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460
Examination
August 2017
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 rn^ – 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 graph below models the height of a remote- control helicopter over 20 seconds during flight.
Over which interval does the helicopter have the slowest average rate of change? (1) 0 to 5 seconds (3) 10 to 15 seconds (2) 5 to 10 seconds (4) 15 to 20 seconds 5 _____
6 In the functions f ( x ) = kx^2 and g ( x ) = | kx |, k is a positive
integer. If k is replaced by 12 , which statement about these new functions is true? (1) The graphs of both f ( x ) and g ( x ) become wider. (2) The graph of f ( x ) becomes narrower and the graph of g ( x ) shifts left. (3) The graphs of both f ( x ) and g ( x ) shift vertically. (4) The graph of f ( x ) shifts left and the graph of g ( x ) becomes wider. 6 _____
7 Wenona sketched the polynomial P ( x ) as shown on the axes below.
Which equation could represent P ( x )? (1) P ( x ) = ( x + 1)( x – 2)^2 (2) P ( x ) = ( x – 1)( x + 2)^2 (3) P ( x ) = ( x + 1)( x – 2) (4) P ( x ) = ( x – 1)( x + 2) 7 _____
8 Which situation does not describe a causal relationship?
(1) The higher the volume on a radio, the louder the sound will be. (2) The faster a student types a research paper, the more pages the research paper will have. (3) The shorter the time a car remains running, the less gasoline it will use. (4) The slower the pace of a runner, the longer it will take the runner to finish the race. 8 _____
12 Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min. If t represents the number of minutes on the treadmill and b represents the number of minutes on the sta- tionary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike? (1) b (3) 45 – b (2) 5 b (4) 250 – 5 b 12 _____
13 Which value of x satisfies the equation 56 ( 38 − x)= 16?
(2) –18.825 (4) –15.6875 13 _____
14 If a population of 100 cells triples every hour, which function represents p ( t ), the population after t hours? (1) p ( t ) = 3(100) t^ (3) p ( t ) = 3 t + 100 (2) p ( t ) = 100(3) t^ (4) p ( t ) = 100 t + 3 14 _____
15 A sequence of blocks is shown in the diagram below.
This sequence can be defined by the recursive func- tion a 1 = 1 and a (^) n = an – 1 + n. Assuming the pattern continues, how many blocks will there be when n = 7? (1) 13 (3) 28 (2) 21 (4) 36 15 _____
16 Mario’s $15,000 car depreciates in value at a rate of 19% per year. The value, V , after t years can be mod- eled by the function V = 15,000(0.81) t. Which func- tion is equivalent to the original function?
(1) V = 15,000(0.9) 9 t^ (3) V = 15,000(0.9)
t )^9
(2) V = 15,000(0.9) 2 t^ (4) V = 15,000(0.9)
t ) (^2) 16 _____
17 The highest possible grade for a book report is 100. The teacher deducts 10 points for each day the report is late. Which kind of function describes this situation? (1) linear (3) exponential growth (2) quadratic (4) exponential decay 17 _____
20 How many of the equations listed below represent the line passing through the points (2, 3) and (4, –7)?
5 x + y = 13 y + 7 = –5( x – 4) y = –5 x + 13 y – 7 = 5( x – 4) (1) 1 (3) 3 (2) 2 (4) 4 20 _____
21 The Ebola virus has an infection rate of 11% per day as compared to the SARS virus, which has a rate of 4% per day. If there were one case of Ebola and 30 cases of SARS initially reported to authorities and cases are reported each day, which statement is true? (1) At day 10 and day 53 there are more Ebola cases. (2) At day 10 and day 53 there are more SARS cases. (3) At day 10 there are more SARS cases, but at day 53 there are more Ebola cases. (4) At day 10 there are more Ebola cases, but at day 53 there are more SARS cases. 21 _____
22 The results of a linear regression are shown below.
y = ax + b a = –1. b = 139. r = –0. r^2 = 0. Which phrase best describes the relationship between x and y? (1) strong negative correlation (2) strong positive correlation (3) weak negative correlation (4) weak positive correlation 22 _____
23 Abigail’s and Gina’s ages are consecutive integers. Abigail is younger than Gina and Gina’s age is repre- sented by x. If the difference of the square of Gina’s age and eight times Abigail’s age is 17, which equation could be used to find Gina’s age? (1) ( x + 1) 2 – 8 x = 17 (2) ( x – 1) 2 – 8 x = 17 (3) x^2 – 8( x + 1) = 17 (4) x^2 – 8( x – 1) = 17 23 _____
24 Which system of equations does not have the same solution as the system below?
4 x + 3 y = 10 –6 x – 5 y = 16
(1) –12 x – 9 y = –30 (3) 24 x + 18 y = 60 12 x + 10 y = 32 –24 x – 20 y = – (2) 20 x + 15 y = 50 (4) 40 x + 30 y = 100 –18 x – 15 y = –48 36 x + 30 y = –96 24 _____
26 Determine and state whether the sequence 1, 3, 9, 27, … displays exponential behavior. Explain how you arrived at your decision.
27 Using the formula for the volume of a cone, express r in terms of V , h , and p.
28 The graph below models the cost of renting video games with a membership in Plan A and Plan B.
Explain why Plan B is the better choice for Dylan if he only has $50 to spend on video games, including a membership fee.
Bobby wants to spend $65 on video games, including a membership fee. Which plan should he choose? Explain your answer.
30 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump , how many jumps it would take this athlete to jump one mile.
31 Write the expression 5 x + 4 x^2 (2 x + 7) – 6 x^2 – 9 x as a polynomial in standard form.
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 Loretta and her family are going on vacation. Their des- tination is 610 miles from their home. Loretta is going to share some of the driving with her dad. Her average speed while driving is 55 mph and her dad’s average speed while driving is 65 mph.
The plan is for Loretta to drive for the first 4 hours of the trip and her dad to drive for the remainder of the trip. Determine the number of hours it will take her family to reach their destination.
After Loretta has been driving for 2 hours, she gets tired and asks her dad to take over. Determine, to the nearest tenth of an hour , how much time the family will save by having Loretta’s dad drive for the remainder of the trip.
34 The heights, in feet, of former New York Knicks basket- ball players are listed below.
Using the heights given, complete the frequency table below.
Question 34 is continued on the next page.
