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TheONE book you need to prepare for the NEW SAT Math! ·1 • [ i * IIH WOIIBOOI FO HENE • * MATH WORKBOOK FOR THE EwSAT Silllon Jang and Tiffany T Jang *SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this book -, \ ,.'-~" G-i_f.'·} DW o • ·l"Lji ',f, c· '-h i\, ·\v LlBRAF y > 0.1, which of the following is less than~ ? y x+O.l a) - y+O.l b) 2x 2y x-O.l C) - y-O.l d) (~)2 y 24 When r is divided by 12, the remainder is What is the remainder when r + is divided by 4? a) b) c) d) 25 The monthly cost of renting an apartment increases every year by 3% John paid $500 per month this year on his rental What is the monthly cost for John's rental n years from now? a) 500 x 0.03 n b) 500 x 1.03 x n c) 500 x 1.03n d) 500 x 1.03n -1 Questions 26 - 27 refer to the following information: Density describes how compact or concentrated a material is It is defined as the ratio between mass and volume, or mass per unit volume The formula to calculate the density is: Mass Density = Voume I 26 The standard gold bar held in gold reserves by central banks and traded among bullion dealers is the 400-troyounce (12,441.4-gram) Good Delivery gold bar If the density of the gold bar is 19.3 grams per cm , what 475 would be the volume of the Good Delivery gold bar, in cm ? a) 592.8 b) 644.6 c) 696.4 d) 748.2 27 If a cylinder gold block has a diameter of centimeters and height of 15 centimeters, what would be its mass, in grams? (Gold has a density of 19.3 grams per cm ) a) 3,638 b) 3,949 c) 9,100 d) 14,552 1, 2, 3, , 5, 28 A three-digit integer is to be formed from the digits listed above If the first digit must be even, either the second or the third digit must be 5, and no digit may be repeated, how many such integers are possible? a) 12 b) 15 c) 18 d) 24 29 If the sum of all consecutive integers from -41 to x, inclusive, is 42, what is the value of x? a) 49 b) 45 c) 43 d) 42 30 July 4th, 2014 is a Friday What day of the week is July 4th, 2050? a) Sunday b) Monday c) Thursday d) Friday 476 Dr Jang's SAT 800 Math Workbook For The New SAT Directions: For questions 31-38, solve the problem and enter your answer in the grid, as described below, on the answer sheet Answer: 12 Write answer~ in the boxes -h~I"ri-=-I~ Answer: 25 Answer: 201 Either position is correct 2 , Grid in results Note: You may start your answers in any column, space permitting Columns not needed should be left blank • • • • • • Mark no more than one circle in any column Because the answer sheet will be machinescored You will receive credit only if the circles are filled in correctly Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately Some problems may have more than one correct answer In such case, grid only one answer No question has a negative answer Mixed numbers such as ~ must be gridded • Decimal Answer: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid The acceptable ways to grid ~ are' ~ ~ ~ 'r- ~ ~ ~ / as 3.5 or ~ (If ~ is gridded, it will be d as 2' 31 mterprete not - ) y 31 In the figure above, if the area of parallelogram OABC is 16, what is the value of x? 32 If the average (arithmetic mean) of 35,50, 20, and x is 40, then find the value of x 33 Gina drove at an average of 40 miles per hour from her house to a bookstore Along the same route, she returned at an average of 60 miles per hour If the entire trip took her hour, how many miles did Gina drive in total? SAT Math Mock Test No 10 477 34 In a poll, 20 people supported the current city mayor, 20 people were against him, and 10 people had no opinion What fraction of those polled supported the city mayor? 