ACT Math: Preparing for Higher Math: Geometry

ACT Math Overview

Welcome, brave math conquerors to the adventures that await you in the math sections of the ACT! This is a quest that will put your mathematical prowess to the test, but fear not! For we shall embark on this journey together, every step of the way…

The ACT Math section is 60 minutes long, and it consists of 60 question. Which means that you should be working at a rate of 1 question per minute. Approximately…Ok, back to work! So, the ACT Math section covers topics from algebra, geometry, and trigonometry, as well as basic arithmetic and data analysis. The questions are presented in multiple choice format, where you’ll choose the best answer from four options. Now, some questions might be more straightforward than others but with the right strategy and knowledge, you’ll be able to pass with flying colours! Let’s quickly check in on the types of questions that show up on the math section. Now, this is to give you an idea of what sections to focus on and improve. 

1. • Pre-algebra and elementary algebra: Questions on basic operations, fractions, decimals, percentages, exponents, and simple linear equations.
2. • Intermediate algebra and coordinate geometry: Quadratics equations, factoring, inequalities, systems of equations, and graphing in the coordinate plane.
3. • Plane geometry: Questions about angles, lines, triangles, quadrilaterals, circles, and other plane figures. Area, perimeter, and volume calculations might be involved.
4. • Trigonometry: Basic trig concepts, rations (sine, cosine and tangent) and solving trigonometric equations.
5. • Data analysis and statistics: Interpreting graphs, charts and tables; calculating measures of central tendency, probability, and statistics from data. The focus of this particular guide is on the concepts of geometry in the ACT Math section. Let’s dive right in! 

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💡 Tips and Tricks

Since time immemorial, students have been given a lot of tips and tricks to achieve instant success on the exam. Almost like instant ramen! But, I’d beg to differ. Tips and tricks act merely as support to your preparation, using which you can save some time and nip some marks here and there. Similarly, the tips and tricks for the ACT Math section allow you to propel your preparation and knowledge in the right manner, saving you some marks and improving your score! 

1. Familiarize yourself with the test format and question types, as well by practicing timed sample tests. Prior to that, focus on understanding the course material well. Learn the formulas. When you understand the theory well in maths, you’d have much more fun doing the questions and doing them right!

2. Because of the MCQ format, use the elimination rule to shorten down the answers until you reach the last option. This increases your chance of choosing the correct answer even if you’re dicey about a question. 

3. In algebra based questions, you’d be asked, on more than one occasion, to find the x in the equation. If you get stuck, simply equate the question using the options given and solve for the correct answer. This has saved my skin a lot of times and will do yours too! 

4. Probably the most important piece of advice I would give to you, as someone who has prepared for these exams, is to stay calm and confident. And I know you’ve heard this a bazillion times, but it’s true. Staying calm and confident allows you to focus on the task at hand and avoid silly mistakes on the test. Also, ensure that you get enough rest the night before the test and have a fresh mindset. 

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📐 Geometry

Now, while there is a particular section for Math on the ACT, there is none for geometry specifically. It will weave itself into questions and will often confuse you. Which is why I have compiled a list of the most core geometric concepts that you should practice for the test: 

• • Triangles: Know and understand the properties of the different types of triangles, the sum of angles in a triangles, and usage of the Pythagorean theorem.
• • Circles: Understand the properties of circles, most importantly the relationships between the radius, chords and arcs. Be familiar with central angles, inscribed angles, and the formula for the circumference and area of a circle.
• • Quadrilaterals: Learn about the properties of rectangles, squares, parallelograms and trapezoids. Practice questions that ask you to solve for a given angle or side. Those are the most frequent questions on the ACT.
• • Polygons: Go through the properties of the polygons and how to find the interior and exterior angles.
• • Coordinate geometry: Practice working with points, lines and equations in the coordinate plane. Understand how to find the distances, slopes, and intersections of lines. These questions stump most students and you want to practice multiple questions in different scenarios to strengthen your coordinate geometry.
• • Three-dimensional figures: This one is not as heavily tested as 2D geometry, but it is helpful to know for certain multi-step questions. Learn the volume and surface area formulas for spheres, cubes and cylinders.
• • Transformations: This is one of the harder sections of geometry but the questions are straightforward and learning the formulas well plus a lot of practice should get you to ace these questions! Most importantly: reflections, rotations, translations, and dilations of figures.
• • Memorize the basic formulas for diagonals, area, and perimeter for the different shapes. Most students omit these formulas and commit a lot of mistakes on the final exam. It’s very basic but very, very important! As I mentioned before, geometry is throughout the ACT Math section. The more you practice questions from the above topics, the better you’d perform on the ACT. But, I understand the anxiety. Which is why, the next section here focuses on similar previous year questions on the above discussed geometric concepts. Solve them yourselves and then look at the given answers and explanations. Oh, and there is a whole other section solely for practice questions on ACT content, so make sure to check that out too! 

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🤓 Applying Your Knowledge: Practice Problems

1. In triangle ABC, angle A measures 40 degrees, and angle B measures 75 degrees. What is the measure of angle C? 

EXPLANATION

The sum of angles in a triangle is always 180 degrees. To find angle C, subtract the measures of angles A and B from 180

**Angle Sum Property of a Triangle: angle A + angle B + angle C = 180 degrees **

40 + 75 + Angle C = 180

Angle C = 180 - (40+75)

Angle C = 180 - 115 

Therefore, Angle C = 65 degrees! 

2. A rectangle has a length of 12 units and a diagonal of 13 units. What is the width of the rectangle? 

EXPLANATION

In a rectangle, the diagonal divides it into 2 right triangles. Let the width be w.  

**Pythagorean theorem: a^2 + b^2 = c^2, where an and b are the two sides of a right-angled triangle and c is the hypotenuse. **

12^2 + w^2 = 13^2

144 + w^2 = 169 

W^2 = 169-144

W = square root of 25

Therefore, w = 5. 

3. Triangle XYZ has side lengths XY = 8 units, XZ = 10 units, and YZ = 12 units. Is triangle XYZ a right angled triangle? 

EXPLANATION 

Using the Pythagorean theorem again, we can use the following equation: 

(XY)^2 + (XZ)^2 = (YZ)^2 

Solving the left side of the equation: 

8^2 + 10^2 = 64+100

= 164 

Solving the right side of the equation: 

12^2 = 144

Therefore, since the right side of the equation is not equal to the left side, thus the triangles is not a right angled triangle. 

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⭐️ Conclusion

As we conclude this overview of the ACT Math section, I want you to remember that you hold the power to excel. Embrace the process, trust your preparation, and approach the test with determination. Believe in yourself, and go out there and shine brightly! Best of luck! 🎉