SAT Algebra 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
Contents
SAT Hardest Problems
If what is the negative number
(A)
(B)
(C)
(D)
(E)
Correct Answer: D
Solution:
Using the technique of completing the square, we can rewrite the given equation as follows: Since is negative,
Therefore, the correct answer is (D).
Incorrect Choices:
(A), (B), (C) and (E)
The solution explains why these choices are wrong.
and are real numbers such that What is the value of
(A)
(B)
(C)
(D)
(E)
Correct Answer: B
Solution:
We rewrite as follows to obtain:
Therefore, the correct answer is (B).
Incorrect Choices:
(A), (C), (D) and (E)
The solution explains why these choices are wrong.
and are real numbers such that If and are the minimum and maximum values of respectively, what is
(A)
(B)
(C)
(D)
(E)
Correct Answer: C
Solution:
Observe that and Then and are the two real roots of the following quadratic equation in Since this equation has real roots, it must be true that its discriminant is non-negative: Now, Since from the range of is Hence and which implies
Therefore, the correct answer is (C).
Incorrect Choices:
(A), (B), (D) and (E)
The solution explains why these choices are wrong.
SAT Tips for Algebra
Algebraic Manipulations
- Follow order of operations.
Polynomials
Exponents
- Know the Rules of Exponents.
- Recognize first few perfect squares (1, 4, 9, ... 400) and cubes (1, 8, 27,... 1000).
- The square of a number is always positive.
Change the Subject
- Know the Rules of Exponents.
Inequalities
- Know the Properties of Inequality.
- Multiplying (or dividing) both sides of an inequality by a negative number reverses its sign.
- Know the properties of numbers between and .
Absolute Value
- Know the Properties of Inequality.
- Multiplying (or dividing) both sides of an inequality by a negative number reverses its sign.
SAT General Tips