m w re FIRST YEAR ALGEBRA SCALES series a By HENRY G. HOTZ Published by Teachers College, Columbia University. ^ Copyright, 1920, by Teachers College School Date.- City „ County.. Write your name here Age When did you begin to study algebra? Month .....Year ADDITION AND SUBTRACTION Carefully perform the operations as indicated. 1. 4r + 3r + 2r = 3. 126 + 66-36 5. 7x-x+6-4 = 9. (4r - 5<) + (s - 3r) = 10. 8c - ( - 6 + 3c) = 12, 5x - [4x - (3x - 1) ] = ^ 3c 3c 13. 4 8 15. 3x a — X c^ — 7? 3 - 2a; 18. 3 2x = 3 - 2x X + 1 22. —^ {x - Vf {x - \y (x - 1) 23. 20 + x/"45" + yTVi 24. a a -2 3 a -2 a+2 4: - a" 577528 FIRST YEAR ALGEBRA SCALES* ' series a By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date City County Write your name here Age When did you begin to study algebra? Month Year MULTIPLICATION AND DIVISION Carefully perform the operations as indicated. Reduce all answers to their simplest forms. 12n \. Z .ly= 2. — = 4 3. 2a . 4a62 = 7. 4x . ( - Sxy^) = ISmhi - 27mn2 9. » 11. (2a2 + 7a - 9) (6a - 1) = 9mn ci-d* c-d 16. ( - 3x1/3)* = 17. . (c - d)2 c2 + d2 p2 _|_ 4p _ 45 p8 _ 8 1 20. p2 + 2p + 4 p2 _ 81 3p,. _ 15^ x8 + 27 3x + 9 2 1 21. 4- 22. 64* X 27* = a;2 + X - 12 X + 4 3 V 6a 23. -— . V12a = 2aV 18 c^ FIRST YEAR ALGEBRA SCALES series a By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date City. County Write your name here Age..._ When did you begin to study algebra? Month Year._ EQUATION AND FORMULA Solve the following equations and formulae: 1. 2x = 4. 2. 7m = 3m + 12. 4. 5a + 5 = 61 - 3a. 6. 10 - llz = 4 - 8z. 8. c - 2(3 - 4c) = 12. 11. The area of a triangle = ibh, in which b = length of the base and h = height of the triangle. How many square feet are there in the area of a triangle whose base is 10 feet, and whose height is 8 feet? X + 3 X + 5 14. 3m + 7n = 34 18. 7m +Sn = 46 X — 2 X — 4. 6x - 2 3x» + 13 19. p« - 5p = 50. 23. — TT ~ ^ = ~1 — ^ ^^ x + 3 x'— 9 24. S = igt^; solve for t. 25. \/x» - 1 - x = - 1. Digitized by the Internet Archive in 2008 with funding from IVIicrosoft Cbrporalid.n http://www.archive.org/detdrls/firstyearalgebraOOhotzrich FIRST YEAR ALGEBRA SCALES series a By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date City County. Write your name here Age When did you begin to study algebra? Month Year PROBLEMS Do not work out the answer to the problem — merely indicate the answer or state the equation in each case. 1. If one coat cost x dollars, how much will 3 coats cost? Answer 1 ; ; 2. A man is m years old; how old was he r years ago? „ ^ Answer 4. A gold watch is worth ten times as much as a silver watch, and both together are worth $132. How much is each worth? Equation. 5. The distance from Chicago to New York by rail is 980 miles. If a train runs v miles an hour, what is the time required for the run? Answer.. 7. The total number of circus tickets sold was 836. The number of tickets sold to adults was 136 less than twice the number of children's tickets. How many were sold of each? Equation., 8. A rectangular box is d inches deep, w inches wide, and contains r cubic inches. What is its length? Answer 9. The area of a square is equal to that of a rectangle. The base of the rectangle is 12 feet longer and its altitude 4 feet shorter than the side of the square. Find the dimensions of both figures. Equation (Turn over. There are problems on the other side) 12. A train leaves a station and travels at the rate of 40 miles an hour. Two hours later a second train leaves the same station and travels in the same direction at the rate of 55 miles an hour. WTiere will the second train pass the first? Equation.. 