### Algebra

Solve each equation:

*x*+ 5 = 12- 3
*x*+ 6 = 18 *x*= 7

Now, solve these problems with signed numbers.

- 1 – 3(–4) =
*x* - –3
*x*+ 6 = –18 - – + 3 = –7

Evaluate these expressions.

- 4
*a*+ 3*b*;*a*= 2 and*b*= –1 - 3
*mn*– 4*m*+ 2*n*;*m*= 3 and*n*= –3 - –2
*x*–*y*+ 4*z*;*x*= 5,*y*= –4, and*z*= 6 - The volume of a cylinder is given by the formula
*V*= π*r*^{2}*h*, where*r*is the radius of the base and*h*is the height of the cylinder. What is the volume of a cylinder with a base radius of 3 and height of 4? (Leave π in your answer.)

Use the previous rules to solve these problems in squares and square roots.

- (3 +
*x*)^{2}= 49

### Geometry

These word problems require you to find the measures of angles.

- In order to paint the second story of his house, Alex leaned a ladder against the side of his house, making an acute angle of 58° with the ground. Find the size of the obtuse angle the ladder made with the ground.
- Confusion Corner is an appropriately named intersection that confuses drivers unfamiliar with the area. Referring to the street plan on the right, find the size of the marked angle.

Determine the measure of the marked angles.

Find the perimeters for these word problems:

- Maryellen has cleared a 10-foot-by-6-foot rectangular plot of ground for her herb garden. She must completely enclose it with a chain-link fence to keep her dog out. How many feet of fencing does she need, excluding the 3-foot gate at the south end of the garden?
- Terri plans to hang a wallpaper border along the top of each wall in her square dressing room. Wallpaper border is sold only in 12-foot strips. If each wall is 8 feet long, how many strips should she buy?

Find the area of the following triangles:

Find the missing angles

Find the perimeter and area of each triangle (Hint: Use the Pythagorean theorem):

- Irene is fishing at the edge of a 40-foot-wide river, directly across from her friend Sam, who is fishing at the edge of the other side. Sam's friend Arthur is fishing 30 feet down the river from Sam. How far is Irene from Arthur?

Following are two word problems involving perimeters of quadrilaterals:

- What is the length of a side of a square room whose perimeter is 58 feet?
- 8 ft.
- 14 ft.
- 14.5 ft.
- 29 ft.
- 232 ft.

- Find the dimensions of a rectangle with perimeter of 16 feet and whose long size is three times its short side.
- 4 ft. by 4 ft.
- 4 ft. by 12 ft.
- 3 ft. by 5 ft.
- 2 ft. by 6 ft.
- 2 ft. by 8 ft.

Now, try some area word problems:

- Tristan is laying 12-inch by 18-inch tiles on the laboratory floor. If the lab measures 15 feet by 18 feet, how many tiles does Tristan need, assuming there's no waste? (Hint: Do all your work in either feet or inches.)
- 12
- 120
- 180
- 216
- 270

- What is the length in feet of a rectangular parking lot that has an area of 8,400 square feet and a width of 70 feet?
- 12
- 120
- 1,200
- 4,000
- 4,130

These word problems require you to find the circumference:

- What is the circumference of a circular room whose diameter is 15 feet?
- 7.5π ft.
- 15π ft.
- 30π ft.
- 45π ft.
- 225π ft.

- What is the approximate circumference of a round tower whose radius is feet?
- 10 ft.
- 20 ft.
- 33 ft.
- 40 ft.
- 48 ft.

- Find the circumference of a water pipe whose radius is 1.2 inches.
- 1.2π in.
- 1.44π in.
- 2.4π in.
- 12π in.
- 24π in.

- What is the area in square inches of the bottom of a beaker with a diameter of 6 inches?
- 6π
- 9π
- 12π
- 18π
- 36π

- James Band is believed to be hiding within a 5-mile radius of his home. What is the approximate area, in square miles, of the region in which he may be hiding?
- 15.7
- 25
- 31.4
- 78.5
- 157

- If a circular parking lot covers an area of 2,826 square feet, what is the size of its radius? (Use 3.14 for π.)
- 30 ft.
- 60 ft.
- 90 ft.
- 450 ft.
- 900 ft.

**a.****e.****d.****e.**- 10
- 6
- 200
**a.****b.**- 15
**c.****e.****c.****b.****d.****b.**- 4
- 8.305
- 0.907
- 1.456
**b.****d.**- .03
- .3392
- .70104
**e.****e.**- 1.4
- 128
- 572
- 1,400
**b.****c.**- 45%
- 0.8%
- 0.12
- 0.875
- 2.5
- 52%
- 9.1
- 75
- 50%
- 300%
- 100
- 8
- 10
**c.****c.****c.****d.****c.****c.****b.**- 24
- 30
- 1,600
- 2.94
- 8 ft.
- 21 km 170 m
- 1 ft. 4 in.
- 7 cm 8 mm
- d.
- b.
- d.
- 7
- 4
- 28
- 13
- 8
- 40
- 5
- –45
- 16
- 36π
- 6
- 7
- 16
- 4
- 122°
- 20°
- 60°
- 91° (The horizontal lines are not parallel.)
- 29 feet
- 3 strips (She will have some extra.)
- 12 square units
- 18 square units
- J = L = 70°
- N = 80°
- Perimeter = 6 + units
- Perimeter = 30 units
- 50 feet
- c.
- d.
- c.
- b.
- b.
- b.
- c.
- b.
- d.
- a.

Try these word problems on the area of a circle:

### Word Problems Answers

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### Decimals Answers

### Percents Answers

### Averages Answers

### Length and Time Answers

### Algebra Answers

### Geometry Answers

Area = 4.5 square units

Area = 30 square units

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