10th Grade Math Test

Print your 10th grade math test before you start.

The test has 40 questions, but it is very comprehensive! For those who love math, I promise fun and challenges with this 10th grade math test.

In this test, you will practice

  • Logic: conditionals, converse, inverse, contrapositive and indirect proof
  • Angles, parallel lines, polygons and circles
  • Triangles: congruence, similarity, right triangles and trigonometry
  • Coordinate geometry, transformations and symmetry
  • Perimeter, area, surface area and volume

Questions 1 to 10

1. What is the perimeter and area of the following running track?

Running track: a rectangle 12 long and 9 wide with a half circle on each short side

2. Sentence: A square is a rectangle

a. Write the sentence as a conditional and identify the hypothesis and the conclusion.

b. Write the converse of the conditional and say if the sentence is a biconditional.

c. Write the inverse and the contrapositive of the conditional and investigate the truthfulness of the inverse and the contrapositive.

3. The measure of an angle is four times as large as its supplement. What is the measure of its supplement?

4. Which line or lines are perpendicular to the line y = 6x − 8?

  • a. y = 6x + 1
  • b. x − 6y = 9
  • c. x + 6y = −3
  • d. y = −6x − 1

5. Find two angles that are supplementary and vertical at the same time.

6. What is the measure of an exterior angle of a regular 10-gon?

7. In the figure below, line n is parallel to line m. Find the measure of all angles inside line n and line m.

Parallel lines n and m cut by two transversals, with angles marked 130°, 4x° and 6x°

8. Find the volume and surface area of a sphere with a radius of 4 cm.

9. What kind of triangle is the one below? Find all 3 angles.

Triangle with a right angle and tick marks on its two legs
  • a. Equilateral
  • b. Right
  • c. Right isosceles
  • d. Scalene

10. In triangle UVW, UV = 9, VW = 7, and UW = 11. Which angle is the biggest?

  • a. Angle U
  • b. Angle V
  • c. Angle W
  • d. not enough information

Questions 11 to 20

11. The surface area of sphere A is 4 times larger than the area of sphere B. How big is the volume of sphere A compared to sphere B?

12. Graph points A (−3, 3), C (4, −3), and D (4, 3). Name the figure and show that segment AD is perpendicular to segment CD. Write equations for all 3 segments.

13. Show all medians and all heights of this triangle. No construction with straightedge and compass is needed!

Obtuse triangle

14. The length of the hypotenuse of an isosceles right triangle is 10 inches. What is the length of one leg?

15. Find the volume and surface area of a rectangular prism 3 cm by 5 cm by 10 cm.

16.

Building with a line from its top to a point 30 meters away on the ground, making a 60° angle with the ground

Use the trigonometric ratio to find the height of this building to the nearest tenth.

Right triangle ABC with the right angle at C, CA = 4 and CB = 12

Which expression will yield the biggest value?

  • a. sin A
  • b. cos A
  • c. tan A
  • d. tan B

17. Tell which congruence postulate can be used to prove congruence. Write down SSS, SAS, ASA, or AAS beneath each triangle. If you cannot prove congruence, write N/A.

Two pairs of triangles with marked equal sides and angles
Two more pairs of triangles with marked equal sides and angles

18. Write an equation of a line that is parallel to y = 12x − 4 and an equation of a line that is perpendicular to it, both passing through (1, 0).

19. What is the standard equation of a circle with center (3, −4) and radius 2?

  • a. (x − 3)2 + (y − 4)2 = 4
  • b. (x − 3)2 + (y + 4)2 = 4
  • c. (x − 4)2 + (y − 3)2 = 4
  • d. (x − 3)2 + (y + 4)2 = 2

20.

Circle with a tangent line and a triangle, angle x marked outside the circle and an angle marked in red

If the angle in red is equal to 50 degrees, what is the measure of angle x?

Questions 21 to 30

21. Graph the triangle X (−2, 2), Y (3, 2), and Z (5, 5).

a. Find the image of triangle XYZ under the translation (x − 3, y − 4)

b. Reflect triangle XYZ across the x-axis.

c. Rotate triangle XYZ 270 degrees counterclockwise about X

d. Dilate triangle XYZ by a factor of 2

22. What is the volume of the figure below?

Rectangular prism 8 by 2 by 4 with a half cylinder on top

23. If the clock says 4:00 PM, what is the measure of the angle formed by the hands?

24. Find the measure of angle a

Circle with chord AB and a tangent line at A, angle a between them, and arc marked 240°

25. Write an equation of the circle with center (−4, 5) and passing through the point (−2, 5)

26. A man is 6 feet tall. When his shadow is 8 feet long, the shadow of his son standing next to him is only 6 feet long. Make a drawing and find out how tall the son is in feet and inches.

27. Use the triangle below to find the lengths of AB and CD

Right triangle ABD with the right angle at D, point C on BD, AC = 12 m, angle B = 30° and angle ACD = 45°

28. When the length of 1 side of a hexagon is 3 meters, the area is 23.38 square meters. What is the area if the hexagon has a side length of 6 meters?

29. Use the triangle below to find y

Right triangle with the altitude drawn to the hypotenuse, hypotenuse parts 4 and 12, and leg y

30. Two sides of a triangle measure 15 and 20. If the angle between these sides is 60 degrees, find the area of the triangle.

Questions 31 to 40

31. Use the triangle below to find x

Triangle with a midsegment 6x and a base 10x + 4

32. Which statements will turn a parallelogram into a rhombus?

a. The diagonals bisect each other.

b. Opposite angles are equal

c. 4 equal sides

d. Opposite sides are equal

e. The diagonals are perpendicular

  • a and b
  • b and c
  • a and e
  • c and e
  • b and d

33. The volume of a cone is one-third the volume of a cylinder with the same base and height. Try to explain why this is the case without doing any math computation.

34. For the shape below

Ice cream cone: a circle on top of a cone with a 40° angle at the tip, the circle touching the cone at A and B, and angle x marked

a. Find the angle x

b. Suppose that the circle represents 1 scoop of ice cream and it weighs 4 ounces. Estimate how much of the ice cream is inside the cone. Hint: The portion that is inside is shown with a blue arc.

35. A boat is traveling west on a river with a speed of 50 miles per hour. The river flows directly south with a speed of 10 miles per hour. What is the boat's resultant speed and direction?

36. How many lines of symmetry are in a regular hexagon?

37. Use the figure below to find x

Two secants from the same outside point: one with outside part 12 and inside part 16, the other with outside part 14 and inside part x

38. Use indirect proof to show that any triangle must have at the most 1 right angle

39. Which figure has rotational symmetry?

Two figures in circles to compare for rotational symmetry

40. Find the surface area of a hexagonal pyramid if one side of the base is equal to 8 inches and the slant height is 12 inches.

Things you need to keep in mind about the 10th grade math test

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