Download Test 1, Additional Problems, Review Sheet

Math 095 – Review Sheet – Practice Problems for Midterm Exam €
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1. Solve each equation. A) 2x +19 = −15 B) −7m + 3m = 36 C) 39 = 6 y − ( y − 9) 1
1 9
D) x + = ( 5x +11) E) 2(3 + 7t ) − (1+15t ) = 2 4
5 8
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3
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F) x − 4 = x + x G) −6t + 5t − 9 = 3(t − 4) − 5 4
2
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H) 7( y − 3) − 4( y +1) = −5( y + 5) I) 2.3x +13.7 = 1.3x + 2.9 €
2
1
4
J) z + 8 = z K) 5x + 9 = 7x + 21 L) − y = −12 3
4
7
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M) 7 − ( m − 4) = −3m + 2( m +1) N) 2 ( 5y + 4) −11 = 3 ( 2y − 7) +16 €
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O) − ( x − 27) + ( x + 3) = x + 67 P) −8(2x + 4) = −4(4x + 8) 9
3
"1
% 2
5
15 x
m m−2
x = 7 $ x − 3' −
=
=
Q) 6
R) S) #6
& 3 66
44
7
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4t + 9 t − 1
3x − 9 2x + 3
T) 3 = 4
U) 8 = 5
2. Solve the formula for the specified variable. 2
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A) V = πr h for h B) P = 2L + 2W for W 1
C) A = h ( b + B) for B 2
D) y = 3mx + 2b for x 3. Solve each problem. A) Nine subtracted from ten times a number is 71. What is the number? B) One angle in a triangle has a measure that is four times as large as the smallest angle. The measure of the third angle is 30 degrees more than that of the smallest angle. Find the measure of the angles. C) A rectangular room is three times as long as it is wide. Its perimeter is 56 feet. Find the dimensions for the room. D) The perimeter of a rectangle is 44 yards. The length is 5 yards less than twice the width. Find the length and the width of the rectangle. E) The sum of five consecutive integers is 265. What is the smallest of the five integers? F) To control a fever, a doctor suggests that a child who weighs 28 kg be given 320 mg of a liquid pain reliever. If the dosage is proportional to the child’s weight, how much of the medication is recommended for a child who weighs 35 kg? G) Ron bicycled 234 miles in 14 days. At this rate, how far would Roy bicycle for 42 days? H) If 2 shirts can be bought for $47, how many shirts can be bought with $200? I) From a point on a straight road, Marco and Gary ride bicycles in the same direction. Marco rides at 10 mph and Gary rides at 12 mph. In how many hours will they be 15 miles apart? J) Two cities are 440 miles apart. A truck leaves City A driving towards City B at an average rate of 60 mph. At the same time, an antique auto leaves City B driving towards City A averaging 28 mph. How long will it take them to meet (assuming they are travelling on the same road)? K) Two trains leave a station at the same time, traveling in opposite directions. The first travels east at 85 km per hr. The second travels west at 95 km per hr. How long will it take for them to be 315 km apart? L) In chemistry class, 12 liters of a 12% alcohol solution must be mixed with a 20% alcohol solution to obtain a 14% alcohol solution. How many liters of the 20% solution is needed? M) How many gallons of a fruit drink that is 50% real juice must be mixed with a fruit drink that is 20% real juice to obtain 12 gallons of a fruit drink that is 40% real juice? N) An artist invests in a bond paying 6% and $6000 more than three times as much in mutual funds paying 5%. Her total interest income from the investments is $825. How much does she invest at each rate? Solutions to Practice Problems for Midterm Exam
1. A) x = -­‐17 B) m = -­‐9 C) y = 6 D) x = -­‐487/215 E) t = 3
F) x = -­‐2 L) y = 21 Q) x = 65 2. A) h =
C) B =
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G) t = 2 I) x = -­‐10.8 J) z = -­‐96/5 K) x = -­‐6 M) no solution N) y = -­‐1/2 O) x = -­‐81 R) 𝑥 = 10 S) 𝑚 = ! T) 𝑡 = −3 U) 𝑥 = −69 B) W =
V
πr
H) y = 0 2
P) all real numbers !
2A − hb
2A
or B =
−b
h
h € 3. A) The number is 8. €
B) 100° ; 55° ; 25° C) width = 7 feet; length = 21 feet D) width = 9 yards; length = 13 yards E) smallest integer is 51 F) 400 mg G) 702 miles H) 8 shirts I) 7.5 hours J) 5 hours K) 1.75 hours L) 4 liters M) 8 gallons N) $2500 at 6%; $13,500 at 5% P − 2L
P
or W = − L 2
2
y − 2b
D) x =
€ 3m