# SAT Math Formula Sheet to help you ace the math section

On the SAT exam students are tested on a vast range of math concepts. In some cases, one can get simple math problems from elementary school but in other cases some difficult questions from senior year curriculum of high school. Therefore, the variety of questions and the fact that one has to remember a lot of formulas from different grades is what makes the SAT test a challenging one.

But don’t worry, this blog is created for all the SAT aspirants planning to take a test in 2022 and want to reinforce math calculations fast by using the new SAT Math Formula Sheet.

This blog briefly explores current SAT formula sheet, some problems with step-by-step explanation, along with best practices to ace your preparation! You will learn:

- Current SAT formula sheet.
- SAT practice test problems with step-by-step solutions.
- Tips from our experts to help you prepare better.

**SAT Formula Sheet **

**Laws of Arithmetic:**

Commutative Law a×b=b×a a+b=b+a

Associative Law (a×b)×c=a×(b×c) (a+b)+c=a+(b+c)

Distributive Law a×(b+c)=a×b+a×c

**Fractions:**

**Ratios and Proportions:**

**Percent:**

**Negatives and Inequalities:**

**Exponents:**

**Roots:**

**Factoring:**

**Handy Translation:**

**Mean, Median and Mode:**

**Rate:**

**Probability:**

**Angles and Lines:**

**Triangles:**

**Pythagorean Theorem and Special Right Triangles:**

**Coordinate Geometry:**

**Perimeters and Area:**

**Similar Figures:**

Note: If two shapes are similar, then all corresponding lengths are proportional, and all corresponding angles are same. |

**3-D Geometry:****Tangents:**

d=2r | |

Note: Tangent line is perpendicular to the radius. |

**Sequence:**

**Function:**

**Transformation of Parabola:**

**Variation:**

**Trigonometric Functions:**

**Complex Numbers:**

**Circle Equation:**

**Degrees to Radian:**

Where, x is in degree, and t is in radian

**Arc and Sectors:**

**Are you now wondering about how to use these SAT math formulas?**

First it will be a good idea for all SAT aspirants to print this SAT math formula sheet and paste it at a visible spot. Like on your study table and then before going through and trying to solve some SAT practice tests on your own, look at the below math problems which have been solved with step-by-step solution provided using the formula sheet shared above.

**Example 1: **What percentage of 16 is 2?

**Explanation: **Use the Handy Translation.

what | means | a,b, etc |

is | means | = |

percent | means | ÷100 |

of | means | X |

**Step 1:** Let us take unknown variable as b. And, plug the meaning from the above table.

**Step 2:** Now, solve fr *b.
Final answer: 12.5%*

**Example 2: **In the following △PQR, what would be the measure of the segment ‾PS?

Option A | 2 |

Option B | 3 |

Option C | 3√‾3 |

Option D | 3√‾2 |

**Explanation: **This problem can be solved by using the special right triangle. From the formula sheet, we know the following property:

30°-60°-90° |

We can see in 30°-60°-90°, the measure of the hypotenuse is twice as the measure of the base.

**Step 1:** Now, in △QRS hypotenuse QR=2RS=6 cm.

RS=6/2=3 cm

Hence, RS=3 cm. Also, we can see from the figure that RS=PS.

So, PS=3 cm.

**Final answer: Option (B). **PS=3 cm

**Example 3: **In the following figure, lines *p* and *q* are parallel, and lines* l* and *m* are parallel. If the measure of angle ∠α is 72°, what would be the measure of angle ∠β?

Option A | 72° |

Option B | 18° |

Option C | 288° |

Option D | 108° |

**Explanation: **We will use the property of angle and lines to solve this problem.

From the figure’s geometry, we can see that ∠α and ∠β are complementary angles. So, they will add up to 180°.

