194 REVIEW AND SUMMARY Oral. 1. State some familiar instance in which letters are used Illustrate. to represent numbers. 2. What is the meaning of a b? What is the value of a b, when a = 2, b = 5? 3. What is the meaning of p v, when p = 4, v = 9? Of a +5 m, when a = = 7, m = 3? 4. When a stands for the altitude of a figure, b for the base, state what stands for the area of: a parallelogram; a rectangle; a triangle. 5. If b and b' represent the bases of a trapezoid and h the altitude, what represents the area? 6. A half of one-seventh of the number of days in a certain month is 2; what month is it? 7. Mary is as old as Clara and the sum of their ages is 24 yr.; how old is each? 8. Who is a commission merchant? What is meant by the rate of commission? Illustrate. 9. A commission merchant sold a car-load of potatoes for $225; what was his commission at the rate of 10%? Oral and written. 10. If the car mentioned in Exercise 9 contained 300 bu. of potatoes, what did the customer receive per bushel? To how many decimal places need one express the result? II. What is a discount? How may there be several discounts for the same list price? Illustrate. 12. To what single discount is 20% and 10% equivalent? 13. What is the meaning of list price? Of net price? Illustrate. 14. What is the meaning of ratio? How may the height of various objects be found by measuring shadows? Illustrate the method. Oral and written. REVIEW AND SUMMARY 195 1. Name one way by which the length of a circle may be measured. Name another way. 2. What is the ratio of the length of any circle to that of its diameter? 3. What is the length of a circle whose diameter is 8 in. ? Of a circle whose diameter is 4 ft.? 3 yd.? 7 in.? 1.2 ft.? 4. How many degrees are there in the angle of a halfopen knife? If convenient, open a knife so as to show an angle of 45°; 90°; 135°; 180°. 5. A belt wheel has 16 spokes; how many degrees are there between each pair of spokes? 6. Windmills in Holland are like the picture; how many degrees are there in the angle between the arms of each pair of sails? 7. How many degrees are traversed by the hour-hand of a clock from 10 o'clock A. M. to 6 P. M. the next day? 8. What is the length of a circle whose radius is 15 in. long? 9. Standard wheels for the front axles of farm-wagons are 44 in. high; those for rear wheels are 55 in. high. How many inches longer is the perimeter of a rear wheel than that of a front wheel? 10. The height of a medium front wheel is 36 in.; how many inches more are there in the perimeter of a standard wheel than in that of a medium wheel? II. A horse that can draw 1,000 lb. on the level can draw 640 lb. on a 31% grade; by how many per cent is the load decreased? 196 PROBLEMS-REVIEW 1. A boy stands so as to face the east and turns to the left through 90°, what point does he face? If he turns through 180°? Through 270°? If he turns to the right through 90°? Through 180°? 2. Through how many degrees does the hour-hand of a watch turn between 12 o'clock and 4 o'clock? Between 2 o'clock and 7 o'clock? 3. Measure the height of the archway in the picture, in which 1 inch represents 10 ft. 4. Measure the distance from the second stone step to the beginning of the halfcircle. 5. From these two heights find the radius of the arch; the diameter; the distance around the outside of the semi-circle. 6. If a man receives 75¢ a 4-foot cord for cutting wood and 50¢ a 4-foot cord for sawing it into stove wood, what is the cost of cutting 125 cords of stove wood? 7. A commission merchant sold 150 bushels of peaches at $2.25 per bushel. His rate of commission was 41%; what was his commission? 8. What is meant by a 21% grade? A 6% grade? A 71% grade? 9. At a special sale a firm offered goods at the following discounts; find the reduced price: MEASUREMENT OF ANGLES 197 The figure shows an instrument used to measure angles. It is called a protractor. The semicircular part is divided into 180 equal parts, each part representing one degree. 5 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 1. How many degrees are there in the angle AOD? How many in the angle A O C? In the angle A OB? In A OE? 2. Draw angles that look like each of the following with sides much longer. Measure each, if a protractor is available. ZL 3. With the protractor construct an angle of 90°. Of 45°. Of 30°. Of 60°. Of 135°. Of 160°. Of 180°. 4. Draw angles of various sizes without using the protractor. Estimate and record the number of degrees in each. Measure each with the protractor and test your estimate. 5. Draw a triangle at random and measure its angles. Find their sum. Repeat with four other triangles. 198 PROBLEMS-ANGLES An angle lettered on its sides and at its vertex as shown is read "Angle A B C.” 1. Read each angle in Figure 1 that is -A less than 90°. Such an angle is called an acute angle. 2. Read each angle in Figure 2 that is greater than 90° and 4. Draw a parallelogram. Measure each angle. What is the sum of the four angles? 5. Treat a trapezoid similarly. 6. Make a figure with at least 2 acute angles, 3 obtuse angles, and 1 right angle. 7. Draw an irregular figure with 4 sides. Measure the angles and find their sum. 8. Compare the results of Exercises 4, 5, and 7. 9. Measure the angles of the triangles in the picture. 10. How many degrees are there in a right angle? In Plate A of of a B D C right angle? In of a right angle? In ? In ? In ? In ? A roof with such a slant is said to have half-pitch. II. In a half-pitch roof, what angle do the sides make at the ridge? What angle do they make with the plate? |