13. A merchant has two kinds of tea, one kind costing 50 cents and the other 65 cents per pound. How many pounds of each must be mixed together to produce a mixture of 20 pounds that shall cost 60 cents per pound? Equation., 14. An open box is made from a square piece of tin by cutting out a 5-inch square from each comer and turning up the sides. How large is the original I— T square, if the box contains 180 cubic inches? I Equation FIRST YEAR ALGEBRA SCALES By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1820, by Teachers College. SERIES A School Date.. Write your name here City _ County... - - Agt When did you begin to study algebra? Month _ Year... GRAPHS 1. The following diagram represents the length of certain rivers: inssissippi ST-UViTajNCE YUKON ARKAMSAS COLUUBIA li I L E S How many miles long is the Arkansas river as represented in this diagram ?.. 3. This graph indicates the population of a certain town for a period of years : vasviATim 3500 A / ^ r '" 3400 .^' ^ y ssoo ^ l^ 3200 1840 1850 YEAR 1860 What was the approximate population of the town in 1856?.. 1870 (Turn ov(M') 4. This table gives the interest at 6 per cent on $100 for a period of years: Years Interest in Dollars 1 6 2 12 3 18 4 24 5 30 6 36 Locate in the adjacent diagram the points corresponding to the above data. Then connect these points by a line. *'^'i 30 25 ■ hi Ul K W -i ■ ^ ^ tZ5 — 1 n io,__: J ' " "■ ~ ~ ~ ~ ^ ^ "" ^ ■■ ■■ ■" ■ LLL ^ ^ ^ „ ^ ^ ^ ^ ^ ^ 2 3 4 5 6 Y £ A B S 5. The following graph is used to convert degrees of temperature from the Fahrenheit scale (F) to the Centigrade scale (C) and from the Centigrade scale to the Fahrenheit scale: Degrees F&hrenheit 160- / / J ipfi. f / 1 no i f / 80 > r / 60 J f Af\- / r on ■ / J r A< / / / > / _^ _ _ _ _ _ ,^_ When it is +20° on the F scale, what is the tem- perature in degrees on the G scale? Degrees Centigrade 6. This graph represents the distance passed over by a man walking at the rate of 3 miles an hour for a number of hours. 30 25 20 0} M ►^ 15 10 ¥- H~i~" J e 7 r J T L ^d 7 r ~/ 7 r "Ite" j_ f T 7 n^ jb 7 r T 7 r J 7 -J Z ^ - _ . : 2 4 6 8 lb 12 14 16 18 20 22 H U B S By the conditions of the problem it may be said that the number of miles travelled equals three times the num- ber of hours, or m = 3 A That is \i h = 2, then m ^ 6; if /i = 4, then m ^ 12; and if A = 6, then m = 18, etc. By locating these points, we have a, b, c, d, etc., of the graph. In the same diagram draw a graph in which m = 2h 7. Find three pairs of values for x and y in the following equation and then draw the graph of X + y = 5 1 Space = 1 Unit ^ (TUTM 0V«C) 10. Plot the following equations and find the values of x and y at the point of intersection of the graphs. y ~~ I + 4y = 11 2x — y = 4 1 Space = 1 Unit 11. A boy begins work with a weekly wage of $9 and receives an increase of 25 cents every week. Another boy starts with a weekly wage of only $6, but re- ceives an increase of 50 cents every week. 1 Draw a graph which shows the wage of each at the beginning of every week for 15 weeks. According to this graph when will their wages be the same ? FIRST YEAR ALGEBRA SCALES series b By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date.