Grima, Mat 120 chapter P Hybrid practice test for the in class Chapter P test.
#1-2: Simplify
1) (4x3y3)(3x2y4)
2) (5st3)(5s2t5)
#3-4: Simplify, assume no denominator equals 0
3)
12𝑥 2
8𝑥 5
4)
9𝑥𝑦 2
12𝑥 2 𝑦
#5-8: Simplify
5) (2x3)4
6) (3x2y3)2
7) (4x2y3)2(2x4y)4
8) (2xy3)3(xy4)3
#9-12: Simplify the expression
9) -x0
10) (-x)0
11) -20
12) (-2)0
#13 – 17: Simplify the expression. Write the answer with positive exponents only.
13) 2-4x-3y2
14)
4𝑥 2 𝑦 −3
16𝑥 −3 𝑦 −5
3𝑥 −2
3 −2
15) (𝑦3 )
16) (5)
17)
𝑥 −5
𝑥 −2
#18-19: Divide
18)
20𝑥 4 𝑦 3 −8𝑥 2 𝑦 3 + 12𝑥𝑦 2
4𝑥𝑦
19)
2𝑥 2 +3𝑥−2
2𝑥−1
Answers:
1) 12x5y7 2) 25s3t8
3)
3
2𝑥 3
4)
3𝑦
4𝑥
5) 16x12 6) 9x4y6 7) 256x20y10
8) 8x6y21 9) -1 10) 1 11) -1 12) 1 13)
16)
25
9
17)
1
𝑥3
𝑦2
16𝑥 3
14)
𝑥 5𝑦2
4
18) 5𝑥 3 𝑦 2 − 2𝑥𝑦 2 + 3𝑦 19) x + 2
15)
𝑦6
9𝑥 2
Grima, Mat 120 chapter 1 Hybrid practice test
1 – 12: Completely factor the polynomial. State if a polynomial is prime.
1) x2 + 2x – 24
2) -3y3 – 6y2 + 9y
3) 2n2 + 11n + 5
4) 16x2 – 25
5) x2 + 25
6) x3 + 8
7) 5m2 + m – 4
8) 3n2 – n - 2
9) x2 + 5x + 6x + 30
10) 4x2 – 2x - 10x + 5
11) x3 – 125
12) x2 + 3x + 7
13 – 18: Solve each equation.
13) (x + 2)(3x + 24)=0
14) x2 – 7x – 18 = 0
15) 5x2 - 8x + 3 =0
16) x(x – 3) = 10
17) 5x2 + 3x - 2 = 0
18) 2x(x +4) = 0
19) A rectangular garden is 2 feet narrower than it is long. The garden has an area of 35 square
feet. Find the dimensions of the garden.
20) The length of the hypotenuse in a right triangle is 5 inches. The longest leg is 1 inch longer
than the length of the shortest leg. Find the length of each side.
Answers:
1) (x + 6)(x – 4) 2) -3y(y+3)(y – 1) 3) (2n+1)(n+5) 4) (4x + 5)(4x – 5)
5) prime 6) (x + 2)(x2 – 2x + 4) 7) (5m – 4)(m + 1) 8) (3n + 2)(n – 1)
9) (x+5)(x+6) 10) (2x – 5)(2x – 1) 11) (x – 5)(x2 + 5x + 25) 12) prime
3
2
13) x = -2, -8 14) x = -2,9 15) x = 5 , 1 16) x = -2, 5 17) x = 5 , −1
18) x = 0,-4 19) width 5 ft length 7 ft 20) short let 3 inches long leg 4 inches
Grima, Mat 120 chapter 2 Practice test
1. Multiply or divide as indicated.
𝑛2 +2𝑛−3
∗
𝑛2 +4𝑛−5
a)
c)
𝑥 2 −𝑥−6
𝑥 2 −𝑥−12
𝑛2 −3𝑛−10
𝑚−2
∗
𝑚+3
b)
𝑛2 +5𝑛+6
𝑚2 +6𝑚+9
𝑚2 −4
𝑥 2 +3𝑥+2
÷ 𝑥 2 −3𝑥−4
2. Find the domain of the given expression; write your answer in a sentence.
𝑥+2
2𝑥+20
3) Solve the rational equations. Be sure to check all solutions. If a solution does not check
state that it is extraneous
a)
𝑥
3
𝑥
1
−4=6
b)
𝑥
𝑥+5
5
14
− 𝑥−5 = 𝑥 2 −25 (hint 13 * 3 = 39)
4) Reduce the rational expression to lowest terms.
a)
c)
14𝑥 2
b)
16𝑥 7
3𝑥 2 −8𝑥+4
𝑥 2 − 5𝑥+6
𝑥 2 +3𝑥−4
𝑥 2 +6𝑥+8
5) Add or subtract as indicated.
a)
3𝑥
𝑥+6
18
+ 𝑥+6
b)
2𝑥−5
𝑥+3
16
+ 𝑥+3
6) One person runs 2 miles per hour slower than another. The faster runner can cover 15 miles
in the same time the other can run 9 miles. Find the speed of each runner.
