Try this ACT math practice question that tests your ability to find the x-intercepts of circles.

The circle $(x+1)^2+(y-2)^2=29$ intersects the $x-$axis in two points, one of which is $(4,0)$. What are the coordinates of the other point where the circle intersects the $x-$axis?

1. $\quad (-7, 0)$
2. $\quad (-6, 0)$
3. $\quad (-\sqrt{29}, 0)$
4. $\quad (-5, 0)$
5. $\quad (-4, 0)$

Choice B

Video explanation

Try this ACT math practice question that tests your ability to algebraically simplify a trigonometric expression using trigonometric identities.

$$\dfrac{\cos \theta}{1 – \sin \theta} \quad – \quad \dfrac{\sin \theta}{\cos \theta}$$

When $\cos \theta \neq 0$ and $\sin \theta \neq 1$, which of the following is equivalent to the expression above?

1. $\quad \sec \theta$
2. $\quad \csc \theta$
3. $\quad \cos \theta$
4. $\quad \cos^{2} \theta$
5. $\quad \dfrac{\cos \theta – \sin \theta}{(\cos \theta)(1 – \sin \theta)}$

Choice A

Video explanation

Try this ACT math practice question on the topics of right triangles, algebraic translation and manipulation.

The perimeter of a right triangle is $18$ inches, and one of the legs of the triangle is $6$ inches long. How many inches longer is the hypotenuse than the length of the shortest leg ?

1. $\quad 1.5$
2. $\quad 2$
3. $\quad 3$
4. $\quad 3.5$
5. $\quad 4$

Choice C

 
Here is a link to the playlist of video explanations to all of the math questions in the 2019 December ACT (Form C03) Test.

Try this ACT math practice question on how to find the terms of an arithmetic progression.

In an arithmetic progression the difference between consecutive terms is a constant. For example, the sequence $3, 7, 11, 15, \ldots$ is an arithmetic progression where the consecutive terms are $4$ apart. If the first term of an arithmetic progression is $4$ and the last term is $54$, and the sum is $609$, then what is the third term?

1. $\quad 8$
2. $\quad 8.5$
3. $\quad 9$
4. $\quad 9.5$
5. $\quad 10$

Choice C