35 In a junior high school with seventh and eighth graders, there is the same number of girls as boys The eighth grade has 220 students, and there are boys for every girls In the seventh grade there are boys for every girls How many girls are in the seventh grade? 36 The graph above is a right triangle Find the area of this right triangle? 37 In the xy-plane aboye, is the center of the circle with a radius of 2, and the measure of L8 is!: radians What is a the value of x + y? (Round your answer to the nearest tenth.) 38 The length of a rectangular piece of cardboard is 15 inches longer than its width If a 5-inch square is cut from each comer of the cardboard, and the remaining piece is folded up to form a box, the volume of the box is 1,250 cubic inches Find the sum of the length and the width, in inches, of the original cardboard 478 Dr Jang' s SAT 800 Math Workbook For The New SAT SAT MATH MOCK TEST No 10 ANSWER KEYS ~1 e e D 11.D 21 D 31.2 ~ ~2 A A B 12 22 A 32.55 e 313 A B A 13 A 23 A 33.48 A t e Section p A ~ ~ 15 B D 11 Section e B T e 14 24 e e e 15 D 25 34 35.80 z e SECTION Answer: (c) The average of these three numbers is 16, so the sum will be x 16 =48 7+ 14 +x =48 x = 48 -21 = 27 Answer: (a) 2x+1 =9 x=4 5(4) - = 16 ill = Answer: (a) Since the two triangles share an angle with the same measure, the sum of their other two angles must be equal a +50 = b + 60 a-b=lO e 16 11 A 26 B 21 A 36 1020 31 2.8 Answer: (c) Consecutive interior angles are supplementary 2x + x = 180 x= 60 Answer: (a) Divide by fj on both sides of the equation y = x fj X = ~ (Then square both sides.) Ito A ~9 145 20 9 D 19 B 29 D e e 10 20 30 B Answer: (d) *x = X2 + 4, X2 + X2 =2, x=±.J2 = 3x2 Answer: (a) Use opposite operations 3x -2 =4 3x -2 + = + 3x = x=2 3(2) + = 10 10 Answer: (a) X2 X2 -16 = = 16 x=±4 3x i =- A Answer: (d) P can be any positive integer, so there are a few cases P < 4: The median would be P = 5: The median would be P P > 6: The median would be w=~=.!L 2 X2 e e 18 28 D 38.55 ~ Answer: (a) w (3x)2 = 3y 9x e ~ D ~8 11 Answer: (c) 3x = a-1 6x = x (3x) = x (a - 1) = 2a - 6x + = 2a - + = 2a - 12 Answer: (a) ~=4 x-5 3x + 13 =4(x - 5) 3x + 13 = 4x - 20 33 =x SAT Math Mock Test No 10 13 Answer: (b) If we triple and subtract from each element in X, we will triple and subtract from the mean of X as well SECTION Answer: (d) Plug in t = 10 and y = 800 in the function 800 = (x)x 2nO/.iJ = x x 22= 4x x=200 Answer: (b) LlOAB is an isosceles A 2x + 2y = 180 x+y=90 x=90-y Answer: (a) 20 pounds: 120 rolls = x : 18 rolls x - = 15 14 Answer: (c) Total selfie-related deaths: 10 +12 = 22 Total shark-related deaths: + = 11 Percent Increase = 22-11 X 100% = 100% 11 15 Answer: (b) 12-10 Percent change of selfie-related deaths: "10 x 100% = 20% Percent change of shark-related deaths: 100% = 167% Difference: 167% - 20% 16 Answer: Weight ofWhole Pie: 3600 18 : 36()O = x : 6()O 18 x 360 60 8-3 -3- x Weight of Piece: 600 = Answer: (c) The length of AC plus CD is equal to the length ofAD AB =! x 12 = CD =8 AD = AC + CD = 12 + = 20 Answer: (b) Let J be the amount of money John initially had and be the amount of monel) Sally initially had Together, they originally had $45 J+5=45 J=45-5 After John gives Sally $5, John will have J - dollars and Sally will have + dollars Therefore: + = 18 Answer: J= -3 -3 ("k)-3 = - (3)3 =~ -8 :2=3~==2: "';=ii Answer: (c) The length of the rectangle is 4r and its width is 2r r=2 Area of Rectangle = 4r x 2r = x = 32 17 Answer: The drcle is tangent to the x-axis, since otherwise it would touch the axis at zero or two points (try drawing it out to see) Its radius is the distance from the center to the x-axis which is k 18 Tolls :n: r = 4:n: ounces k x pounds 120 Tolls 120x = 20 x 18 (Cross multiply) x = pounds -=X 20 pounds ' - = : = 147% = 479 k=6 19 Answer: 145 a + (90 - 55)0 = 1800 a = 1450 20 Answer: Let x be the number of students in Ms DePietro's Arts class 3x + = x + 5) x x=9 ex - 2(J - 5) + = 2(45 -5 -5) =80-25 =25 Plug J = 45 - into the equation above to get J = $20 Answer: (c) Let the number be x = 30 x = 75 -x x 75 = 15 480 Dr Jang's SAT 800 Math Workbook For The New SAT Answer: (c) Percent Increase = 2013 Population-2012 Population x 2012 Population 100% Total Population in 2012 = 20 + 30 + 25 + 15 + 40 = 130 tlwusand Total Population in 2013= 25 + 35 + 20 + 10 + 25 = 115 tlwusand 115-130 X 130 100% = -11.5% 16 Answer: (c) Solve this problem usiug proportions 'Tltere were 4% (52% - 48%) more Sedans sold than all other cars combined 4% :50= 100% :x x = 1,250 cars 17 Answer: (a) (3 x 6) x (3 x 8) Answer: (d) All sides are equal in length 4x -5 =2x + x=3 Perimeter = x (2 x + 1) = 21 10 Answer: (c) Use the Pythagorean theorem (x - 1)2 + (x - 3)2 = 102 X2 - 2x + + X2 -6x + = 100 2X2 - 8x + 10 = 100 X2 - 4x -45 = (x -9) (x +5) = x=9 13 Answer: (c) Every digits are repeated The remainder of 303 divided by is so the 303 rd digit is same as tlte 3rd digit after the decimal point, both of which are 19 Answer: (b) : "> ' ;t iO; _ [[11 20 Answer: (c) c Answer: (a) B is located in the quadrant I which has positive x and y coordinates (6-2)XIBO Number of Elements in (A u B) = + - = Answer: (d) The lowest price Jor 31 tickets is to purchase books of 12, book of and single tickets $75 x + $40 + $7.5 = $197.5 = 120 (each mterlOr angle) 1BGC is a 30-60-90 special right triangle Answer: (c) A u B = A + B - (A n 8) A = {1, 3, 8,10, lS} B= (2,4, 6, 8, lO) An B = (8, lO) 15 : Use the exterior angle theorem x = 46 +40 =86 (a, b) 14 432 square feet 18 Answer: (c) Let k be the number of books Ken read, j be the number of books Justin read, and t be the number of books Tiff read j = 3k t = 2j = 2(3k) = 6k Given that k + j + t = 90 Substitute for j and t: k + 3k + 6k = 90 k=9 j =3k = 27 11 Answer: (d) If the median number of D VDs checked out Jor the whole week was 83, the number ofDVDs checked out on either Saturday or Sunday should be more than 83 12 = =Be x -,f32 =6 x -,f32 =3vr-;3 BD = 2BG = /3 BG 21 Answer: (d) The sum of any polygon's exterior angles is 360° a + b + c = 360 a + b = 360 - c = 360 - 130 = 230 22 Answer: (a) ((((((2+1)x 2)+1)x 2)+1)x 2) = 30 SAT Math Mock Test No 10 23 Answer: (a) x> y > 0.1 Plug in x = 2, and y = Only answer (a), 2.1, less than 31 1 24 Answer: (c) r = 12 x q + (Remainder Theorem) r + = 12 x q + 10 Since 12 x q is divisible by 4, the remainder of r + divided by is equal to the remainder of 10 divided by 4, which is Or just simply pick an easy number to try out this question, such as 21 (12 + 9) in this case 25 Answer: (c) Increasing every year by 3% is to multiply (1 + 2-.) 