ISEE Middle Level Quiz: Function Rules And Output

20 questions · exam conditions

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Function Rules And OutputQuestion 1 of 20

Commission rule: $c = 5s - 2$ . Find $c$ when $s = 7$ .

ISEE Middle Level Quiz

ISEE Middle Level Quiz: Function Rules And Output

Practice Function Rules And Output in ISEE Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Function Rules And Output, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Commission rule: $c = 5s - 2$ . Find $c$ when $s = 7$ .

33 (correct answer)
17
37
23

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the commission rule c = 5s - 2 is used to find commission c when sales s = 7. Choice A is correct because substituting 7 for s yields c = 5(7) - 2 = 35 - 2 = 33, demonstrating proper function application. Choice C (37) might result from adding 2 instead of subtracting, while Choice D (23) could come from calculating 5(5) - 2. Choice B (17) appears to result from a calculation error. To help students, stress careful attention to operations (subtraction vs. addition) and systematic substitution. Commission problems provide real-world context that makes abstract algebra more meaningful.

Question 2

Car distance rule: $d = 40t + 5$ . Find $d$ when $t = 2$ .

85 (correct answer)
45
80
90

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the car distance rule d = 40t + 5 is used to find distance d when time t = 2. Choice A is correct because substituting 2 for t yields d = 40(2) + 5 = 80 + 5 = 85, demonstrating proper function application and order of operations. Choice C (80) represents the common error of forgetting to add the constant term, calculating only 40(2). Choice D (90) might result from calculating 40(2) + 10, while Choice B (45) could come from adding before multiplying. To help students, stress the importance of following order of operations systematically. Using distance-time relationships helps students connect algebra to physics concepts.

Question 3

The "zip" of a positive integer $n$ is a value calculated by a special rule: add the whole number quotient and twice the remainder when $n$ is divided by 5.

What is the "zip" of the number 38?

10
13 (correct answer)
42
44

Explanation: The correct answer is 13. First, divide 38 by 5.

38 \div 5 = 7

with a remainder of 3. So, the whole number quotient is 7 and the remainder is 3. The rule is to add the quotient (7) and twice the remainder (

2 \times 3 = 6

). The result is

7 + 6 = 13

Question 4

To convert a temperature from degrees Celsius ( $C$ ) to degrees Fahrenheit ( $F$ ), the function $F(C) = \frac{9}{5}C + 32$ is used. An oven must be preheated to 200°C. What is this temperature in degrees Fahrenheit?

143°F
360°F
392°F (correct answer)
418°F

Explanation: The correct answer is 392°F. Substitute

C = 200

into the function:

F(200) = \frac{9}{5}(200) + 32

. First, multiply

\frac{9}{5}

by 200. This is

9 \times (200 \div 5) = 9 \times 40 = 360

. Then, add 32:

360 + 32 = 392

. The temperature is 392°F.

Question 5

A monthly phone bill, $B$ , is calculated using the function $B(d) = 25 + 0.05(d - 500)$ for data usage, $d$ , greater than 500 megabytes. If data usage is 500 MB or less, the bill is a flat $25.

What is the total bill for a month where 860 MB of data were used?

$18.00
$43.00 (correct answer)
$68.00
$80.00

Explanation: The correct answer is $43.00. Since 860 MB is greater than 500 MB, the function

B(d) = 25 + 0.05(d - 500)

applies. First, find the amount of data over 500 MB:

860 - 500 = 360

MB. Next, calculate the cost for this extra data:

0.05 \times 360 = 18

. Finally, add this to the base cost of $25:

25 + 18 = 43

. The total bill is $43.00.

Question 6

A point $(x, y)$ on a coordinate plane is transformed using the rule $T(x, y) = (y - 3, 2x)$ to produce a new point.

If the point $(5, -1)$ is transformed by this rule, what are the coordinates of the new point?

(-4, 10) (correct answer)
(2, -2)
(2, 10)
(10, -4)

Explanation: The correct answer is (-4, 10). The original point is

(x, y) = (5, -1)

. The rule for the new point's coordinates is

(y - 3, 2x)

. To find the new x-coordinate, use the original y-coordinate:

y - 3 = -1 - 3 = -4

. To find the new y-coordinate, use the original x-coordinate:

2x = 2(5) = 10

. Therefore, the new point is at (-4, 10).

Question 7

The number of blocks in Figure $n$ of a pattern is given by the function $B(n) = 2n^2 - n$ .

How many more blocks are in Figure 5 than in Figure 4 of the pattern?

9
17 (correct answer)
18
27

Explanation: The correct answer is 17. First, calculate the number of blocks in Figure 5 by substituting

n=5

into the function:

B(5) = 2(5^2) - 5 = 2(25) - 5 = 50 - 5 = 45

. Next, calculate the number of blocks in Figure 4 by substituting

n=4

B(4) = 2(4^2) - 4 = 2(16) - 4 = 32 - 4 = 28

. Finally, find the difference between the two figures:

45 - 28 = 17

Question 8

The function $C(k) = 1.61k$ converts a distance in kilometers, $k$ , to miles. The function $F(m) = 5280m$ converts a distance in miles, $m$ , to feet. Approximately how many feet are in a 10-kilometer race?

