Mathematics: Math Practice Tests, Exercises of Mathematics

Download Mathematics: Math Practice Tests and more Exercises Mathematics in PDF only on Docsity! Class ID. Name. Practice Set 1 Parabola parts 1) x2 = 16y A) (0,4), y=~4, y-axis ©) 4 0), y =4, y-axis 1 -—x2= 2) o 7Y A) (-20, 0), x = 10, x-ais C) @, 10), y= -10, y-axis 3) x=9y2 A) x0 x=, ass oz af x=- gents 4) y2=-12x - A) G, 0), x= -3, x-axis © (0, -3), y=3, y-axis 5) (x + 2)2 = -28(y - 5) A) (-2,-2), y= 12, x=5 © (-2,-2), y= 12,x=6 6) (y - 5)? =-4(x + 4) A) (-5, 4), x=-3, y=5 © (-5,5),x=-4,y=5 7) (y ~ 22 = 20(x - 3) A) (7,3),x=-3,y=3 © 8,2),x=-2,y=2 8) (+ 4)2=4(y - 2) A) (2,-3), y=-5,x=2 © (-4,1),x=3,y=2 dimgutierrez Date. a B) (4, 0), x = 4, x-axis D) (0, -4), x= -4, x-axis B) (0, -10), y = 10, y-axis D) (0, -10), y= 10, x-axis 1 1 B) 36 OL x= 36" axis S| a 36> D)|0, 1 y-axis a 36 B) (-3, 0), x = 3, x-axis D) (-3, 0), y = 3, y-axis B) (-2, -2), y= 12,x=-2 D) (-9,-2), y= 12, x=-2 B) (-5,5),x=-3, y=-4 D) (-5,5),x=-3,y=5 B) (2,-2),x=-8, y=-2 D) (-2,2),x=8, y=2 B) (4,-1), y=-3,x=4 D) (-4,3), y=1,x=-4 Score. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the focus, directrix, and axis for the parabola. Also Lined te principal axis, egmarion , Vevbives , ete. 1) 2) 3) 4) 5) 6) 8) Practice Set 2 Parabola equations dimgutierrez Class ID. Name. Date. Score. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. « Write an equation for the parabola with vertex at the origin. 1) Focus (5, 0) 1) A) y2=5x B) y2 = 20x ©) x2 =20y D) x2 =5y 2) Focus (0,9) 2) A) y2 = 9x B) y2 = 36x © x2=9y D) x2 = 36y 3) Through (-7, 7), opening to the left 3) A) y2=-7x 4B) x= 3 OQ) x=-7y2 D) x2=7y 4) Through (7, 6), opening to the right 4) -_ 36 36 49 _ 36 A) yr=->x B)x=y? 1) doy D) yra>x 5) Through (\/7, 7), opening upward 5) A) y=7x2 B) y =x2 Qx=y D) x=y2 6) Through (5, -10), opening downward 6) --2,2 2=_5, 2=_2 =2,2 A) x= 5% B) x zy Q~x 5 D)y=5x i 7) Through (6, -6,/6), symmetric with respect to the x-axis 7) A) x = 36y2 B) x = /6y2 ©) y2 =36x D) x2 = Joy | 8) Through (6, 6), symmetric with respect to the y-axis 8) | A) x2=6y B) y = 6x2 © x=-6y2 D) y2=6x | Write an equation for the parabola. | 9) vertex (4, 10), focus (4, 12) 9) { A) 2(y - 10) = (x- 4)2 B) (y - 10)2 = 8(x- 4) | ©) y-10=8(x- 492 D) 8(y ~ 10) = (x-4)2 | | 10) vertex (7, -9), focus (10, -9) 10) A) (x-7)2 = 12(y +9) B)x-7=3(y +92 ©) (y+9)2=12(x-7) D) 36 -1=(y+9)2 = B) 10: 5 -10 : “5 -10: D) 30 -50 -50! 2) 3) 4x2 + 64y2 = 256 B) 2 y 10 104 5 b Hier Hee HEH 5 4 -10 10: °Q D) ¥ 10 1of sf st -10 S10 5 } 10 5 10: 2 = Add ) 49x2 + Oy: 4 °) D) 4) Practice Set 4 Ellipse parts dimgutierrez Class ID. Name. Date. Score. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ‘ Write an equation for the ellipse. 1) center at origin; length of major axis 10; y-intercepts +4 1) A ad pi 9 2a p22 setae 6 25 = as 25 4671 2) foci at (-2, 6), (-2, 0); major axis length of 10 2) (y= 32 | (x= 2)2 _ (x-32 | (y-2)2 _ A * 167! Be et (y= 3) , (+2)? _ &=3P (y= 2)? | Oe * 16 -t Ds * ie! 3) minor axis from (-5, -4) to (-1, -4); major axis from (-3, -8) to (-3, 0) 3) Gea 2P (y= 4) G3? , (ya? Nate! Boat ae ot 9 (+4 (y +3? | D) (+32 (y+4ye _, 4 16 4 16 4) eccentricity 2 foci at (3, 0), (-3, 0) 4) 22 22 22 2 Ap +agel Bagtty=l Oag+tget Dog tage! 5) foci at (0, 9), (0, -9), through the pon | 5) x2 2 x A) j600 * Tea * | Dota! yt 2 x2 yd ° F681 * To00 =! a ta7! Practice Set) Hyperbola and graphs Class ID. Name. Date. Score. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the hyperbola. 2° 2 LX. D5-a 7! 10: -10 9 10: -10 me B) D) 1) 2) 5) 4y2 - 25x2 = 100 10: -10: 10: B) -10 25 “5 10: 10 10 6) * x 2 e > 7 > 2% o's 8 7 8 2 7 « s a Practice Set 6 Hyperbola parts dimgutierrez. Class ID. Name, Date. Score. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the center, foci, and asymptotes of the hyperbola. x owe 0 9 16 1 0 A) C: (0, 0); F: (0, -4), (0,4); Ar y= $e y=-x B) C: (0,0); F: (0, -4), (0,4); Ary = du ye-de ©) C:(0,0);F: (5, 05.6.0); A: ya$uy=-$e D) C: (0, 0); F: (-5, 0), (5, 0); A: y=3x, ya-dx 2) Bi x2 =P) Ga 2) A) C: (0, 0); F: (-8, 0), (8, 0); A: y= Su y=-dx B) C: (0, 0); F: 0, -10), (0, 10); Ary = Su y=-dx ©) C: (0, 0); F: (0, -8), (0, 8); A: y= x y=-— D) C: (0, 0); F: (-18, 0), (10, 0); A: y=> Sx y=-dx (x+32 (y+ 3)2 | 3 a 3) A) C5(-3, 3), F(-3, -8), (3, Be Ary= Bx -Z, your a B) C: (-3, -3); F: (-8, -3), (2, -3); A: y= i +Ly=- $x -7 ©) C:€3,-3):F:C7,-9), (1-3); Arya exe ya tex eZ D) C3, -3); F:(-3, Vi 3,1); Ary =x Ly eer Practice Set 11 Limits algebraic functions Class ID. Name. dimgutierrez Date. Score. 6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it exists. x2 - 2x - 15 1) lim x03 x5 A) -8 B) Does not exist 3 2 2) tim 222 12x? - 5x x30 5x * A)5 *\ B) Does not exist 29x 3) tim 2242x=80 x>8 x2-64 A)O ae A)2 B)4 5) lim 2 h-0 V3h+4+2 A) 1/2 B) Does not exist 7x+h 6 peesctleaege, ) h—> 0 x3(x-h) A) az B) Does not exist x4 3 _ x3 7) tim Gothen h>0 h A) 3x2 + 3xh + h2 B)O 8) lim Ni+x-1 x20 x A) Does not exist B) 1/2 1/3. 9) lim (1+hy1/3_ 1 hoo h A) 1/3 B)3 O5 Q-1 1 O-5 C) Does not exist Q2 ©) Does not exist oO 14 Dd) 0 D)0 D) Does not exist D)0 D)1 7 pe 3 D) 3x2 D)0 D) Does not exist ) 2) 3) 4) 5) 6) 7) 8) 9) Practice Set 12 One-sided limits: special pe-wise defined functions dimgutierrez Class ID. Name. Date. Score, SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ‘ Use the graph of the greatest integer function y= | x | to find the limit. i 1) tim Ld 1) x>2- * 2) tim Lx 2) x2 x 3) lim [3x] A 3) x0.57 x 4) lim [3x] 4) x0.5+ 5) lim [x/3] 5) x>0.5+ 6) lim [x/3] 6) x05 Find the limit. 7) tim LL 7) x>0t * 8) tim Ll 8) x0- * 9) tim x=2L 9) opt Xn2 10) lim x2} 10) xo2- x>2 1) tim 2=xt 1) x2 2 °K 12) tim =x 12) xp 27% 13) tim (x-3) +t 13) ete xel " Practice Set 13 One-sided limits: concepts dimgutierrez Class ID. Name. Date. Score. ‘ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Given lim f(x)=Ly, lim f(x)=Ly,and Ly «Ly, which of the following statements is true? 1) x07 x0+ lL lim f= x0 I. im fO) =Ly x30 Ill. lim. f(x) does net exist. x20 * A) Hl B) none Ol D)I 2) If lim f(x) = L, which of the following expressions are true? 2) x0 I. lim f(x) does not exist. x0- IL lim f(x) does not exist. x>0t I. lim (&)=L x07 IV. lim f(X)=L x Ot A) Ill and IV only B) Tand IV only C) Land II only D) Hand Il only 3) If lim f(x) =1 and f(x) is an odd function, which of the following statements are true? 3) : x07 t L lim f()=1 xo I. lim f(x)=-1 x>0t Ill. lim_ f(x) does not exist. x0 A) Iland IIT only B) Land IIT only © Land Il only D) 1, 0, and Ill 4) If lim f(x)=1, lim f(x)=-1, and f(x) is an even function, which of the following statements are 4) x1- xalt true? Lo lim {()=-1 x17 I. lim f(x) =-1 x>-1* TIL lim f(x) does not exist. x->-1 A) 1H, and IIL B) Tand TI only C) Land I only D) Iand II only