Step 1: Now,

∠α+∠β=180°

We have ∠α as 72°,

72°+∠β=180°

∠β=180°-72°=108°

**Final answer: Option (D). **108°

**Example 4: **Solve the following equation for *x.*

5x²+4=-12x

**Explanation: **We will rewrite the following equation and solve for *x*.

5x²+4=-12x

**Step 1**: Now, rewrite the equation.

5x²+12x+4=0

5x²+10x+2x+4=0

**Step 2:** Factor the common terms.

5xx+2+2x+2=0

5x+2x+2=0

5x+2=0;x=-2/5

x+2=0;x=-2

**Final answer: Option (B). **–2/5,-2

**Example 5:** Line *l *contains points (7,3) and (4,5). What is the slope of the line?

Option A | 7/3 |

Option B | –4/5 |

Option C | –2/3 |

Option D | 3/2 |

**Explanation: **We will use the formula of slope.

Let point (7,3) be (x1,y1) and point (4,5) be (x2,y2)

**Step 1:** Now, plug the values in the formula.

**Final answer: Option (C). **–2/3

**Example 6:** If √¯10x-25=x, what is the value of x?

Option A | 0 |

Option B | 3 |

Option C | 6 |

Option D | 5 |

**Explanation: **We will isolate the variable and solve for *x.*

**S****tep 1:** Square both sides with respect to *x*.

**Explanation: **We will isolate the variable and solve for *x.*

**S****tep 1:** Square both sides with respect to *x*.

**Step 2:** Factor the quadratic equation.

x²-10x+25=0

x²-5x-5x+25=0

xx-5-5x-5=0

x-5x-5=0

**Step 3:** Separate the solution.

x=5, x=5

**Final answer: Option (D). **5

**Example 7:** Compute the sum of 5+3i+2-4i, where i=√‾-1.

Option A | 22-6i |

Option B | 1+5i |

Option C | 7-i |

Option D | 9+5i |

**Explanation: **We will combine the real and imaginary parts separately.

Step 1: Combine the like terms.

5+3i+2-4i=5+2+(3i-4i)

7-i

**Final answer: Option (C). **7-i

**Example 8:** (x+2)²+y²=4 represent an equation of the circle. Write the circle equation by translating it 2 units right on a *xy-*plane.

Option A | x²+y²=4 |

Option B | (x+2)²+y²=4 |

Option C | (x+2)²+y²=2 |

Option D | x²+(y-2)²=4 |

**Explanation: **We will use the standard equation of the circle (x-h)²+(y-k)²=r², to compare the given equation, where the center is (h,k).

Option A | x2+y2=4 |

Option B | x+22+y2=4 |

Option C | x+22+y2=2 |

Option D | x2+y-22=4 |

**Explanation: **We will use the standard equation of the circle x-h2+y-k2=r2, to compare the given equation, where the center is (h,k).

Step 1: Compare the given equation.

(x+2)²+y²=4

(x-h)²+(y-k)²=r²

So, the center of the given circle would be (-2,0).

**Step 2:** Translated 2 units right on the *xy-*plane.

The center would become (-2+2,0)=(0,0).

Hence, the new equation of circle would be x²+y²=4.

**Final answer: Option (A). **x²+y²=4

**Example 9:** Analyze the following graph and identify its x-intercept on the *xy*-plane.

Option A | 1 |

Option B | -4 |

Option C | -2.5 |

Option D | 0 |

**Explanation: ***x*-intercept is the point where the graph of function crosses the *x*-axis. And, in the above graph, it crosses the *x*-axis only at x=-4.

**Final answer: Option (B). **-4

**Example 10:** If h(x)=x²+2(x+3), and g(x)=h(x)-4. Find the value of g(4)?

Option A | 8 |

Option B | 16 |

Option C | 34 |

Option D | 26 |

**Explanation: **We will plug the values in the given equation, and solve for g(4).

**Step 1:** Plug h(x)=x²+2(x+3) in the function g(x).

g(x)=x²+2(x+3)-4

**Explanation: **We will plug the values in the given equation, and solve for g(4).

**Step 1:** Plug hx=x2+2x+3 in the function gx.

gx=x2+2x+3-4

**Step 2:** Now, plug x=4

g(4)=4²+2(4+3)-4

g(4)=16+2(7)-4=16+14-4=26

**Final answer: Option (D). **26

**Tips that will help you ace the math section of SAT **

By now we hope that our reader got a good idea about what to expect on SAT math section and how to use the formula sheet to solve quickly and correctly. But formula sheet alone is not going to get you that dream score, here are a few tips and tricks that will go a long way and help you get a high SAT score:

- A multiple-choice problem always shows one option as the correct answer.
- In some problems, starting the work from the answer will be helpful. We know, one solution is correct amongst the given options. Substitute the answer in the question, and you may find the right choice.
- Skip any problem that seems too difficult. Highlight that number of the question in the question paper, and come back to that later.
- It would be best to use a scientific calculator with a graphing utility like
*TI 83*, to attempt the calculator allowed section in the SAT.