# Tenth grade math test

Name _____________________ Date:_____________________

**Solve the following problems**

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

**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?

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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.

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

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

a. Equilareral 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

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

**12.** Graph poins 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!

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

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

**16.**

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

b. 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.

**18.** Write an equation of a line parallel and perpendicular to y = 12x - 4 and 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.**

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

**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. Rotage 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?

**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

**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 tall, the shadow of his son standing next to him is only 6 feet. 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

**28.**
When the length of 1 side of 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

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

**31.** Use the triangle below to find x

**32.**
Which statement 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 that of the cylinder. Try to explain why this is the case without doing any math computation.

**34. **For the shape below

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

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

**39.** Which figure has 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