10th Grade Precalculus Practice: Questions, Answers and Tips

Looking for 10th grade precalculus practice? Below are worked examples, the mistakes students make most, and practice questions with an answer key.

Every example below comes from BAMS Academy's Precalculus practice, the same questions students answer on the site.

Precalculus in 10th grade, skill by skill

Functions, sequences, and preparing for calculus. BAMS Academy breaks the unit into the skills below (part of all 10th grade math topics). Each comes with one of its practice questions.

Find terms and sums of arithmetic sequences

An arithmetic sequence starts at 10 with a common difference of 2. What is the 5th term? (Choices: 42; 18; 19; 20.)

Answer: 18. Aₙ = a₁ + (n − 1)d = 10 + (5 − 1)(2) = 18.

An arithmetic sequence starts at 5 with a common difference of 4. What is the 9th term? (Choices: 41; 37; 38; 44.)

Answer: 37. Aₙ = a₁ + (n − 1)d = 5 + (9 − 1)(4) = 37.

Find terms and sums of geometric sequences

A geometric sequence starts at 3 with a common ratio of 3. What is the 5th term? (Choices: 243; 81; 15; 729.)

Answer: 243. Aₙ = a₁ × r^(n−1) = 3 × 3^4 = 243.

A geometric sequence starts at 5 with a common ratio of 2. What is the 5th term? (Choices: 40; 13; 80; 160.)

Answer: 80. Aₙ = a₁ × r^(n−1) = 5 × 2^4 = 80.

Evaluate a composite function f(g(x))

If f(x) = 5x + 3 and g(x) = 4x + 5, what is g(f(5))? (Choices: 117; 25; 128; 53.)

Answer: 117. First find f(5) = 5(5) + 3 = 28. Then g(28) = 4(28) + 5 = 117.

If f(x) = 5x + 9 and g(x) = 2x + 1, what is f(g(5))? (Choices: 64; 34; 45; 69.)

Answer: 64. First find g(5) = 2(5) + 1 = 11. Then f(11) = 5(11) + 9 = 64.

Worked examples

Example 1

Question: A savings account starts with $197 and increases by $13 every month (no interest). How much is in the account after 3 months?

1. $223
2. $26
3. $236
4. $591

How to solve it: Balance = first + (n − 1) × increase = 197 + (3 − 1)(13) = 223.

Answer: $223

Why the other choices don't work:

• A student who picks "$26" usually reported only the total increase, forgetting the starting balance.
• A student who picks "$236" usually used n months of increases instead of (n-1) — the first month has no increase yet.
• A student who picks "$591" usually multiplied the starting amount by the number of months.

Example 2

Question: A savings account starts with $55 and increases by $18 every month (no interest). How much is in the account after 3 months?

1. $36
2. $109
3. $91
4. $165

How to solve it: Balance = first + (n − 1) × increase = 55 + (3 − 1)(18) = 91.

Answer: $91

Why the other choices don't work:

• A student who picks "$36" usually reported only the total increase, forgetting the starting balance.
• A student who picks "$109" usually used n months of increases instead of (n-1) — the first month has no increase yet.
• A student who picks "$165" usually multiplied the starting amount by the number of months.

Common mistakes to watch for

• Question: An arithmetic sequence starts at 3 with a common difference of 3. What is the 4th term? (Choices: 13; 12; 15; 10.)

  Answer: 12.

  A student who picks "15" usually used n instead of (n-1) steps from the first term.

• Question: An arithmetic sequence starts at 9 with a common difference of 6. What is the 5th term? (Choices: 39; 34; 33; 42.)

  Answer: 33.

  A student who picks "42" usually confused the common difference with the first term.

• Question: A geometric sequence starts at 3 with a common ratio of 3. What is the 5th term? (Choices: 243; 81; 15; 729.)

  Answer: 243.

  A student who picks "15" usually multiplied by the ratio n times additively instead of exponentially.

• Question: A geometric sequence starts at 5 with a common ratio of 2. What is the 5th term? (Choices: 40; 13; 80; 160.)

  Answer: 80.

  A student who picks "160" usually used n as the exponent instead of (n-1).

• Question: If f(x) = 5x + 3 and g(x) = 4x + 5, what is g(f(5))? (Choices: 117; 25; 128; 53.)

  Answer: 117.

  A student who picks "128" usually computed f(g(x)) instead of g(f(x)) — applied the functions in the wrong order.

• Question: If f(x) = 5x + 9 and g(x) = 2x + 1, what is f(g(5))? (Choices: 64; 34; 45; 69.)

  Answer: 64.

  A student who picks "69" usually computed g(f(x)) instead of f(g(x)) — applied the functions in the wrong order.

Try these practice questions

1. An arithmetic sequence starts at 3 with a common difference of 3. What is the 4th term?

   1. 13
   2. 12
   3. 15
   4. 10

2. An arithmetic sequence starts at 9 with a common difference of 6. What is the 5th term?

   1. 39
   2. 34
   3. 33
   4. 42

3. A savings account starts with $88 and increases by $46 every month (no interest). How much is in the account after 9 months?

   1. $456
   2. $792
   3. $368
   4. $502

4. An arithmetic sequence starts at 6 with a common difference of 2. What is the 8th term?

   1. 21
   2. 20
   3. 44
   4. 22

5. An arithmetic sequence starts at 8 with a common difference of 5. What is the 5th term?

   1. 33
   2. 29
   3. 28
   4. 37

6. A savings account starts with $75 and increases by $43 every month (no interest). How much is in the account after 7 months?

   1. $525
   2. $258
   3. $376
   4. $333

Answer key

1. 12 — Aₙ = a₁ + (n − 1)d = 3 + (4 − 1)(3) = 12.
2. 33 — Aₙ = a₁ + (n − 1)d = 9 + (5 − 1)(6) = 33.
3. $456 — Balance = first + (n − 1) × increase = 88 + (9 − 1)(46) = 456.
4. 20 — Aₙ = a₁ + (n − 1)d = 6 + (8 − 1)(2) = 20.
5. 28 — Aₙ = a₁ + (n − 1)d = 8 + (5 − 1)(5) = 28.
6. $333 — Balance = first + (n − 1) × increase = 75 + (7 − 1)(43) = 333.

Keep practicing

The fastest way to build confidence is a few questions at a time, with feedback on each answer. Start with Precalculus practice for grade 10, where every question comes with a step-by-step explanation.

More from BAMS Academy:

• All 10th grade math topics
• Geometry practice
• Algebra I practice
• BAMS Academy math practice by grade
• Every 10th grade subject