Download Algebra I High School Math Reference Sheet for June 2018 Examination and more Exercises Algebra in PDF only on Docsity!
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Examination
June 2018
Algebra I
HIGH SCHOOL MATH REFERENCE SHEET
Conversions 1 inch = 2.54 centimeters 1 cup = 8 fluid ounces 1 meter = 39.37 inches 1 pint = 2 cups 1 mile = 5280 feet 1 quart = 2 pints 1 mile = 1760 yards 1 gallon = 4 quarts 1 mile = 1.609 kilometers 1 gallon = 3.785 liters 1 liter = 0.264 gallon 1 kilometer = 0.62 mile 1 liter = 1000 cubic centimeters 1 pound = 16 ounces 1 pound = 0.454 kilogram 1 kilogram = 2.2 pounds 1 ton = 2000 pounds
Formulas Triangle A = 1 2
bh
Parallelogram A = bh Circle A = π r^2 Circle C = π d or C = 2 π r
Formulas (continued)
General Prisms V = Bh
Cylinder V = π r^2 h
Sphere V = 4 3
π r^3
Cone V = 1 3
π r^2 h
Pyramid V = 1 3
Bh
Pythagorean Theorem a^2 + b^2 = c^2
Quadratic Formula x = b^ b^ ac a
Arithmetic Sequence a (^) n = a 1 + ( n – 1) d
Geometric Sequence a (^) n = a 1 r n^ – 1
Geometric Series S (^) n = a^ a r 1 r
n 1 − 1 −
where r ≠ 1
Radians 1 radian = 180 π
degrees
Degrees 1 degree = 180
π (^) radians
Exponential Growth/Decay A = A 0 e k ( t^ –^ t 0 )^ + B 0
5 The box plot below summarizes the data for the aver- age monthly high temperatures in degrees Fahrenheit for Orlando, Florida.
The third quartile is (1) 92 (3) 83 (2) 90 (4) 71 5 _____
6 Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. If she only has $ to spend on berries, which inequality represents the situation where she buys x pounds of strawberries and y pounds of raspberries? (1) 1.60 x + 1.75 y ≤ 10 (3) 1.75 x + 1.60 y ≤ 10 (2) 1.60 x + 1.75 y ≥ 10 (4) 1.75 x + 1.60 y ≥ 10 6 _____
7 On the main floor of the Kodak Hall at the Eastman Theater, the number of seats per row increases at a constant rate. Steven counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20? (1) 65 (3) 69 (2) 67 (4) 71 7 _____
8 Which ordered pair below is not a solution to f ( x ) = x^2 – 3 x + 4? (1) (0, 4) (3) (5, 14) (2) (1.5, 1.75) (4) (–1, 6) 8 _____
9 Students were asked to name their favorite sport from a list of basketball, soccer, or tennis. The results are shown in the table below.
What percentage of the students chose soccer as their favorite sport? (1) 39.6% (3) 50.4% (2) 41.4% (4) 58.6% 9 _____
10 The trinomial x^2 – 14 x + 49 can be expressed as
(1) ( x – 7)^2 (3) ( x – 7)( x + 7) (2) ( x + 7)^2 (4) ( x – 7)( x + 2) 10 _____
11 A function is defined as {(0, 1), (2, 3), (5, 8), (7, 2)}. Isaac is asked to create one more ordered pair for the function. Which ordered pair can he add to the set to keep it a function? (1) (0, 2) (3) (7, 0) (2) (5, 3) (4) (1, 3) 11 _____
15 The Utica Boilermaker is a 15-kilometer road race. Sara is signed up to run this race and has done the fol- lowing training runs: I. 10 miles II. 44,880 feet III. 15,560 yards
Which run(s) are at least 15 kilometers? (1) I, only (3) I and III (2) II, only (4) II and III 15 _____
16 If f ( x ) = x^2 + 2, which interval describes the range of this function? (1) (–∞, ∞) (3) [2, ∞) (2) [0, ∞) (4) (–∞, 2] 16 _____
17 The amount Mike gets paid weekly can be repre- sented by the expression 2.50 a + 290, where a is the number of cell phone accessories he sells that week. What is the constant term in this expression and what does it represent? (1) 2.50 a , the amount he is guaranteed to be paid each week (2) 2.50 a , the amount he earns when he sells a acces- sories (3) 290, the amount he is guaranteed to be paid each week (4) 290, the amount he earns when he sells a accessories 17 _____
18 A cubic function is graphed on the set of axes below.
Which function could represent this graph? (1) f ( x ) = ( x – 3)( x – 1)( x + 1) (2) g ( x ) = ( x + 3)( x + 1)( x – 1) (3) h ( x ) = ( x – 3)( x – 1)( x + 3) (4) k ( x ) = ( x + 3)( x + 1)( x – 3) 18 _____
19 Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. I. 15 x^4 – 6 x + 3 x^2 – 1 II. 12 x^3 + 8 x + 4 III. 2 x^5 + 8 x^2 + 10 x
Which student’s response is correct? (1) Tyler said I and II because the coefficients are decreasing. (2) Susan said only II because all the numbers are decreasing. (3) Fred said II and III because the exponents are decreasing. (4) Alyssa said II and III because they each have three terms. 19 _____
22 How many real-number solutions does 4 x^2 + 2 x + 5 = 0 have? (1) one (3) zero (2) two (4) infinitely many 22 _____
23 Students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p = 2 + 2 w. Three of their responses are shown below.
I. = 1 2
p – w
II. = 1
( p – 2 w )
III. =
p − w
Which responses are correct? (1) I and II, only (3) I and III, only (2) II and III, only (4) I, II, and III 23 _____
24 If an = n ( an – 1) and a 1 = 1, what is the value of a 5?
(1) 5 (3) 120 (2) 20 (4) 720 24 _____
PART II
Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [16 credits]
25 Graph f ( x ) = x + 2 over the domain –2 ≤ x ≤ 7.
27 Solve for x to the nearest tenth : x^2 + x – 5 = 0.
28 The graph of the function p ( x ) is represented below. On the same set of axes, sketch the function p ( x + 2).
30 Solve the equation below algebraically for the exact value of x.
6 – 23 ( x + 5) = 4 x
31 Is the product of (^) 16 and
7 rational or irrational? Explain your reasoning.
PART III
Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [16 credits]
33 A population of rabbits in a lab, p ( x ), can be mod- eled by the function p ( x ) = 20(1.014) x , where x repre- sents the number of days since the population was first counted.
Explain what 20 and 1.014 represent in the context of the problem.
Determine, to the nearest tenth , the average rate of change from day 50 to day 100.
34 There are two parking garages in Beacon Falls. Garage A charges $7.00 to park for the first 2 hours, and each additional hour costs $3.00. Garage B charges $3.25 per hour to park.
When a person parks for at least 2 hours, write equa- tions to model the cost of parking for a total of x hours in Garage A and Garage B.
Determine algebraically the number of hours when the cost of parking at both garages will be the same.