5,280
16,100
52,800
85,000 (correct answer)

Explanation: The correct answer is 85,000. This requires two steps. First, convert 10 kilometers to miles using

C(k)

C(10) = 1.61 \times 10 = 16.1

miles. Second, convert 16.1 miles to feet using

F(m)

F(16.1) = 5280 \times 16.1

. We can approximate this as

5300 \times 16 = 84800

. The closest answer is 85,000.

Question 9

A number, $x_0$ , is processed by a machine using the rule $f(x) = \frac{1}{2}x + 4$ to produce an output $x_1$ . The output $x_1$ is then immediately processed by the same machine using the same rule to produce a second output, $x_2$ .

If the starting number $x_0$ is 20, what is the value of the second output, $x_2$ ?

8
11 (correct answer)
14
25

Explanation: The correct answer is 11. This is a two-step process. First, find the first output,

x_1

, by applying the rule to

x_0 = 20

x_1 = f(20) = \frac{1}{2}(20) + 4 = 10 + 4 = 14

. Now, use this output as the new input to find

x_2

x_2 = f(14) = \frac{1}{2}(14) + 4 = 7 + 4 = 11

Question 10

A mathematical function machine has two different rules. If the input, $x$ , is an even number, the output is $3x - 4$ . If the input, $x$ , is an odd number, the output is $x^2 + 2$ .

What is the sum of the machine's output for an input of 6 and the output for an input of 5?

25
41 (correct answer)
49
65

Explanation: The correct answer is 41. First, find the output for each input. The input 6 is even, so use the even rule:

3(6) - 4 = 18 - 4 = 14

. The input 5 is odd, so use the odd rule:

5^2 + 2 = 25 + 2 = 27

. Finally, find the sum of the two outputs:

14 + 27 = 41

Question 11

A baker uses a function $F(p) = \frac{3}{4}(\frac{p}{12})$ to calculate the cups of flour needed for $p$ pancakes. If he uses a different function $S(p) = \frac{1}{3}(\frac{p}{12})$ for the cups of sugar, how much more flour than sugar is needed for 48 pancakes?

$1 \frac{2}{3}$ cups (correct answer)
$\frac{5}{4}$ cups
$\frac{5}{12}$ cup
$4 \frac{1}{3}$ cups

Explanation: When you encounter function problems involving real-world applications, focus on substituting the given value and then comparing the results. This question tests your ability to evaluate functions and perform arithmetic with fractions. First, calculate the flour needed using

F(p) = \frac{3}{4}(\frac{p}{12})

. Substituting

p = 48

F(48) = \frac{3}{4} \times \frac{48}{12} = \frac{3}{4} \times 4 = 3

cups of flour. Next, calculate the sugar needed using

S(p) = \frac{1}{3}(\frac{p}{12})

. Substituting

p = 48

S(48) = \frac{1}{3} \times \frac{48}{12} = \frac{1}{3} \times 4 = \frac{4}{3}

cups of sugar. The difference is:

3 - \frac{4}{3} = \frac{9}{3} - \frac{4}{3} = \frac{5}{3} = 1\frac{2}{3}

cups more flour than sugar. Answer choice (A)

1\frac{2}{3}

cups is correct. Choice (B)

\frac{5}{4}

cups likely results from calculation errors in fraction arithmetic. Choice (C)

\frac{5}{12}

cup suggests confusion with the denominator 12 from the original functions, possibly from incorrectly combining fractions. Choice (D)

4\frac{1}{3}

cups appears to add the flour and sugar amounts instead of finding their difference. Remember: when working with function problems, substitute carefully, simplify step-by-step, and double-check your fraction arithmetic. Converting mixed numbers to improper fractions can help avoid calculation errors.

Question 12

The surface area, $A$ , of a cube with side length $s$ is given by the function $A(s) = 6s^2$ .

A craftsman builds two cubes. The first cube has a side length of 3 cm. The second cube has a side length twice as long as the first. What is the total surface area of both cubes combined?

270 cm² (correct answer)
216 cm²
108 cm²
486 cm²

Explanation: This problem tests your ability to work with function notation and apply formulas to related scenarios. When you see surface area problems involving cubes, remember that a cube has 6 identical square faces, each with area

s^2

. Let's find the surface area of each cube using the given formula

A(s) = 6s^2

. The first cube has side length 3 cm, so its surface area is

A(3) = 6(3^2) = 6(9) = 54

cm². The second cube has side length twice as long, which is

2 \times 3 = 6

cm. Its surface area is

A(6) = 6(6^2) = 6(36) = 216

cm². The total surface area of both cubes combined is

54 + 216 = 270

cm². Looking at the wrong answers: Choice B (216 cm²) gives only the surface area of the larger cube, ignoring the smaller one entirely. Choice C (108 cm²) appears to double the smaller cube's surface area (

54 \times 2 = 108

), perhaps from incorrectly thinking that doubling the side length doubles the surface area. Choice D (486 cm²) might result from miscalculating one of the surface areas or making an arithmetic error in the final addition. Remember that when a linear dimension is scaled by a factor, the surface area scales by the square of that factor. Here, doubling the side length means the surface area increases by

2^2 = 4

times (from 54 to 216 cm²). Always calculate each part separately, then combine your results.

