SAT/ACT Math: Basic Concepts Students Tend To Forget (But Should Not!)

The SAT and the ACT math sections test a plethora of topics. However, there are only a handful of concepts that most students across the globe forget, and miss out on a perfect score!

0 is an even number

Question:
Which of the following can be the sum of three consecutive even integers?

A) -7

B) 0

C) 4

D) 8

Explanation:
As we are adding three even consecutive integers, the sum must be even. Hence, (A) is easy to eliminate.
For the other answer choices, let’s try some numbers.
B) 0 = -2 + 0 + 2 (Three consecutive even integers)
C) 4 - No three consecutive even integers can add to 4
D) 8 - No three consecutive even integers can add to 4

Hence, the answer is (B).

The inequality sign is reversed when multiplied or divided by a negative number.

Question:
-20x ≤ -10(x - 2)
Which of the following represents the solution for the inequality above?
A) x ≤ -2
B) x ≥ -2
C) x ≤ 2
D) x ≥ 2

Explanation:
If -20x ≤ -10(x - 2), then
-20x ≤ -10x + 20
=> -20x + 10x ≤ 20
=> -10x ≤ 20

=> -x ≤ 2
=> x ≥ 2

Hence, the answer is (D).

Absolute value of an expression is always non-negative.

Question:
For what value of x is |x – 1| + 1 equal to 0?
A) 0
B) 1
C) 2
D) There is no such value of x

Explanation:
As the value of an absolute expression is always non-negative i.e ≥ 0, there is no possible value to make |x - 1| + 1 equal to 0.
Hence, the answer is (D).

The third side of a triangle is always shorter than the sum of the other two sides of the triangle.

Question:
In an isosceles triangle ABC, AB = 9 and BC = 4. Which of the following is the perimeter of the triangle?
A) 16
B) 17
C) 18
D) 22

Explanation:
In an isosceles triangle, two sides are equal. Hence, the triangle must have the sides as 9, 4, and 4 or 9, 9, and 4.
Hence, the possible perimeters are 9 + 4 + 4 = 17 or 9 + 9 + 4 = 22.
This eliminates answer choices (A) and (C).

However, a triangle with side lengths as 9, 4, and 4 is not possible as the sum of two of its sides (4 + 4 = 8) is not more than the third side (9).

Hence, the answer is (D).

Keep these 4 concepts in mind to improve your chances of getting a perfect score.

Happy Prepping!