What kind of geometry is on the act

The mathematics section is designed to assess the mathematical skills students have typically acquired in courses taken up to the beginning of grade Most questions are self-contained. Some questions may belong to a set of several questions e. The material covered emphasizes the major content areas that are prerequisites to successful performance in entry-level courses in college mathematics.

Knowledge of basic formulas and computational skills are assumed as background for the problems, but recall of complex formulas and extensive computation are not required. Note: You may use a calculator on the mathematics section.

See www. Nine scores are reported for the mathematics section: a score for the section overall and eight reporting category scores based on specific mathematical knowledge and skills. The approximate percentage of the section devoted to each reporting category is:. There are two kind of cones--right cones and oblique cones. For the purposes of the ACT, you only have to concern yourself with right cones. Oblique cones will never appear on the ACT.

This makes sense logically, as a cone is basically a cylinder with one base collapsed into a point. Pyramids are geometric solids that are similar to cones, except that they have a polygon for a base and flat, triangular sides that meet at an apex. There are many types of pyramids, defined by the shape of their base and the angle of their apex, but for the sake of the ACT, you only need to concern yourself with right, square pyramids.

A right, square pyramid has a square base each side has an equal length and an apex directly above the center of the base. A sphere is essentially a 3D circle. In a circle, any straight line drawn from the center to any point on the circumference will all be equidistant. In a sphere, this radius can extend in three dimensions, so all lines from the surface of the sphere to the center of the sphere are equidistant.

The most common inscribed solids on the ACT math section will be "cube inside a sphere" and "sphere inside a cube. The question is most often a test of whether you know the solid geometry principles and formulas for each shape individually well enough to be able to put them together.

When dealing with inscribed shapes, draw on the diagram they give you. Understand that when you are given a solid inside another solid, it's for a reason. It may look confusing to you, but the ACT will always give you enough information to solve a problem. For example, the same line will have a different meaning for each shape, and this is often the key to solving the problem. Now because we have a sphere inside a cube, you can see that the radius of the sphere is always half the length of any side of the cube because a cube by definition has all equal sides.

This is a trick answer designed to trap you. For the vast majority of inscribed solids questions, the radius or diameter of the circle will be the key to solving the question. The radius of the sphere will be equal to half the length of the side of a cube if the cube is inside the sphere as in the question above.

This means that the diameter of the sphere will be equal to one side of the cube, because the diameter is twice the radius. But what happens when you have a sphere inside a cube? In this case, the diameter of the sphere actually becomes the diagonal of the cube.

What is the maximum possible volume of a cube, in cubic inches, that could be inscribed inside a sphere with a radius of 3 inches? You can see that, unlike when the sphere was inscribed in the cube, the side of the cube is not twice the radius of the circle because there are gaps between the cube's sides and the circumference of the sphere.

The only straight line of the cube that touches two opposite sides of the sphere is the cube's diagonal. Why is the diagonal 6? Though solid geometry may seem confusing at first, practice and attention to detail will have you navigating the way to the correct answer.

The solid geometry questions on the ACT will always ask you about volume, surface area, or the distance between points on the figure. The way they make it tricky is by making you compare the elements of different figures or by making you take multiple steps per problem.

But you can always break down any ACT question into smaller pieces. Is the problem asking about cubes or spheres? Are you being asked to find the volume or the surface area of a figure? Make sure you understand which formulas you'll need and what elements of the geometric solid s you're dealing with. Draw a picture any time they describe a solid without providing you with a picture.

This will often make it easier to see exactly what information you have and how you can use that information to find what the question is asking you to provide. Once you've identified the formulas you'll need, it's often a simple matter of plugging in your given information.

If you cannot remember your formulas like the formula for a diagonal, for example , use alternative methods to come to the answer, like the Pythagorean Theorem. Did you make sure to label your work? The makers of the test know that it's easy for students to get sloppy in a high-stress environment and they put in "bait" answers accordingly.

So make sure you label the volume for your cylinder and the volume for your cube accordingly. And don't forget to give your answer a double-check if you have time! Does it make sense to say that a box with a height of 20 feet can fit inside a box with a volume of 15 cubic feet? Definitely not! Make sure all the elements of your answer and your work are in the right place before you finish. Follow the steps to solving your solid geometry problems and you'll get that gold.

Solid geometry is often not as complex as it looks; it is simply flat geometry that has been taken into the third dimension. What types of questions can you expect on the ACT Math test? The ACT Math Test usually breaks down into 6 questions types: pre-algebra, elementary algebra, and intermediate algebra questions; plane geometry and coordinate geometry questions; and some trigonometry questions. This means you need to memorize relevant formulas, so you can recall them quickly as needed.

Because ACT is so specific about the types of questions it expects you to answer, you can easily prepare to tackle them. Not all standardized tests allow calculators. Fortunately, ACT does. Your calculator can help to save a ton of time on operations that are easy to mess up like multiplying decimals or working with big numbers. The place where you have to be really careful with your calculator, though, is on the easy ones.

Be careful with negative numbers! You are permitted to use a calculator for these questions. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator. Example Question 1 : Plane Geometry. Two angles are supplementary and have a ratio of What is the size of the smaller angle?

Possible Answers:. Correct answer:. Explanation : Since the angles are supplementary, their sum is degrees. Report an Error. Explanation : The angles are equal. Figure not drawn to scale. Possible Answers: Correct answer: Explanation : Let x equal the measure of angle DPB. The answer is Multiply both sides by 2 to get rid of the fraction.

Add x to both sides. Divide both sides by 5. Now, we can substitute 36 as the value of x and then solve for z. Subtract 36 from both sides. Explanation : Refer to the following diagram while reading the explanation: We know that angle b has to be equal to its vertical angle the angle directly "across" the intersection. Let the measure of angle AEB equal x degrees. Let the measure of angle BEC equal y degrees. Let the measure of angle CED equal z degrees.

Possible Answers: — y. Explanation : Intersecting lines create two pairs of vertical angles which are congruent. Example Question 5 : Geometry. Explanation :. The answer to this problem is