Simple Functional Relationships
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ISEE Upper Level: Quantitative Reasoning › Simple Functional Relationships
A bike travels at 12 miles per hour. Using input $t$ (hours), output $d$ (miles), which rule fits?
$t=12d$
$d=t-12$
$d=12+t$
$d=12t$
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a bike traveling at a constant speed of 12 miles per hour, with input as time in hours and output as distance in miles. Choice B is correct because it accurately follows the function rule d = 12t, which multiplies the constant speed by time to get distance, matching the proportional relationship. Choice A is incorrect because it assumes d = 12 + t, which is a common mistake when confusing constant addition with multiplication in rate problems. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A town’s population increases by 200 each year from 5,000. What conclusion best describes input year to output population?
Output increases by 200 yearly
Output stays constant each year
Output doubles every year
Output decreases by 200 yearly
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a town’s population starting at 5,000 and increasing by 200 each year, with input as years and output as population. Choice A is correct because it accurately follows the function rule of linear growth, describing a constant annual increase of 200. Choice B is incorrect because it assumes exponential doubling, which is a common mistake when confusing linear and exponential relationships. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
Temperature converts by input $C$ to output $F$ using $F=\frac{9}{5}C+32$. How does $F$ change when $C$ increases by 5?
It increases by 9
It decreases by 9
It increases by 32
It increases by 5
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by the temperature conversion formula F = (9/5)C + 32, with input as Celsius and output as Fahrenheit. Choice B is correct because it accurately follows the function rule, showing that an increase of 5 in C leads to an increase of (9/5)*5 = 9 in F. Choice A is incorrect because it assumes the increase is just 5, which is a common mistake when ignoring the multiplication factor in linear conversions. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A gym charges a $15 membership plus $3 per visit. Which rule gives output cost $C$ from input visits $v$?
$C=18v$
$C=3v+15$
$C=15-3v$
$C=15v+3$
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a gym charging a $15 membership plus $3 per visit, with input as visits and output as cost. Choice A is correct because it accurately follows the function rule C = 3v + 15, combining fixed and variable costs. Choice B is incorrect because it assumes C = 15v + 3, which is a common mistake when swapping coefficients in linear equations. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A taxi fare follows input miles $m$ to output cost $c$: 1→7, 2→9, 3→11. Which function rule is correct?
$c=2m+5$
$c=m+7$
$c=2m-5$
$c=5m+2$
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by input miles m to output cost c: 1→7, 2→9, 3→11. Choice A is correct because it accurately follows the function rule c = 2m + 5, matching the linear pattern with a slope of 2 and intercept of 5. Choice B is incorrect because it assumes c = 5m + 2, which is a common mistake when reversing the coefficients in the equation. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A plant grows 2 cm each week from 10 cm. How would the output height change if input weeks increases by 4?
It increases by 10 cm
It increases by 2 cm
It increases by 4 cm
It increases by 8 cm
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a plant growing 2 cm each week from an initial 10 cm, with input as weeks and output as height. Choice C is correct because it accurately follows the function rule, showing that an increase of 4 weeks leads to 4 * 2 = 8 cm growth. Choice B is incorrect because it assumes 4 cm, which is a common mistake when using the weekly rate without multiplying by the change in input. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A population starts at 2,000 and grows by 100 yearly. What is the output population after 5 years?
2,100
2,500
3,000
2,050
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a population starting at 2,000 and growing by 100 yearly, with input as years and output as population. Choice C is correct because it accurately follows the function rule of 2000 + 100 * 5 = 2500 after 5 years. Choice B is incorrect because it assumes 2100, which is a common mistake when adding 100 * 1 instead of for all years. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A printer makes 30 pages per minute. If input is minutes, what is the output when input equals 7?
240 pages
210 pages
180 pages
200 pages
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a printer making 30 pages per minute, with input as minutes and output as pages. Choice C is correct because it accurately follows the function rule of output = 30 * input, calculating 30 * 7 = 210 pages. Choice B is incorrect because it assumes 200, which is a common mistake when miscalculating 30 * 6 + 20 or similar arithmetic errors. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A swimmer completes 4 laps every 10 minutes. Based on this relationship, how does output laps change if input minutes doubles?
Laps double
Laps increase by 4
Laps stay the same
Laps decrease by half
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a swimmer completing 4 laps every 10 minutes, with input as minutes and output as laps. Choice B is correct because it accurately follows the function rule of proportional rate, so doubling minutes doubles the laps. Choice C is incorrect because it assumes laps increase by 4, which is a common mistake when adding the base amount instead of scaling proportionally. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.
A streaming service charges $8 monthly plus $2 per movie. Which output occurs when input movies equals 5?
$10$
$26$
$18$
$16$
Explanation
This question tests ISEE Upper Level quantitative reasoning skills, specifically interpreting simple functional relationships. A functional relationship describes how one quantity changes in response to another, often represented using a rule, table, or graph. In this question, the relationship is illustrated by a streaming service charging $8 monthly plus $2 per movie, with input as movies and output as total cost. Choice C is correct because it accurately follows the function rule 8 + 25 = 18 for 5 movies. Choice B is incorrect because it assumes 16, which is a common mistake when calculating 8 + 24 or off-by-one in multiplication. To help students: Teach them to carefully analyze the given data and check if their interpretation aligns with the rule. Practice identifying and correcting common errors like misreading tables or graphs. Encourage using estimation to verify the plausibility of their answers.