Answers:
1a)
𝑛−5
𝑛+5
1b)
𝑚+3
𝑚+2
1c)
𝑥−3
𝑥+3
2) The domain is all real numbers except x = -10
okay to write (−∞, −10) ∪ (−10, ∞) also okay to write shorthand answer
3a) x = 2
3b) x = -3 and x = 13
4a)
7
8𝑥 5
6) fast runner 5 mph slow runner 3 mph
4b)
3𝑥−2
𝑥−3
4c)
𝑥−1
𝑥+2
5a) 3
5b)
2𝑥+11
𝑥+3
MAT 120 Chapter 4 Practice test
1) Simplify the expression.
𝑎) 274⁄3
25 −1⁄2
𝑏) 25−3⁄2
𝑐) (49)
2) Create a table of values and sketch a graph of the function. You may use your calculator and should
round to two decimal places when needed. Use the graph to find the domain and range of the function
in interval notation.
𝑓(𝑥) = √𝑥 − 2
3) Simplify the radical expression. (Assume all variables represent positive real numbers.)
3
√125𝑦 6
4
4) Simplify the expression. Write your answer using only positive exponents. (3𝑦 1⁄2 𝑦 5⁄2 )
5) Write the expression using radical notation (3𝑥)1⁄2
3
6) Write the expression using rational exponents. 4 √𝑥
7) Simplify. √20𝑥𝑦 4 𝑧 5
8) Add 5√20 + 3√80
9) Simplify the expressions √−20
10) Subtract, write your answer in the form a+ bi (5-2i) – (6-3i)
#11-13: Solve the radical equation if possible.
11) √𝑥 + 2 = 4
12) 3√2𝑥 − 2 = 10
13) √𝑥 − 2 = 𝑥 − 8
Answers:
1a) 81 1b)
1
125
1c)
7
5
2) domain (−∞, ∞) range 𝑥 ≥ 2 𝑜𝑟 [2, ∞) (table and graph will be shown in class. They take up a
lot of room)
3) 5y2 4) 81y12 5) √3𝑥 6) 4𝑥 1⁄3 7) 2𝑦 2 𝑧 2 √5𝑥𝑧 8) 22√5
10) -1 + I 11) x = 14 12) x = 8 13) x = 11
9) 2√5𝑖
MAT 122 Chapter 5 Hybrid practice test
1. Find the vertex and axis of symmetry and sketch a graph.
a) y = (x-4)2 - 3
b) y = -2(x+5)2 + 4
2. Find the vertex by using the vertex formula then make a table of values and sketch a graph.
a) T(x) = 3x2 – 18x + 19
b) s(x) = 2x2 – 20x + 40
3. Solve the equation using the quadratic formula. (6 points each)
6x2 + 5x = 3
4. Solve by the square root property.
a) (q+2)2 = 5
b) (t - 6)2 = -25
5. Solve the quadratic equation by completing the square and applying the square root property.
(0 points for a correct answer gotten by another method)
p2 + 4p + 8 = 0
6. Solve
a) 𝑝 − 2√𝑝 = 8
b) x4 - 7x2 - 18 = 0
c) (x-2)2 + 5(x-2) – 6 = 0
7) Solve and write your answer in interval notation. x2 + 3x – 10 < 0
Answers:
1a) vertex (4,3) axis of symmetry x = 4 graph will be shown in class
1b) vertex (-5, 4) axis of symmetry x = -5 graph will be shown in class
2a) vertex (3, -8) graph will be shown in class
2b) vertex (5, -10) graph will be shown in class
3)
−5±√97
12
4a) 𝑞 = −2 ± √5 4b) 𝑡 = 6 ± 5𝑖
5) need to show these steps or get no credit
p2 + 4p = -8
p2 + 4p + 16 = - 8 + 16
(p+4)2 = 8
𝑝 + 4 = ±√8
𝑝 + 4 = ±2√2
answer 𝑝 = −2 ± 2√2
6a) p = 16 6b) 𝑥 = ±3𝑖, ±√2𝑖 6c) x = 3, -4 7) (-5, 2)
MAT 120 Chapter 7 Practice test
#1-3: Plot 5 points and sketch a graph of the function, state the domain and range of the function. You
may round to 1 decimal, or use fractions when appropriate.
1) 𝑚(𝑥) = 2𝑥−1
1 𝑥−2
2) 𝑓(𝑥) = 3𝑥
3) 𝑔(𝑥) = (3)
#4 - 11: Solve the exponential equation by writing each side of the equation with the same base then
equating the exponents.
4) 3x = 81
1 𝑥
5) 2x+4 = 32
1 3𝑥+5
6) (3) = 27
7) (2)
= 32
8) 25𝑥−2 = 5
9) 25x-3 = 1254x+3
10) 4x+2 = 8x
11) 49x+3 = 7
12) Use the exponential growth function: P(t) = P0ert (where P0 is the initial population, r is the growth
rate as a %, and t is time) to answer the following questions.
The population of the Arizona is currently 5.5 million and is growing at a rate of .75% per year. Estimate
the population of Arizona in 20 years. Round to 2 decimals.
𝑟 𝑛𝑡
13) Use the compound interest formula 𝐴 = 𝑃 (1 + 𝑛)
to answer the following.
An initial deposit of $10,000 earns 3% interest compounded quarterly. How much will be in the account
after 5 years?