- City. County._ Write your name here Age : WTien did you begin to study algebra? Month Year.„ ADDITION AND SUBTRACTION Carefully perform the operations as indicated. 1. 4r + 3r + 2r = 2. 2x + 3a; = 3. 126 + 66 - 36 = 4. 2c + §c = 5. 7a- - a- + 6 - 4 = 6. 3a - 46 + 5a - 26 = 7. 5m + ( -4to) = 8. 20a; - (10a; + 5a;) = 9. (4r - 5t) + (* - 3r) = 10. 8c - ( - 6 + 3c) = 11, 3a2 - 36 - (2a2 + 36 - 4) = 12. bx - [Ax - (3x - 1) ] 3c 3c 3a; — 2 a; + 4 13. = 14. \ 4 8 3 6 (Turn over. There are exercises on the other side) . 3x 15. a — X (fi — x^ r r 16. — \ r + z r — 17. oa + 1 3a - 2 6a 2a 3 - 2x 18. 3 2x 19. lOx + Sy 3x + 5y 2xhf xy^ a a — 4 20. a + 1 a2-a + l a3+l 15 21. x2 - 5x + 6 x2 + 2x - 15 3 - 2a: a; + 1 1 22. + ix - 1)3 (x - 1)2 {x - 1) 23. V 20 + V 45 + V ^, = 24. a - 2 3 + a - 2 a + 2 4-a2 FIRST YEAR ALGEBRA SCALES series b By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School ...Date.-. City. County. Write your name here Age When did you begin to study algebra? Month Year MULTIPLICATION AND DIVISION Carefully perform the operations as indicated. Reduce all answers to their simplest forms. 12n I. 3 • 7y = 2. = 4 3. 2a . 4a62 = 4. 6c3 ^ 2c2 = 5. I of 9??i = 8a% 4a2 7. Ax ' (- 3xy^) = 8. a3 . (- 3a) • (- 2a) 18^% — 21mrfl Ax^ 9. ^ 10. H- 2a;2 = 9mn 5 n4 + 7n2 - 30 11. (2a2 + 7a - 9) (5a - 1) = 12. n2 - 3 7a 7a2 - I2x2y2 . (x - 2) 13. — -^ — = 14. 15 20 - 3x2^/2 (Turn over. There are exercises on the other side) 15. m -\- n a m^ — 7j2 16. ( - 3x2/3)4 = 17. d'^ c - d {C - d)2 c2 + ^2 1 3 18. 3x2 . 43-2 19. a2 + 2 " ~ 1 a + 2 20. p2 + 4p — 43 p3 _ 3 p2 + 2p + 4 p2 - 81 Spr - 15r 21. x3 + 27 3x + 9 x2 + X - 12 X + 4 2 1 22. 643 X 273 = 3 V 6a 23. ^— . V 12a = 2a V 18 c^Ts ^ t:::c3Uxcc«-«-«-^->*-«-«- ''";:5 FIRST YEAR ALGEBRA SCALES series b By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date City.. County- Write your name here Age... When did you begin to study algebra? Month ...Year EQUATION AND FORMULA Solve the following equations and formulae: 1. 2x = 4. 2. 7m = 3m + 12. 3. 3.r + 3 = 9. 4. 5a + 5 = 61 - 3a. 5. 7» - 12 - 3n + 4 = 0. 6. 10 - llz = 4 - 82. 7. |z = 6. 8. c - 2(3 - 4c) = 12. 2x 5 i.r + i.r = 3. 10. — = — 3 8 11. The area of a triangle = ^bh, in which b = length of the base and h = height of the triangle. How many square feet are there in the area of a triangle whose base is 10 feet, and whose height is 8 feet? y 5 y 12. — = — . 13. Kx- + 5) = 5. 3 2 4 (Turn over. There are exercises on the other side) 14. 3m + 7n = 34 15. = 7m + 8n = 46 3 - a; 1 + x 16. The area of a circle = ttt^, in which r = radius of the circle and TT = 3| Find the area in square feet of circle whose radius is 7 feet. 17. In the formula RM = El, find value of M. X + 3 X + 5 18. = 19. p^ - 5p = 50. X — 2 X — 4 2 3 12 20. = 21. — + — = 1 x2 + 4x + 3 a;2 + 3x + 2 x y 4 4 X y 22. F = temperature in Fahrenheit degrees C = temperature in Centigrade degrees 9C andF = h 32°. 5 Solve for C when F = 70°. 6x - 2 3x2 + 13 23. 3 = X + 3 x2 - 9 24. S = ^gfi; solve for t. 25. V x2 - 1 - X = - 1. 