Advanced algebra and geometry problems are included in the college-level math section of the Accuplacer.

Geometry questions will cover: midpoints, x and y intercepts, slope, arcs, chords, cones, and triangles.

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Example 1:

Find the coordinates (x, y) of the midpoint of the line segment on a graph that connects the points (5, 2) and (1, -10).

Solution 1:

In order to find midpoints on a line, you need to use the following formula:

For two points on a graph (x₁, y₁) and (x₂, y₂), the midpoint is:

(x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2

Now calculate for x and y:

(5 + 1) ÷ 2 = midpoint x, (2 + -10) ÷ 2 = midpoint y

6 ÷ 2 = midpoint x, -8 ÷ 2 = midpoint y

-3 = midpoint x, -4 = midpoint y

(3, -4)

Example 2:

Consider the vertex of an angle at the center of a circle. The diameter of the circle is 4. If the angle measures 90 degrees, what is the arc length relating to the angle?

Solution 2:

To solve this problem, you need these three principles:

(1) Arc length is the distance on the outside (or circumference) of a circle.

(2) The circumference of a circle is always π times the diameter.

(3) There are 360 degrees in a circle.

The angle in this problem is 90 degrees.

360 ÷ 90 = 4

In other words, we are dealing with the circumference of 1/4 of the circle.

Given that the circumference the circle is 4π, and we are dealing only with 1/4 of the circle, then the arc length for this angle is:

4π ÷ 4 = π

Example 3:

You will have at least one question on combinations or permutations.

How many 2 letter combinations can be made from the letter set: H A N D Y?

Solution 3:

To determine the number of combinations of S at a time that can be made from a set containing N items, you need this formula:

(N!) ÷ (N - S)! x S!

In the example above, S = 2 and N = 5 (because there are five letters in the set).

Now substitute the values for S and N:

(5 x 4 x 3 x 2 x 1) ÷ ((5 - 2)! x 2!) =

(5 x 4 x 3 x 2) ÷ ((3 x 2 x 1) x (2 x 1)) =

120 ÷ (6 x 2) =

120 ÷ 12 = 10

So 10 two-letter combinations can be made from a five letter set.

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