7th Grade Math Pre-Algebra Unit 4 - Algebra and Geometry

The square root of - 64 is:
1. - 8
2. 8
3. A negative number has no square root.
4. + 8 or - 8
Check which statements below are true for rational numbers.
1. These numbers can be expressed as a fraction.
2. These numbers are not termimnating or repeating decimals.
3. These numbers are terminating or repeating decimals.
4. All square roots are rational numbers.
5. Rational numbers are part of the set of Real Numbers.
6. A whole number is always a rational number.
Solve the following equation:

0.0016 = x²

x = _____
Check the statements below that are correct:
1. √25 is a rational integer
2. -3.4 > - √10
3. √85 < 9.3
4. A fraction can only be classified as a rational number.
5. The greatest number of:
  - √17, 4 1/3, 4.42, 17/4
  is 4.42
Solve the folowing equation for a to the nearest whole number where b = 8:

a² = b³/126

a = ______________
Check the statements below that are correct:
1. The measure of an acute angle is between 90^o and 180^o.
2. The measure of an obtuse angle is between 90^o and 180^o.
3. The measure of a right angle is equal to 90^o
4. The measure of a straight angle is 360^o
5. The measure of an acute angle is between 0^o and 90^o.
Using your protractor you measure an angle that is 132^o. This angle is:
1. a right angle
2. an obtuse angle
3. an acute angle
4. a straight angle
The sum of the measures of the three angles is a triangle is always _______ degrees
In an acute triangle, all of the angles are ___________ 90^o
1. less than
2. equal to
3. greater than
Congruent sides means the sides have the same __________.
A scalene triangle has _________ congruent sides.
1. two
2. three
3. no
In an equilateral triangle, the measure of each angle is always the same.
1. True
2. False
An isoceles triangle has __________ congruent sides.
1. one
2. two
3. three
4. no
The length of one side of a right triangle is 6 cm. The length of its hypotenuse is 10 cm. What is the length of the remaining side?

_________ cm
The hypotenuse of a right triangle that is also an isoceles triangle is the square root of 288 ft. What is the length of each side of this triangle?

______ ft
What is the distance between the following pair of points:

A( -2 3/4, 8) , B( 7 1/2 , - 6)

Round to the nearest tenth.

Distance = ___________ units
What are the coordinates of the midpoint of the following line segment:

C(14, - 5) , D(- 8, 13)

The coordinates of the midpoint of CD is _________
What is the midpoint of the hypotenuse of a right triangle is its other two sides are 9 ft and 16 ft long?
Give your answer to the nearest whole number.

The midpoint is ______ ft from one of the vertices.
Check the true statements below:
1. Similar triangles have both the same shape and the same size.
2. Similar triangles have corresponding sides and corresponding angles.
3. The correspponding angles of similar triangles have the same measure.
4. The corresponding sides of similar triangles are not proportional.
5. If two triangles have corresponding sides that are proportional, and corresponding angles that have the same measure, those triangle are similar.
Triangles ABC and JKL are similar triangles.

The length of side AB is 5 in, and the length of its corresponding side JK is 15 in.
If the length of side BC is 7 in, what is the length of its corresponding side KL?

_______ in
Beth is trying to figure out how high her school is. Starting at the front door, she walks 150 ft. from the school. Using her protractor she figures that the angle between the line from her position back to the base of the school and the line going from her position to the top of the school is 32^o.

How tall is the school to the nearest ft?
In a right triangle with a hypotenuse of 45 in, , what is the length of the side opposite the angle that mesures 23^o?

Give your answer to the nearest tenth of an in.

______ in
The tangent of an angle is the ratio of the measure of the opposite leg to the measure of the adjacent leg.
1. True
2. False
Draw a right triangle that has one leg that is 30 cm, one leg that is 16 cm, and a hypotenuse that is 34 cm.

Look at the angle, A, between the 16 cm leg and the 34 cm hypotenuse.

For the angle A, which Trigonometric ratio is the greatest?
1. sin A
2. cos A
3. tan A
One of the angles of a right triangle is 64^o. The adjacent side of this angle is 14 ft. What is the length of the opposite side from this angle.

