Series Binomial Theorem Limits Test – Precalculus Math (Printable PDF)

Question 1 Evaluating a Sum (2 points)

Evaluate ∑_k=1⁸ (5k − 3).

Question 2 Twenty-five Terms (2 points)

An arithmetic sequence has first term −6 and common difference 4. Find the sum of its first 25 terms.

Question 3 A Geometric Sum (2 points)

A geometric sequence has first term 6 and common ratio −2. Find the sum of its first 8 terms.

Question 4 Infinite Series (3 points)

Consider the series 18 − 12 + 8 − ….

1. Find the common ratio and explain why the series has a sum. (1 point)
2. Find the sum. (1 point)
3. Write 0.181818… as a fraction using an infinite geometric series. (1 point)

Question 5 Expanding a Binomial (2 points)

Expand (x − 2)⁴.

Question 6 A Term of an Expansion (2 points)

Find the fourth term of the expansion of (3x − y)⁵, in order of descending powers of x.

Question 7 Reading a Graph (3 points)

The graph of a function g is shown. g(x) = x + 1 except at x = 3.

1. Find lim_x→3 g(x). (1 point)
2. Find g(3). (1 point)
3. Is g continuous at x = 3? Explain. (1 point)

Question 8 Two Limits (2 points)

Find each limit.

1. lim_x→−2 x² + x − 2x + 2 (1 point)
2. lim_n→∞ 4n + 7n + 1 (1 point)

Question 9 Bouncing Ball (2 points)

A ball is dropped from 8 feet. Each rebound reaches 3/4 of the previous height. Find the total distance the ball travels before it stops.