## Official ACT Prep Guide 2018: Almost identical to last year

- The practice tests are a patchwork of questions from the the 5 tests in the Real ACT Guide and recently released ACT tests from 2015.
- First Practice Test: The math section in the first practice test in the guide has around 40 questions from the June 2015 ACT test (Form 73C), and the remainder are a combination of new questions and questions from the five tests in the Real ACT Guide.
- Second Practice Test: Half of the math questions are from the Test#2 from Real ACT guide and the remainder are either new or from the other tests in the Real ACT guide.
- Third Practice Test: Half of the math questions are from April 2015 ACT test (Form 73G) and the rest are from Test#4 from the Real ACT Guide.
- Because they have reused part of the tests that are in the older Real ACT guide, this makes the practice tests in the older guide useless. I don't know if this was done deliberately to ensure "planned obsolescence" of the older guide.

My final recommendation would be to use the April and June 2015 ACT tests on their own, and use the five practice tests in the Real ACT Guide, 3rd Edition for additional practice. I do not recommend buying this guide.

As I have said before, this analysis is based on the math section only, but I am pretty certain it will be mirrored in the remaining sections of the tests as well. I will leave it to others to analyze those sections.

## 2017 April ACT Form 74F: Video Explanations

## ACT Math Practice Question: Simplifying algebraic fractions

- \(\quad -\dfrac{a}{b}\)
- \(\quad -\dfrac{b}{a}\)
- \(\quad 1\)
- \(\quad \dfrac{a}{b}\)
- \(\quad \dfrac{b}{a}\)

## Exponents: All the rules you need to know for ACT Math

**Exponents: All you need to know for ACT Math**

Here is a brief summary of all the exponent rules and manipulations that you are expected to know for the math section of the ACT test. You need to memorize these rules, and ensure that you can apply them in different situations.

**Exponent Rules**

**Exponents: Algebraic Manipulation**

**Exponents: Adding and Subtracting Terms**

Additional Examples

$$ 2^4 + 2^4 + 2^4 + 2^4 = 2^4(1 + 1 + 1 + 1) = 2^4(4) = 2^4(2^2) = 2^{4+2} = 2^6 $$ $$ 2^{20} - 3(2^{18}) = 2^{18}(2^2 - 3) = 2^{18}(4-3) =2^{18} $$ $$ 2^{x} + 2^{x+1} = 2^x + (2^{x})(2^1) = 2^{x}(1+2) =3(2^x)$$ $$\dfrac{1}{2^{9}} - \dfrac{1}{2^{10}} = \dfrac{1}{2^{9}}\left(1 - \dfrac{1}{2}\right) = \dfrac{1}{2^{9}}\left(\dfrac{1}{2}\right) = \dfrac{1}{2^{10}} \quad \text{Or} \quad \dfrac{1}{2^{9}} - \dfrac{1}{2^{10}} = \dfrac{2}{2^{10}} - \dfrac{1}{2^{10}} = \dfrac{2-1}{2^{10}} = \dfrac{1}{2^{10}}$$
**Radicals and Fractional Exponents**

- A square root of a number $n$ is a number that, when squared, is equal to $n$ or $(\sqrt{n})^2 = n$.
- An exponent of $\dfrac{1}{2}$ is the same as taking the square root of a number, $\sqrt{n} = n^{\frac{1}{2}}$.
- A cube root of a number $n$ is a number that, when cubed, is equal to $n$ or $(\sqrt[3]{n})^3 = n$.
- An exponent of $\dfrac{1}{3}$ is the same as taking the cube root of a number, $\sqrt[3]{n} = n^{\frac{1}{3}}$.

**Common Mistakes**