Give your answer to the nearest whole number.

Opposite side = ________ ft.
Check the correct statements below:
1. If the sum of the measures of two angles is 90^o, the angles are supplementary.
2. The two pairs of opoosite angles formed when two line intersect are called vertical angles.
3. For two angles to be complimentary, the sum of the measure of these two angles must be 90^o.
4. Adjacent angles have a common vertex, but they do not have a common side.
5. Right angles are formed at the intersection of two perpendicular lines.
What is the measure of angle 2 in the following figure>

______ degrees
If angles A and B are complimentary, and if

m∠ A = x - 8, and m∠ B = x + 6,

what is m∠ B ?

________ degrees
Check which statements below are true about congruent triangles:
1. The may not be the same size.
2. They are always the same shape.
3. Their corresponding angles are equal.
4. Their corresponding sides may not be equal.
5. If you know the length of the side in one traingle, you know the length of its corresponding side in the other triangle.
If Δ ABC ≅ Δ JKL, then which statements below are true?

(The symbol ≅ means "congruent with" )

It will be helpful if you sketch these triangles on a piece of paper.
1. AB ≅ JK
2. ∠ ACB ≅ ∠ LJK
3. ∠ CBA ≅ ∠ LKJ
4. BC ≅ LJ
5. The measure of (AB + BC + CA) = the measure of (JK + KL + LJ)
In a ____________, you flip a figure over a lilne in the coordinate plane.
1. rotation
2. translation
3. reflection
4. dilation
You are asked to translate a figure in a coordinate plane 7 units to the right and 3 units down.

Which statements best describes this translation?
1. (x,y) → (x - 7, y - 3)
2. (x,y) → (x + 7, y - 3)
3. (x,y) → (x - 7, y + 3)
4. (x,y) → (x + 7, y + 3)
Dilations change the ______ of a figure in a coordinate plane.
The sum of the angle measures in a rectangle is always _______^o
What is the area in units of the following figure?

_______ units
In the following trapezoid, the bottom is 5 in, the top is 8 in, and the height is 6 in.

What is the area of this trapezoid? _______ sq in
In the following figure, which shapes are polygons?
1. A
2. B
3. C
4. D
5. E
If the diameter of a circle is 14 miles, then the area of this circle is about ________ sq mi.

(Round your answer to the nearest whole sqaure mile.)
The sum of the measures of the interior angles of an 8 sided polygon is n times 360^o.
n = ______
In a circle, Π is:

( Π is the symbol for Pi.)
1. the ratio of the measure of the diameter of the circle to the measure of its radius.
2. the ratio of the the measure of the radius of the circle to the measure of its circumference.
3. the ration of the the measure of the circumference of a circle to the measure of its radius.
4. the ratio of the the measure of the circumference of a circle to the measure of its diameter.
A pyrimid is a polyhedron with one base that is any polygon and its other faces are all ____________.
Check the statements below that are true:
1. E is a circular prism.
2. C is a pyramid.
3. The bases of B are congruent.
4. A is a prism.
5. D is a pyramid.
The volume of a prism or a cylinder is:
1. 1/2 the area of the base times the height
2. 1/3 the area of the base times the height
3. the area of the base times the height
4. the sum of the areas of the faces
Find the volume of the following solid.

-------- cu in
What is the volume of the following solid?

Round your answer to the nearest tenth of a cu in.

___________ cu in
What is the area of the following solid whose 2 faces are equilateral triangles?
The dimensions of the base are shown on the right.

_______ sq in
Sketch a pyramid with the following properties:

The base is a square that is 15 m on each side.
The lateral height of each face is 28 m.
What is the surface area of this pyramid?

_________ sq m
The slant height of a cone can be measured from any point on the base. It is the distance from that point to the tip of the cone.
1. True
2. False
What is the surface area of the following cone?

Round your answer to the nearest hundreth of a sq cm.
You have two similar cylinders. The radius of one cylinder is 4 ft. The radius of the other cylinder is 28 ft. If the length of the first cylinder is 100 ft, what is the length of the other cylinder?

______ ft.