100 for each additional year CCnY = (1.03)11 x 500 = 500(1.03)11 19.3=~ Volume Volume =~ = 644.6 19.3 27 Answer: (a) = = Volume TCr h TC X 22 xiS Mass = 19.3 x 60TC = 3,638 28 Answer: (d) 1st digit must be even: choices If2 11d digit is 5, then 2" d digit has choice, and 3rd digit has choices Tf2'''' digit is not 5, then 3rd digit is 5: 2" d digit has choices and 3rd digit has choice Answer: Area of OABC = Base x Height = (x+2) x (2x) = 16 2X2 + 4x - 16 = x2 + 2x - =0 (x + 4)(x - 2) = x = -4 ( not applicable, x must be positive) or x = 32 Answer: 55 35+50+20+x = 40 160 - 50 - 35 - 20 = 55 X = 33 Answer: 48 Let one trip have x miles Total Time = tgo + tback x x 1 l=-+-=x(-+-) ~ x=24 40 60 40 60 Total miles: x 24 = 48 miles 34 26 Answer: (b) Mass Denstty = Volume Answer: - Part Whole - 20 20 50 20+20+10 35 Answer: 80 In the eighth grade, there are 220 x _5_ = 6+5 So the number of boys in 7t1• grade is ~x The total number of boys in two grades is the same as girls: 100 + ~4 x = 120 + x ~x=20 ~ x=80 36 Answer: 1020 Answer: (d) The sum of all integers from -41 to +41 is O The next term is 42 Therefore x = 42 30 Answer: (b) Count the number of days between July 4tll, 2014 and July 4tI., 2050 There are 2050 -2014 = 36 years 2048-2016 There are + = leap years m between So the total number of days: 36 x 365 + = 13,149 days The remainder of13149 -;- is Three days after Friday is Monday 100 boys and 220 -100 = 120 girls Let x be the number of girls in seventh grade Boys of 7t1• Grade: Girls of 7t1• Grade = : x x + x x = 24 29 481 A B c = LA + LACD LDCB + LACD LA LDCB LADC = LCDB = 90° /lADC -1:1CDB CD BD h 50 -=-=-=- = AD CD 18 = 90° h h = 18 x SO = 900 h = 30 Area = 2" (SO + 18)(30) = 1020 482 Dr Jang's SAT 800 Math Workbook For The New SAT 37 Answer: 2.B x = TCOS(O) = x cos G) = 1.618 Y = Tsin(O) = x sin (~) = 1.176 x+y = 2.8 38 Answer: 55 If the width of the cardboard is x inches, the length of the carboard is 15 + x inches After 5-inch square is cut from each corner and the cardboard is folded to form a box, the width will be x - 10, the length will be x + 5, and the height will be inches The volume of the box is given, so (x - 10)(x + 5)(5) = 1250 x - 5x - 50 = 250 x - 5x - 300 = (x + 15)(x - 20) = x = 20 inches 20 + (20 + 15) = 55 Index Index AA (Angle-Angle) Similarity Theorem, 239 acute angle, 208 algebraic expression, Alternate interior angles, 216 Angles, 207 arc,270 Arithmetic Sequence, 133 Average, 93 Bar graphs, 102 base, 196 Central Angles, 270, 272 chord,270 circumference, 271 cofunction, 306 Combinations, 122 common difference, 133 common factor, 154, 188 common ratio, 133 complementary angles, 209 complex conjugates, 174 complex number, 174 Concave Polygon, 255 Cones, 284 Consecutive interior angles, 216 Convex Polygon, 255 Corresponding angles, 216 Cross multiplying, 151 Cubes, 284 Cylinders, 284 degree, 208 dependent variable, 158 diameter, 270 Difference of Two Squares, 154 directly proportional, 68 Discount, 85 discriminant, 181 distance formula, 290 Distributive Law, domain, 158 Elimination, 34 equation, 13 equilateral triangle, 229 Euclid's Algorithm, 148 Exterior Angle Theorem, 221 Factor Theorem, 189 factorial, 121 Factoring Trinomial, 188 FOIL, Fraction, 151 Functions, 158 Geometric Probability, 128 Geometric Sequence 133 imaginary number, 175 independent variable, 158 Inequality,37 Inscribed Angles, 272 inversely proportional, 68 isosceles triangle, 229 Like Terms, Line graphs, 104 line of reflection, 294 line of symmetry, 294 Line Segments, 207 Lines, 207, 215 major arc, 270 Mean, 94 Median, 94 midpoint formula, 290 