Math 80a Exam #1 Review

Transcription

1 4 2) 1 zx 6x Math 80a Exam 1 Review This is a preview of the test Any questions from the homework are possible on the exam i) Please practice every problem on this review two or three times ii) Find problems like them in the homework and practice those iii) Create your own exam using homework problems place two hours on a timer and take the exam iv) Practice the problems you missed and find ones like them to practice v) Create a new exam and take it Repeat if needed 1 Solve a) 3x b) 3 x 7 5 3x 10 4J } at 1 nosing b) 4[6 (1 + 2x)] + 10x 2(10 3x) + 8x c) 93x x 4[ 6 ] + + sex tzx [54] Ilz 212* ' zo IF 14 z " d) 1 (n 2) ' n e) 2x 1 5 [ I 4x ] ( n (2 1)(4 +5)+28 zn th 23 ) zs ho@ I ][ ]

2 2 Apply the formulas for determining a child's body surface area and a child's dose of medication S is a child's body surface area k is the weight of the child in kilograms C is the child's dose of medication in milligrams D is the usual adult dose in milligrams S 4k+7 k+90 C body surface area in square meeters 17 xd a) Find the body surface area to the nearest hundredth of a child with a weight of 26 kg 542* b) If the usual adult dose of a medication is 250 mg what is the child's dose to the nearest unit for a child that weighs 26 kg ( my 1140 mg 3 a) Solve for x b) Solve for y ax + b c b 3x + 4 xy + 2y 3 +4 ( xt a Ft Ft xc? 3f L ) c) Solve for p d) Solve for z A pt 3p 1 2) 2 z (x + 3z) 5y * *xe ±% IF i eo g zl0yj@ 2

3 4 Translate the phrase into an algebraic expression a) Three more than onehalf of the square of p 3 + tzpz b) The product of four and the total of x and seven 4 ( X + 7) 4 ( xt 7 ) c) The quotient of six less than m and twice m ( ni : 6) Km ) d) 5 less than the product of z and 4 z C 4) 4z 5 e) A number decreased by the difference between three and the number X ( 3 x ) s f) 8 divided by the difference between a and 3 8 ( a 3) 5 Solve graph and write answer in interval notation a) 4x 6 2x ±E Answer b) n 4 2 6n EZZ 2 93t3n< 8 24N C a 3) 6 + 3h HEP +27N E 8 de Answer ] C a } ] 5 3

4 c) 4x or 2x in re XE 1 Y E E Answer IC qos ) e/2 XEIZ : I [4/12] 11<3 XZG [ 6 0 g 4 2 zy E 3 F ±4 B d) x and x Answer e) x < 3 and x 6 Answer f) x and 4x 9 15 XEY 7 XEG f XEG ] 6 Answer Interval notation } C 04 ] 4

5 6 Solve graph and write answer in interval notation 4 3 2x J Has Efeffz ± > < I Graph FE 7 Solve 3 5x Is or 5 22 * s s g * o~xf 8 Solve graph and write answer in interval notation 4 3x 5 or tgrcatcr Graph e x? 5 } or XE 't C a 's ] U [ 30 ) 9 Solve graph and write answer in interval notation 3 x in Wee 0 E E4 3 J 1*4 esstnand Graph 8I [ 04 ] 5

6 10 Translate the phrase into an algebraic equation Do not solve a) 25 less than twice a number is seven more than the number zs F zs>tx6 b) The product of six and a number is 30 times the difference of 14 and the number 1130 ( 14 x ) 11 A piggy bank contains 29 coins in quarters and nickels The have a value of $505 Find the number of each coin type a) Express in terms of x: queer dimes X nickels 29 X quarter Nicked Quarks X X 5 X sx Sos Quarters X o 360 c) dimes Make 11 quarters Turtle and Vince sell reptiles Specifically they sell tortoises and lizards They have 8 more lizards than tortoises and the total value of the reptiles is $260 The value of a lizard is $5 and the value of a tortoise is $32 How $225 many of each type of reptile do they have? a) Express in terms of x: tortoises lizards t 8th SX check : LizardsTortoises s stt 32 t t > t 225 t 32 32T 8th 5 4o+st 8t X 22g 225 Chcckitmurelizuib 3 > t 185 t5 32(s)ts( B) 2zs 5 c) tortoises lizards 13 6

7 Gft 13 A 16ft steel beam is to be cut into two pieces so that one piece is 1 foot longer than twice the other Find the length of each piece L + z X a) Express in terms of x: One of the pieces ltzx The other piece Is check : Ntsb $3 1t3 is s b c) One of the pieces The other piece 5 14 Find three consecutive even integers such that the sum of the least integer and the greatest integer is 12 more than the middle integer a) Write in terms of x: 1st integer 2nd integer xtz 3rd integer xt4 b) Equation: Xtxt 412+1/+2 xt4ly x+44 to y c) 1st integer 10 2nd integer 12 3rd integer it 15 How many liters of a 10% alcohol solution must be mixed with 40 L of a 50% solution to obtain a 40% Solution? 10% 50% 40% Extn liters of 40% Hak acid + 40 liters of 24% acid liters of 28% acid t4o X x 1667L Soak 5667 Hak 7

8 otsx ' 16 A total of $7000 is deposited into two simple interest accounts On one account the annual simple interest rate is 10% and on the second account the annual simple interest rate is 15% How much should be invested in each account so that the total annual interest earned is $800? a) Fill in the table Principle Rate Interest 010 0MX 7 ooo 015 wso check : W Vzocotsoouilooo s 8oO tlokadtoiso)sw ( oso toso * to Sooo $5000 $2000 c) 15% 17 Two planes start at the same time from the same point and fly in opposite directions The first plane is flying 100 mph faster than the second plane In 3 h the two planes are 1050 mi apart Find the rate of each plane Pi R a) picture 1050 Check : X distance for plane I X 3 3X d (22s)( 3) 675mm dptnncefer & + dz I US 0 dz@s)( 3) X 125 to 6 loot plane miles c) Answer: Planet is flying at zzsmph and plane 2 is traveling at hsmph 8 2

9 18 A bicyclist traveling 15 mph heads out at 8 AM At 10 AM a motorcyclist heads out in the same direction traveling 45 mph At what time will the motorcyclist pass the bicyclist? a) picture Bike Motorcycle Bike time Is ttz 1st +30 HZ h 8am +311 an M 4 " 4g + yst I h loamtl Ham 1St E t\t_t Check ; Bike dpls( 374 smile c) Answer: t t Mdwcyok dm4s( 1) 4Smilg The motorcyclist will pass the bike at 11am 19 To pass Algebra a student must have an average of at least 70 on five tests On the first four tests the student has the scores of and 71 What possible scores on the fifth test would guarantee a passing grade in the class X TX I

10 z 20 a) Write in y mx b form: 3x 4y 8 b) Find the x and y intercepts Tx Px F yo 4y CD Y *@ X0 4y8 } 8 4y8 F x y 2 o ) ( o xintercept: yintercept: c) Fill in the table d) Graph y 24 2 x 0 y Y G) 22 4 y2l YZT 21 Graph a) x 4 b) y 2 ^ r v 10