New SAT Math Diagnostic Test

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1 New SAT Math Diagnstic Test Answer Key Slve and Graph Linear Equatins 1. Slve fr z: 4 + z (+ z) z (5 ) = z = 61. Given the table f values: x y ?. y = 5 If the values in the table represent a linear relatinship, what is the missing value?. If the graph f the line y = -5x + 8 is shifted dwn units and left units, what is the slpe f the new line? A stre breaks even when its sales equal its expenses. Jn perates a surfbard stre where he buys each surfbard whlesale fr $80 and has fixed mnthly expenses f $600. He sells each surfbard fr $10. Hw many surfbards des Jn need t sell in a mnth t break even? surfbards Slving Systems 5. Slve the system: 8x 5y = 6 15x + 5y + 18 = (, 4) 6. A ty stre sells small stuffed pandas fr $.50 and giant stuffed pandas fr $ If the stre sells 9 pandas and made $17 in revenue in ne week, hw many small stuffed pandas were sld? Given the system: x 9y = 6 1 x y = c 7. c = -1 If the system has infinitely many slutins and c is a cnstant, then what is the value f c?

2 Slving Inequalities 8. Graph the linear inequality: 5x y > 6 8. See Graph 1 9. Slve the inequality: (7 b ) > 5 9. b < Marc is paid $80 per day plus $15 per hur vertime. If he wrks five days per week and wants t make a minimum f $50 this week, what is the fewest number f hurs f vertime he must wrk? 10. At least 8 Linear and Prprtinal Relatinships 11. Quinn wants t rent a self-strage unit. She estimates that she will need 700 cubic feet f strage space, but the self-strage prvider measures its units in cubic meters. If 1 meter is apprximately.8 feet, abut hw many cubic meters f space will Quinn need? 11. abut A tutring service ffers a free ne-hur tutring sessin. After a client signs up, the next 10 hurs f tutring are billed at a rate f $0 per hur. Fr all hurs after that, the client receives a discunted rate. If the client pays $664 fr 5 hurs f tutring, what is the service s discunted hurly rate? 1. $6 per hur 1. Marg purchases a cffee maker with an riginal price f $6.00. After a sale discunt, she gets an additinal 10% ff fr using her stre credit card. She ends up paying $41.85, nt including tax. What was the amunt f the riginal sale discunt as a percent? 1. 5%

3 Scatterplts 14. Which f the fllwing is the best estimate fr the slpe f the line that best fits the data shwn in the scatterplt belw? 14. A A. - B. 1 C. 1 D. 15. Match each f the scatterplts belw with the regressin equatin that best mdels the Relatinship f the data: B. C 1. y = ax + b, where a > 0 A.. A 4. D. y = ax + b, where a < 0 B.. y = ax + bx + c, where a < 0 C. 4. kx y = ab, where k < 0 D. 16. What is the y-value f the data pint that has the highest percent errr frm the mean f the data shwn in the scatterplt belw? 16.

4 Prbability and Statistics 17. A fair cin is flipped five times. What is the prbability that at least fur f the Five flips will be heads? = Given the table f results belw frm a breakfast study: What percent f the participants wh were utside a healthy range ate breakfast ne r fewer times per week? 18. abut 51.5% 19. Given the distributin f histry grades and crrespnding GPA scres amng a grup f students shwn belw: What is the mean histry GPA fr this class f students? On a used car lt, 50% f the vehicles are cars, 4 f which have autmatic transmissins Of the cars with autmatic transmissins, 1 have leather interirs. If a vehicle is chsen frm the lt at randm, what is the prbability that it will be a car with an autmatic transmissin and a leather interir? Expnents, Plynmials, Radicals 1. Simplify: ( 4 j k ) 4 1 k 1. 9 j. Simplify: x x y y

5 . Simplify: 4x + 8y 4x 1. x + y x 1 x Slve fr x: 8 + = 9 4. x = -10 Advanced Plynmial and Ratinal Operatins 5. Slve fr x: 4 + = x x 8 x 8x 5. x = 5 6. What is the remainder when 16a + is divided by 4 a Factr: 5x y 1 7. (5xy + 1)(5 xy 1) Functins 8. If g ( x) = x + 7x, what is the value f g ( )? Given the piecewise functin defined belw: x + 1, if x 0 x f ( x) = 1, if 0 < x 4 x, if x > What is the value f f ( ) 0. A cmpany uses the functin P( x) x = 150x t determine hw much prfit the cmpany will make when it sells 150 units f a certain prduct that sells fr x dllars per unit. Hw much mre prfit per unit will the cmpany make if it charges $5 fr the prduct than if it charges $0? 0. $.50

6 Quadratics 1. Simplify: x 10x + 5 x x 5 ( x + 5). Find the x-intercepts f the functin f ( x) = x x 8. 4 x =, x =. Sketch a graph f the equatin y = x + x 8 shwing the x-intercepts, y-intercept, and vertex. x-int = -4, y-int = -8 vertex = (-1, -9) 4. Slve the system: y = x x + y = ( 4, 4) ( 4, 4) r ( 6,4 6) ( 6, 4 6) 5. Find the axis f symmetry f the graph f y = x + 1x 8 5. x = - Imaginary Numbers 6. Simplify: ( i ) (6 + 4i) 6. 9 i 7. Slve fr x: y = x 4x x = ± i 8. Simplify: 14 i + i Simplify: + i 5 i (write yur answer in a + bi frm) i 6 6

7 Angles and Triangles 40. Given: angle F is a right angle perimeter f rectangle ABCD = 0 AB = 6 FD = DC Find the length f FA in the figure A 6 B F D C 40. FA = 45 = Find the value f x in the diagram: y 4y 41. x = 100 x + 0 Similarity and Cngruence 4. Given the triangles shwn at the right: B E A C F 4. B E If A D and AB DE, what additinal infrmatin Is needed t prve ABC DEF by the ASA therem? D 4. If TIM ~ JOE, m T = 40, and m I = 65, what is the measure f E? 4. E = 75 Circles 44. Find the length f the chrd PQ in the circle Given the radius f the circle = 4 and R is a right angle Q PQ = 4 R P 45. If the area f the shaded sectr in circle O is 14 π square units, and the measure f AOB = 140 find the radius f the circle. A 45. Radius = 6 O 140 B

8 Slids 46. Find the vlume f a cubical bx that has a surface are f 1,176 square inches cubic inches 47. Find the vlume f a cne with base diameter = 14 cm and height = 6 cm π cm Trignmetry 48. If 7 tan x =, then what is sin x? sin x = Find the length f minr arc AB in the figure. A 5π AB = 5π B 50. A 17 ft ladder leans against the side f a huse and makes a 65 angle with the grund. Hw far is the base f ladder frm the huse? 50. abut 7.18 feet