For those of you preparing for the SAT, the Math section is certainly something you're familiar with. As you know, SAT Math covers fundamental knowledge learned from middle and high school. But what exactly is this knowledge? In today's article, Clever Academy will introduce you to a comprehensive system of SAT Math knowledge so you can gain a more detailed understanding of the SAT Math section.
SAT Math Test Structure: divided into 2 sections (Calculator and No Calculator). In total, there are 58 questions to be completed in 80 minutes (averaging 1 minute 25 seconds per question). The Math section without a calculator has 20 questions (15 multiple-choice questions and 5 student-produced response questions) completed in 25 minutes (averaging 1 minute 15 seconds per question). The calculator section has 38 questions (30 multiple-choice questions and 8 student-produced response questions) completed in 55 minutes (approximately 1 minute 30 seconds per question).
What does SAT Math assess? The Math section focuses on evaluating test-takers' analytical and logical problem-solving abilities. Through this, it assesses students' information analysis skills (including Statistics, Structure, and Discrete Information). According to research by the U.S. Department of Education, students with strong analytical and information-processing abilities will succeed in undergraduate and graduate programs. Additionally, the calculator Math section also assesses students' decision-making abilities and their connecting skills with mathematical algorithms.
In the SAT Math section, you will be provided with 12 formulas and 3 geometry laws in both the Calculator and No Calculator sections. Geometry knowledge accounts for very few points in this section, so you should focus on Algebra and Trigonometry formulas.
Knowledge provided in the SAT Math section:
- Area of a circle
- Circumference of a circle
- Area of a rectangle
- Area of a triangle
- Pythagorean theorem
- Properties of a 45-45-90 right triangle
- Properties of a 30-60-90 right triangle
- Volume of a rectangular solid
- Volume of a cylinder
- Volume of a sphere
- Volume of a cone
- Volume of a pyramid
- Laws:
+ The number of degrees in a circle is 360
+ The number of radians in a circle is 2π
+ The number of degrees in a triangle is 180
Knowledge not provided in the SAT Math test
- Slope and graphs
Slope formula
- Given two points A(x1,y1), B(x2,y2), find the slope of the line connecting them:
m = (y2-y1)/(x2-x1) = Δy/Δx
How to write the equation of a line
The equation of a line is written as:
y = mx+b
Where:
- m is the slope of the line.
- b is the y-intercept (the point where the line touches the y-axis).
- If the line passes through the origin (0,0), the line is written as y = mx.
Midpoint formula:
((x1+x2)/2, (y1+y2)/2)
Distance formula:
Given two points A(x1,y1), B(x2,y2), find the distance between them:
√[(x2-x1)² + (y2-y1)²]
You don't need this formula, because you can simply plot your points and then create a right triangle from them. The distance will be the hypotenuse, which you can find using the Pythagorean theorem.
- Circle
Arc length
- Given the radius and central angle of an arc, find the arc length
- Use the formula of circumference multiplied by the arc's angle divided by the total degree measure of the circle (360)
L arc = 2πr(Arc angle/360)
Arc area
- Given the radius and central angle of an arc, find the area of the sector
- Use the formula of area multiplied by the arc's angle divided by the total degree measure of the circle
A = (πr²)(Arc angle/360)
- Algebra
Quadratic equation
Given a polynomial in the form ax² + bx + c. Find x.
x = (-b + √(b² – 4ac)) / 2a
x = (-b - √(b² – 4ac)) / 2a
Average
Find the average/mean of a set of numbers/terms
Mean = Sum of terms / Number of terms
Find average speed
Speed = Total distance / Total time
Probability
- Probability is a representation of the likelihood of something happening.
Probability of an outcome = Number of desired outcomes / Total number of outcomes
- A probability of 1 is guaranteed to happen. A probability of 0 will never happen.
Percentage
- Find x percent of a given number n.
n(x/100)
- Find what percent a number n is of another number m
(n/m) × 100
Trigonometry
Trigonometry is a new addition to the 2016 redesigned SAT Math section. Although it accounts for less than 5% of math questions, you won't be able to answer trigonometry questions without knowing the following formulas.
- Find the sine of an angle given the lengths of the sides of a triangle:
Sin(x) = Length of opposite side / Length of hypotenuse
- Find the cosine of an angle given the lengths of the sides of a triangle:
Cos(x) = Length of adjacent side / Length of hypotenuse
- Find the tangent of an angle given the lengths of the sides of a triangle:
Tan(x) = Length of opposite side / Length of adjacent side
Above are the basic math formulas you need to know while preparing for the SAT Math section. Besides memorizing formulas, you need to practice doing exercises regularly to know when to use them and which formula can be applied to solve problems most quickly.
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