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.

Is there an answer key?

Yes, every sheet can be printed with answers.

Are these grade 10 math worksheets free?

Yes, free to print as PDF, with no account.

Grade 10Common Core (CCSS) · Math

Aligned with the Common Core State Standards · All grades

Math · Grade 1010th Grade Math Worksheets — Geometry

A ready-made mixed sheet for grade 10 at the top, and a practice pack below: Geometry: similarity, the Pythagorean theorem, right-triangle trigonometry, circles, distance, quadratic functions and polynomial equations.

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Mixed review of all areas · Grade 10

Name: ____________________

Worked examples

Similarity and scale factor

Similar figures have the same shape; every side is scaled by the same scale factor.
Scale factor = matching side in the new figure / side in the first. Example: DE / AB = 24 / 12 = 2.
Multiply the known side by the scale factor: EF = BC · 2 = 16 · 2 = 32 cm.

Distance between points

The goal: work out the straight-line distance between two points on a grid.
Distance between two points: √((x₂ − x₁)² + (y₂ − y₁)²).
Example: (1, 2) and (4, 6). Differences: 4 − 1 = 3 and 6 − 2 = 4.
√(3² + 4²) = √(9 + 16) = √25 = 5. It's Pythagoras in the coordinate system!
Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓

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.

Quadratic functions and zeros

Find two numbers whose sum and product match the coefficients: write (x − a)(x − b).
The zeros are x = a and x = b.
Example: x² − 5x + 6 = (x − 2)(x − 3), so x = 2 and x = 3.

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.

Triangle area, sine and cosine rules

Area: A = ½ · a · b · sin C.
Cosine rule: c² = a² + b² − 2ab · cos C.
Sine rule: a / sin A = b / sin B, so b = a · sin B / sin A.

Inequalities

Solve like an equation: move terms and divide.
Dividing by a negative number flips the inequality.
Example: 5 − 2x > 11 gives −2x > 6, so x < −3.

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.

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.

A 5 m tall flagpole casts a 5 m long shadow. At the same time a tree casts a 12.5 m long shadow. How tall is the tree? Answer with the correct unit.

Distance between (5, 4) and (17, 13) =

A bracket is shaped like a right triangle. Find the opposite side: hypotenuse 9 cm, angle 69° (1 decimal) Answer with the correct unit.

Find the zeros: y = x² − 3x − 28

Calculate: A circle with center (0, 0) passes through (7, 24). Find the radius.

Find the third side (cosine rule): sides 6 cm and 8 cm, angle between them 107° (1 decimal)

Distance between (0, 3) and (−5, 15) =

Solve: 3x + 2 > 11

Triangles ABC and DEF are similar: A matches D, B matches E and C matches F. So side AB matches DE and side BC matches EF. AB = 16 cm, DE = 32 cm and BC = 14 cm. Calculate EF.

10.

Calculate u + v: u = (-1, -9), v = (3, -9)

11.

A support is shaped like a right triangle. Find the opposite side: hypotenuse 32 cm, angle 38° (1 decimal) Answer with the correct unit.

12.

Solve: x³ = 64x

13.

Calculate: A circle with center (0, 0) passes through (8, 15). Find the radius.

14.

Calculate u + v: u = (7, -2), v = (2, 6)

15.

Distance between (1, 1) and (−20, 21) =

16.

A 3 m tall flagpole casts a 4 m long shadow. At the same time a tree casts a 12 m long shadow. How tall is the tree? Answer with the correct unit.

17.

A 4 m tall flagpole casts a 4 m long shadow. At the same time a tree casts a 6 m long shadow. How tall is the tree? Answer with the correct unit.

18.

Find the adjacent side: hypotenuse 16 cm, angle 62° (1 decimal)

19.

A ramp model is shaped like a right triangle. Find the adjacent side: hypotenuse 17 cm, angle 52° (1 decimal) Answer with the correct unit.

20.

Find the opposite side: hypotenuse 21 cm, angle 25° (1 decimal)

Answer key

1. 12.5 m
2. 15
3. 8.4 cm
4. x = -4, x = 7
5. r = 25
6. 11.3 cm
7. 13
8. x > 3
9. EF = 28 cm
10. (2, -18)
11. 19.7 cm
12. x = -8, x = 0, x = 8
13. r = 17
14. (9, 4)
15. 29
16. 9 m
17. 6 m
18. 7.5 cm
19. 10.5 cm
20. 8.9 cm

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Geometry · 3

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Exercise type: Mixed review of all areas
Grade: 10 (ages 15–16)
Difficulty: Medium
Number of tasks: 20
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Paper size: US Letter

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Area: Review
Exercise type: Mixed review of all areas
Grade: 10 (ages 15–16)
Difficulty: Medium
Number of tasks: 20
Task format: Mixed
Paper size: US Letter

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This page gathers typical high school topics for grade 10: Geometry: similarity, the Pythagorean theorem, right-triangle trigonometry, circles, distance, quadratic functions and polynomial equations. 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 10: Linear functions · Systems of equations · Powers & roots · Interest & percent change · Pythagorean theorem · Quadratic functions · Trigonometry · Vectors · Exponential functions · Statistics · Inequalities · Equation of a circle

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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 10 maths?: Typically Geometry: similarity, the Pythagorean theorem, right-triangle trigonometry, circles, distance, quadratic functions and polynomial equations.
Is there an answer key?: Yes, every sheet can be printed with answers.
Are these grade 10 math worksheets free?: Yes, free to print as PDF, with no account.