ACT Math – Section 2 – Test 3

The equations below are linear equations of a system where a, b, and c are positive integers.

                                                       ay + bx = c

                                                       ay − bx = c

Which of the following describes the graph of at least 1 such system of equations in the standard (x,y) coordinate plane?

I.  2 parallel lines

II.  2 intersecting lines

III. A single line

According to the measurements given in the figure below, which of the following expressions gives the distance, in miles, from the boat to the dock?

The circle graph below shows the distribution of registered voters, by age, for a community. Registered voters are randomly selected from this distribution to be called for jury duty. What are the odds (in the age range: not in the age range) that the first person called for jury duty is in the age range of 25 – 35 years?

The figure below shows the design of a circular stained- glass panel on display at Hopewell’s Antique Shop. Seams separate the pieces of the panel. All red triangular pieces shown are congruent and have a common vertex with each adjoining triangular piece. The 2 squares shown are inscribed in the circle. The diameter of the panel is 2 feet.

The design of the stained-glass panel has how many lines of symmetry in the plane of the panel?

The figure below shows the design of a circular stained- glass panel on display at Hopewell’s Antique Shop. Seams separate the pieces of the panel. All red triangular pieces shown are congruent and have a common vertex with each adjoining triangular piece. The 2 squares shown are inscribed in the circle. The diameter of the panel is 2 feet.

What is the area of the stained-glass panel, to the nearest 0.1 square foot?

The figure below shows the design of a circular stained- glass panel on display at Hopewell’s Antique Shop. Seams separate the pieces of the panel. All red triangular pieces shown are congruent and have a common vertex with each adjoining triangular piece. The 2 squares shown are inscribed in the circle. The diameter of the panel is 2 feet.

Kaya wants to install a new circular stained-glass window in her living room. The design of the window will be identical to that of the panel. The diameter of the new window will be 75% longer than the diameter of the panel. The new window will be how many feet in diameter?

For what value of a would the following system of equations have an infinite number of solutions?

2x –   y = 8

6x – 3y = 4a

Marcia makes and sells handcrafted picture frames in 2 sizes: small and large. It takes her 2 hours to make a small frame and 3 hours to make a large frame. The shaded triangular region shown below is the graph of a system of inequalities representing weekly constraints Marcia has in making the frames. For making and selling s small frames and l large frames, Marcia makes a profit of 30s + 70l dollars. Marcia sells all the frames she makes.

The weekly constraint represented by the horizontal line segment containing (9,2) means that each week Marcia makes a minimum of:

Marcia makes and sells handcrafted picture frames in 2 sizes: small and large. It takes her 2 hours to make a small frame and 3 hours to make a large frame. The shaded triangular region shown below is the graph of a system of inequalities representing weekly constraints Marcia has in making the frames. For making and selling s small frames and l large frames, Marcia makes a profit of 30s + 70l dollars. Marcia sells all the frames she makes.

For every hour that Marcia spends making frames in the second week of December each year, she donates $3 from that week’s profit to a local charity. This year, Marcia made 4 large frames and 2 small frames in that week. Which of the following is closest to the percent of that week’s profit Marcia donated to the charity?

Marcia makes and sells handcrafted picture frames in 2 sizes: small and large. It takes her 2 hours to make a small frame and 3 hours to make a large frame. The shaded triangular region shown below is the graph of a system of inequalities representing weekly constraints Marcia has in making the frames. For making and selling s small frames and l large frames, Marcia makes a profit of 30s + 70l dollars. Marcia sells all the frames she makes.

What is the maximum profit Marcia can earn from the picture frames she makes in 1 week?

A formula for finding the value, A dollars, of P dollars invested at i% interest compounded annually for n years is A = P(1 + 0.01i)ⁿ. Which of the following is an expression for P in terms of i, n, and A?

If x and y are real numbers such that x > 1 and y < −1, then which of the following inequalities must be true?

What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13 ?

In the equation x² + mx + n = 0, m and n are integers. The only possible value for x is -3. What is the value of m?

The solution set of which of the following equations is the set of real numbers that are 5 units from −3 ?