Grade 12Common Core (CCSS) · Math
Aligned with the Common Core State Standards · All grades
Math · Grade 1212th Grade Math Worksheets — Precalculus & Calculus
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Mixed review of all areas · Grade 12
Name: ____________________Worked examples
Derivatives of polynomials
- Differentiate term by term: axⁿ becomes n·a·xⁿ⁻¹, constants become 0.
- Put the x-value into f′(x).
- Example: f(x) = x³ + 2x gives f′(x) = 3x² + 2, so f′(1) = 5.
Arithmetic sequences
- Each term grows by d.
- aₙ = a₁ + (n − 1)·d; sum = n·(a₁ + aₙ)/2.
- Example: a₁ = 3, d = 4 gives a₁₀ = 3 + 9·4 = 39.
Definite integrals
- Find an antiderivative: axⁿ becomes a·xⁿ⁺¹/(n + 1).
- Calculate F(upper limit) − F(0).
- Example: ∫₀² 2x dx = [x²] = 4 − 0 = 4.
Polynomial equations
- x³ = a: take the cube root of both sides.
- x³ = kx: move everything to one side and factor out x, so x = 0 is one solution.
- (x − a)(x − b)(x − c) = 0: the zero-product property gives x = a, x = b and x = c.
Logarithms
- log_b(n) asks: which power of b gives n?
- Write n as a power of b.
- Example: log₂(8) = 3 because 2³ = 8.
Exponential growth and decay
- The growth factor is 1 + p/100 (or 1 − p/100 for a decrease).
- Multiply the start value by the factor to the power of the years.
- Example: 1,000 · 1.05³ ≈ 1,158.
The circle's equation
- The circle x² + y² = r² has centre at the origin and radius r.
- The radius is the distance between centre (h, k) and a point (a, b): r = √((a − h)² + (b − k)²).
- Example: centre (0, 0) through (3, 4) gives r = √(9 + 16) = 5.
Vectors
- Length: |(a, b)| = √(a² + b²).
- Sum: add the x- and y-coordinates separately.
- Dot product: u · v = u₁v₁ + u₂v₂. Example: (2, 3) · (4, −1) = 8 − 3 = 5.
Statistics: mean, median and standard deviation
- Mean = sum / count. Median = middle value when sorted.
- Range = largest − smallest.
- Standard deviation: square each deviation from the mean, average them and take the square root.
Trigonometry in right triangles
- sin v = opposite/hypotenuse, cos v = adjacent/hypotenuse.
- Multiply the hypotenuse by sin v or cos v.
- Example: 10 · sin 30° = 5 cm.
Find f′(2): f(x) = −4x³ + 6x² + 5x − 2
The plan counts minutes per week. The first amount is a₁ and the increase is d. Find the term: a₁ = 19, d = 3. a₂₇ = ? Answer with the correct unit.
Calculate the integral: ∫₀⁵ (−8x + 4) dx =
Solve: x³ = 64x
Solve: 10ˣ = 493 (2 decimals)
The model for club capital uses amounts in kr. Find the value: 2000 decreases by 7 % per year for 10 years (whole number) Answer with the correct unit.
The model for club capital uses amounts in kr. Find the value: 50,000 grows by 3 % per year for 3 years (whole number) Answer with the correct unit.
Calculate: A circle with center (0, 0) passes through (-6, 8). Find the radius.
Find f′(-1): f(x) = −2x³ + 3x² − 3x + 3
Calculate u + v: u = (-1, -9), v = (3, -9)
Calculate the integral: ∫₀⁵ (6x + 2) dx =
Find the range and median: 48, 11, 41, 33, 16, 23
Solve: 10ˣ = 219 (2 decimals)
A bracket is shaped like a right triangle. Find the adjacent side: hypotenuse 35 cm, angle 53° (1 decimal) Answer with the correct unit.
Find the value: 50,000 grows by 10 % per year for 7 years (whole number)
Find f′(-1): f(x) = 2x³ + x² − 4x − 2
Find f′(0): f(x) = −2x³ + 9x − 7
Calculate the integral: ∫₀² (4x + 1) dx =
Calculate the integral: ∫₀³ (8x) dx =
Calculate the integral: ∫₀³ (−6x) dx =
Answer key
- 1. -19
- 2. 97 min
- 3. -80
- 4. x = -8, x = 0, x = 8
- 5. x ≈ 2.69
- 6. 968 kr
- 7. 54,636 kr
- 8. r = 10
- 9. -15
- 10. (2, -18)
- 11. 85
- 12. 37; median 28
- 13. x ≈ 2.34
- 14. 21.1 cm
- 15. 97,436
- 16. 0
- 17. 9
- 18. 10
- 19. 36
- 20. -27
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- Mixed review of all areas
- Grade
- 12 (ages 17–18)
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Your choices
- Area
- Review
- Exercise type
- Mixed review of all areas
- Grade
- 12 (ages 17–18)
- Difficulty
- Medium
- Number of tasks
- 20
- Task format
- Mixed
- Paper size
- US Letter
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A ready-made mixed sheet for grade 12 at the top, and a practice pack below: Precalculus & Calculus: derivatives of polynomials, definite integrals, logarithms, exponential models, sequences, vectors and trigonometry.
How to use the tool
- Print the mixed sheet directly, or adjust level and number of tasks.
- Open each sheet in the practice pack for every topic.
- “Create new version” gives new numbers every time.
About this generator
This page gathers typical high school topics for grade 12: Precalculus & Calculus: derivatives of polynomials, definite integrals, logarithms, exponential models, sequences, vectors and trigonometry. Every sheet has an answer key calculated by the website. No sign-up and no personal data are needed.
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More sheets for grade 12: Derivatives · Integrals · Logarithms · Exponential functions · Polynomial equations · Inequalities · Sequences · Trigonometry · Sine & cosine rules · Vectors · Equation of a circle · Statistics
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Open each sheet, print it with answers, and you have a full week of math.
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Frequently asked questions
- How do I pick the right level?
- Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
- Can I see the problems before printing?
- Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
- How do I include an answer key?
- Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
- What does the question mark next to a problem do?
- It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
- What do students learn in grade 12 maths?
- Typically Precalculus & Calculus: derivatives of polynomials, definite integrals, logarithms, exponential models, sequences, vectors and trigonometry.
- Is there an answer key?
- Yes, every sheet can be printed with answers.
- Are these grade 12 math worksheets free?
- Yes, free to print as PDF, with no account.