minor arc, 270 Mode, 94 obtuse angle, 208 Opposite Operations, 13 parallelogram, 259 Percent Change, 84 percentage, 83 Perfect Square of Trinomial, 155 Permutations, 122 Pictographs, 102 Pie graphs, 103 Point-slope Form, 22 polygon, 255 Polynomial, 188 power, 196 Prime Factorization, 148 Prime Number, 148 probability, 128 proportion, 68 483 484 Dr Jang's SAT 800 Math Workbook For The New SAT Pyramid, 284 Pythagorean theorem, 229 Quadratic Equation, 180 Quadratic Function, 180 Radians, 308 radical, 202 radius, 270 range, 158 Rate formula, 69 ratio, 68 Rays, 207 reciprocal, rectangle, 260 Rectangular Prisms, 284 reference angle, 307 reflection, 294 regular polygon, 255 Remainder Theorem, 189 rhombus, 260 right angle, 208 right triangle, 229 SAS (Side-Angie-Side) Similarity Theorem, 239 Scatterplots, 104 sector, 272 semicircles, 270 sequence, 133 Similarity Theorems, 239 Simple Interest Rate, 86 Slope, 22, 290 Slope-intercept Form, 22, 291 Special Right Triangles, 229 square, 260 square root, 202 SSS (Side-Side-Side) Similarity Theorem, 239 Standard Form, 291 straight line, 208 Substitution, 34 Sum, 93 Sum of Interior Angles Theorem, 221 supplementary angles, 208 symmetric, 294 system of equations, 34 Tables, 103 tangent line, 270 terms, translation, 292 transversal, 216 Trapezoid, 266 Triangle Inequality Theorem, 250 Trigonometry,304 trinomial, 155 unit circle, 305 unlike terms, variable, Venn Diagram, 64,121 Vertical angles, 209, 216 Vertical Line Test, 158 Zero-Product Rule, 180 STAY TUNED FOR MORE BOOKS BY DR JANG! Dr Tang's SAT 800 Series: Dr Jang's SAT 800 Math Workbook (2013, co-authored with Tiffany Jang) Dr Jang's SAT 800 Math Subject Test Level (co-authored with Tiffany Jang) Dr Jang's SAT 800 Chemistry Subject Test (2015) Dr Jang' s SAT 800 Physics Subject Test Dr Tang's AP Series: Dr Jang's AP Calculus AB/BC Workbook Dr Jang's AP Physics & Workbook Dr Jang's AP Physics C: Mechanics Workbook Dr Jang's AP Physics C: Electricity and Magnetism Workbook Dr Jang's AP Chemistry Workbook Check Out More Services on Our Website: www.DrJang800.com The Goals of Dr Jang's Books: ~For students: To help you study based on your skill level ~For teachers: To help you plan lessons based on students' needs "Giving instruction based on each student's characteristics and ability will ~ Confucius achieve the best educational results." IIIII111 !~1'17Aoo2" m Made in the USA Middletown, DE 04 February 2016 Authors th marrfed to both erlng ~""'r J Te m1Ii~ "~''''''''''g t all nolo91 Through teS, Dr; dents can dramatically Improve their score on SAT Math section in a short amount of tJrne if they have the right materials He has spent years devetoping materials that can introduce a new student to the subject and remedy each student's weaknesses to help them efficiently prepare for the new SAT Math exam Visil our webslle: lrlllllll.colD ... is the area of the circle? Dr Jang's SAT 800 Math Workbook For The New SAT xxii 5cm 3cm 4cm 50 In the figure above, is the center of the two circles H the bigger circle has a radius of and the. .. practice problems for you to reinforce your understanding of the material and pinpoint the weak areas you need to improve on 11 Dr Jang's SAT 800 Math Workbook For The New SAT There are some parts... Their methods can both introduce a new student to the subject and remedy a student's weaknesses to help them efficiently prepare for the SA Math exam IV Dr Jang's SAT 800 Math Workbook For The