Construction

See pp. 102, 123, 222.

1. Draw a right triangle with the hypotenuse 4 inches long and an angle of 65°.

2. Draw an isosceles triangle with one of the equal sides 3 inches long and with an angle of 95°.

3. Draw a line 3 inches long. Regarding this line as a diagonal of a square, construct the square.

4. Draw a line 4 inches long. Regarding this line as a diagonal of a parallelogram, construct the parallelogram. 5. Draw a line 4 inches long. Regarding this line as

a diagonal of a trapezoid, construct the trapezoid.

6. Construct a regular pentagon with sides 18 inches. long. Find the center of the figure and find the area of the pentagon.

7. Construct a regular hexagon with sides 21 inches long. Find the center and the area of the hexagon.

8. Make a square 3 inches long. Draw the diagonals. With a radius equal to the distance from the center to the middle point of one side, inscribe a circle. With a radius equal to one half of the diagonal of the square, circumscribe a circle. Find the area of the inscribed circle. Find the area of the circumscribed circle. Find the area of the space between the inscribed circle and the circumscribed circle.

9. Make a circle with a radius 2 inches long. Draw the diameters perpendicular to each other. Draw straight lines connecting the extremities of the diameters. What figure is formed by the lines? Inscribe a circle within the square. Find the area of the circumscribed circle. Find the area of the inscribed circle. Find the area of the square.

Review

1. Add twenty-seven and thirty-five hundredths; one hundred five and fifteen thousandths; two hundred five hundred-thousandths.

2. Add one thousand twenty and seventeen thousandths; twenty-five thousand and twenty-five thousandths; seven and two hundred-eight ten-thousandths.

3. From one thousand nine hundred and thirty-eight thousandths take eight hundred-forty and four hundredths.

4. From twelve thousand and twenty-four ten-thousandths take seven thousand four and nine thousandths.

Original Problems

Make problems and solve them:

1. A square is inscribed in a circle whose radius is 8 inches.

2. A circle is inscribed in a square that is 4 feet square.

3. The heart of an average person pumps 6 ounces of blood at each beat.

4. A cannon ball weighing 20 pounds is moving at the rate of 600 feet a second.

5. A square lot of land contains 9216 square feet.

6. A cubical block contains 15,625 cubic inches.

7. A ball weighing 20 pounds rolls at the rate of 10 feet a second. Another weighing 8 pounds meets it, coming in the opposite direction, at the rate of 15 feet a second.

8. A locomotive weighing 50 tons is moving at the rate of 20 miles an hour.

9. A merchant's price for goods was 30% above cost, but he discounted this price 10%.

10. 20% is gained by selling cloth at 30 cents a yard. 11. A fraction, when squared, becomes 2.

12. A fraction, when cubed, becomes 216

343

13. The diameter of a sphere is 18 inches.

14. The circumference of a sphere is 44 inches.

15. A 12-inch cubical block is turned in a lathe so as to form a sphere.

16. A certain farm is 25 chains long, and 22 chains 2 rods wide.

17. A cellar is dug 36 feet long, 22 feet wide, and 6 feet deep.

25. Find a mean proportional between 5 and 20.

26. Find a mean proportional between 16 and 36.

27. If 7 pencils cost 12 cents, how much will 25 pencils cost at the same rate?

28. If 5000 yards of cloth are manufactured at a certain mill each day, when the mill runs 9 hours a day, how many yards will be manufactured when the mill runs 101⁄2 hours a day.

29. If 9 men can do a piece of work in 5 days, in how many days can 4 men do the same work?

30. If 8 men can paint 5 houses in a week, how many can 40 men paint in the same time?

Problems for Arithmetic or Algebra

1. The difference between and of a certain number What is the number?

is 15.

2.

and of a certain number equals 22. What is the number?

3. If from of my age remainder will be 6 years.

of my age is subtracted, the How old am I?

4. Divide $15 between 2 men, giving the first $3 more than of what the second receives.

5. In a school there are 420 pupils. There are twice as many girls as boys. How many are there of each?

6. The difference between two numbers is 6, and their sum is 20. What are the numbers?

7. A boy having a certain number of tops lost 5 and bought 8, and then had 12. How many had he at first?

8. A boy having a certain number of cents earned 12 more and spent 16, and then had 25. How many had he at first?

9. A man spent much as he had left.

How much had he at

of his money, and then earned as He then had $10 more than at first. first?

How

10. In an orchard there are 7 more than twice as many apple trees as pear trees. In all there are 133 trees. many are there of each kind ?

11. The difference of two numbers is 24, and the smaller number equals of the larger number. What are the numbers?

12. The difference of two numbers is 12, and the numbers are to each other as 7 to 10. What are the numbers? Let 7 x = one number and 10x the other. 10 x-7 x = 12.