0,\ V. R^JTY OF CALIFORNIA BtRKELEY. CAUIFOkinIm, SERIES B FIRST YEAR ALGEBRA SCALES Hems G. Hotz School Date City - County.. Write your name here _ Age When did you begin to study algebra ? Month Year _. PROBLEMS Do not work out the answer to the problem — merely indicate the answer or stale the equation in each case. I . If one coat cost x dollars, how much will 3 coats cost > Answer _ _ 2. A man is m years old; how old was he r years ago? Answer. 3. A boy has a marbles and buys b more; how many has he then? Answer 4. A gold watch is worth ten limes as much as a silver watch, and both together are worth $132. How much is each worth? Elquation _ : - 5. The distance from Chicago to New York by rail is 980 miles. If a train runs v miles an hour, what is the time required for the run ? Answer 6. The width of a basket ball court is 20 feet less than its length. The perimeter of the court (distance around) is 240 feet. Find the dimensions. Equation.. 7. The total number of circus rickets sole' was 836. The number of tickets sold to adults was 1 36 less than twice the number of children's rickets. How many were sold of each? Equarioo.. (Turn over. There are problems on the other side) 8. A rectangular box is d inches deep, w inches wide, and contains r cubic inches. What is its length > Answer 9. The area of a square is equal to that of a rectangle. The base of the rectangle is 12 feet longer and its altitude 4 feet shorter than the side of the square. Find the dimensions of both figures. Equation 1 0. A tower casts a shadow of 20 feet. A man. 5 feet 9 inches high, who is near at the same time, casts a shadow of 2 feet 6 inches. Find the height of the tower. Proportion 1 1 . Five thousand dollars is invested in two banks, part in one at 3 per cent and the rest in the other at 4 per cent The annual income from die two investments is $172. How much is each investment? Equation. 12. A train leaves a station and travels at the rate of 40 miles an hour. Two hours later a second train leaves the same station and travels in the same direction at the rate of 55 miles an hour. Where will the second train pass the first? Equation- 1 3. A merchant has two kinds of tea, one kind costing 50 cents and the other 65 cents per pound. How many pounds of each must be mixed together to produce a mixture of 20 pounds that shall cost 60 cents per pound? Equation.- 14. An open box is made from a square piece of tin by cutting out a 5 inch square from each comer and turning up the sides. How large is the original square, if the box contains 180 cubic inches? I ^^» Equation.. PUBUSHEO BY TEACHERS COLLEGE, COLUIIBIA UNIVEBSITY COmUGHT, 1920, BY TEACHEBS COIXEGE r.t r LANOe LIBRARY OF EDUCATtnw UMV^RSITY OF CAUFOR^N^'f "* BERKELEY. CALIFORNIA FIRST YEAR ALGEBRA SCALES series a By HENRY G. HOTZ Published by Teachers College, Columbia University. Copyright, 1920, by Teachers College School Date City County- Write your name here Age When did you begin to study algebra? Month._ Year ADDITION AND SUBTRACTION Carefully perform the operations as indicated. 1. 4r+3r + 2r = 3. 126 + 66 - 36 = 5. 7a;-x+6-4 = 9. (4r - 50 + (s - 3r) = 10. 8c - ( - 6 + 3c) = 12. 5x -[4x - (3x - 1) ] = .. 3c 3c 13. = 4 8 15. Sx a — X a? — x^ 18. 3 2x = 22. 3 - 2x X + 1 {x - \y {x - \y (x - 1) 23. ^r^ + a/Is" + vOi" a a -2 3 24. r- + ■ a -2 a +2 4-0^ • 577528 L UNIVERSITY OF CALIFORNIA UBRARY ^mmmmm^'