avoid them
SAT Hardest Problems
For two sets and a function satisfies How many such functions are there?
(A)
(B)
(C)
(D)
(E)
Correct Answer: C
Solution:
If the range of is only one element of we have Since both satisfy the given condition we have found two such functions.
Now, if the range of is both elements of we have the following four functions such that
Therefore, there are a total of functions from to that satisfy Hence, the correct answer is (C).
Incorrect Choices:
(A), (B), (D), and (E)
The solution explains why these choices are wrong.
What is the area of the triangle bounded by the three lines
(A)
(B)
(C)
(D)
(E)
Correct Answer: C
Solution:
72902wiki
As shown in the above graph, the triangle of interest is a right triangle because and are perpendicular. The area of is then Let us now calculate and
Equating and gives Substituting this into gives which implies Then
Similarly, equating and gives Substituting this into gives which implies Then
Substituting and into the area of is
Therefore, the correct answer is (C).
Incorrect Choices:
(A)
If you multiply only once, you will get this wrong number.(B)
If you mistakenly multiply twice when calculating of the area the triangle, you will get this wrong number.(D)
If you forget about multiplying when calculating of the area the triangle, you will get this wrong number.(E)
If you miscalculate you will get this wrong number.
72961wiki
The above is the graph of the quadratic function Which of the following statements is true?
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II and III
Correct Answer: C
Solution:
72961wikiS1
First, since from the above graph, the first statement is true.
Now, observe that the equation of the graph can be rewritten as Then the axis of symmetry is
Since the parabola intercepts the -axis at and also at a point in the interval it must be true that lies to the left of This is because if the parabola intercepted the -axis at and the axis of symmetry would be Thus, which makes the second statement false.Finally, since we have which makes the third statement true.
Therefore, only statements I and III are true and the correct answer is (C).
Incorrect Choices:
(A), (B), (D), and (E)
The solution explains how to eliminate these choices.
SAT Tips for Functions
Functions
- Don't switch the and coordinates of a point.
- The domain of is the set of all in the domain of such that is in the domain of .
- For
Linear Functions
- The slope of a line is defined as
- A line with a positive slope rises from left to right.
- A line with a negative slope falls from left to right.
- Slope-intercept form: where is the line's slope, and its -intercept.
- Point-slope form: where is the line's slope, and is a point on the line.
- The line is a vertical line that crosses the x-axis as
- The line is a horizontal line that crosses the -axis at
- If two lines are parallel, their slopes are equal.
- If two lines are perpendicular, their slopes are negative reciprocals of each other.
- If two functions intersect at point then .
- Don't switch the and coordinates of a point.
- When transforming graphs, trace what happens to each point.
Quadratic Functions
- The parabola opens up if
- The parabola opens down if
- The parabola opens up if
- The parabola opens down if
- The parabola has a intercept at
- The parabola has a vertex at
- The parabola has an axis of symmetry at
- The parabola has a vertex at
- The parabola has an axis of symmetry at
Coordinate Geometry
- The line is a vertical line that crosses the x-axis as
- The line is a horizontal line that crosses the -axis at
- If two lines are parallel, their slopes are equal.
- If two lines are perpendicular, their slopes are negative reciprocals of each other.
- If two functions intersect at point then .
- Don't switch the and coordinates of a point.
- Distance formula:
- Midpoint formula:
- When transforming graphs, trace what happens to each point.
Functions as Models
- Exponential growth: , where and
- Exponential decay: , where and
Newly Defined Functions
- Follow directions exactly.
Direct and Inverse Variation
- Direct variation:
- Inverse variation:
Translating Word Problems
Word Problemes
- Distance = Rate Time.
Student-Produced Response
SAT General Tips