Question 13

A number-processing machine follows a two-step rule. First, it multiplies the input number by -3. Second, it subtracts 7 from the result. If the input number is -5, what is the final output?

-22
8 (correct answer)
22
36

Explanation: The correct answer is 8. The function rule has two steps. Step 1: Multiply the input by -3. So,

(-5) \times (-3) = 15

. Step 2: Subtract 7 from the result. So,

15 - 7 = 8

. The final output is 8.

Question 14

Commission rule: $c = 3s + 10$ . Find $c$ when $s = 6$ .

28 (correct answer)
13
18
16

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the commission rule c = 3s + 10 is used to find commission c when sales s = 6. Choice A is correct because substituting 6 for s yields c = 3(6) + 10 = 18 + 10 = 28, demonstrating proper function application. Choice C (18) represents the common error of forgetting to add the constant term, calculating only 3(6). Choice D (16) might result from adding before multiplying, while Choice B (13) could come from various calculation errors. To help students, stress the importance of following each step carefully and checking work. Real-world contexts like commission calculations make abstract concepts more concrete and meaningful.

Question 15

Car distance rule: $d = 30t$ . Find $d$ when $t = 4$ .

120 (correct answer)
34
90
300

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the car distance rule d = 30t is used to find distance d when time t = 4. Choice A is correct because substituting 4 for t yields d = 30(4) = 120, demonstrating proper function application through simple multiplication. Choice C (90) might result from calculating 30(3), while Choice B (34) could come from adding 30 + 4. Choice D (300) appears to result from multiplying by 10 instead of 4. To help students, emphasize careful multiplication and the direct proportional relationship in this function. Distance-time problems provide intuitive context for understanding linear functions without constant terms.

Question 16

Discount rule: $y = 10x - 5$ . Find $y$ when $x = 4$ .

35 (correct answer)
45
5
25

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the discount rule y = 10x - 5 is used to find the discounted price y when x = 4. Choice A is correct because substituting 4 for x yields y = 10(4) - 5 = 40 - 5 = 35, demonstrating proper function application. Choice B (45) might result from adding 5 instead of subtracting, while Choice D (25) could come from calculating 10(4) - 15. Choice C (5) appears to be an error in calculation or misunderstanding of the function. To help students, emphasize the difference between addition and subtraction in function rules. Real-world contexts like discounts help students understand practical applications of linear functions.

Question 17

Store cost rule: $y = 6x + 1$ . Find $y$ when $x = 3$ .

19 (correct answer)
18
10
7

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the store cost rule y = 6x + 1 is used to find total cost y when x = 3. Choice A is correct because substituting 3 for x yields y = 6(3) + 1 = 18 + 1 = 19, demonstrating proper function application and order of operations. Choice B (18) represents the common error of forgetting to add the constant term, calculating only 6(3). Choice C (10) might result from calculating 3(3) + 1, while Choice D (7) could come from adding 6 + 1. To help students, stress the importance of following each step: multiply first, then add. Store pricing contexts help students connect abstract algebra to everyday situations.

Question 18

Store total cost: $y = 4x + 2$ . Find $y$ when $x = 5$ .

22 (correct answer)
28
14
18

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the function y = 4x + 2 represents total cost at a store, where we need to find y when x = 5. Choice A is correct because substituting 5 for x yields y = 4(5) + 2 = 20 + 2 = 22, demonstrating proper function application and order of operations. Choice B (28) might result from incorrectly calculating 4(5) as 26, while Choice C (14) could come from only calculating 4(5) - 6. To help students, emphasize following order of operations: multiply first, then add. Using real-world contexts like store pricing helps students connect abstract algebra to practical situations.

Question 19

A car travels at constant speed: $d = 50t$ . Find $d$ when $t = 3$ .

150 (correct answer)
53
47
100

Explanation: This question tests middle school quantitative reasoning skills, specifically using a function rule to determine output. Function rules allow us to calculate output values by substituting input values into an algebraic expression. In this question, the function d = 50t represents distance traveled at constant speed, where we need to find d when t = 3. Choice A is correct because substituting 3 for t yields d = 50(3) = 150, demonstrating proper function application. The other choices represent common errors: Choice C (47) and B (53) might result from subtraction or addition errors, while Choice D (100) could come from multiplying by 2 instead of 3. To help students, emphasize the importance of careful substitution and multiplication. Practice with real-world contexts like distance-speed relationships helps students understand the practical application of function rules.

Question 20

A function is defined by the rule $g(x) = |2x - 15| + x$ . What is the value of $g(-5)$ ?

-30
-10
20 (correct answer)
30

Explanation: The correct answer is 20. Substitute

x=-5

into the function:

g(-5) = |2(-5) - 15| + (-5)

. First, evaluate the expression inside the absolute value bars:

2(-5) - 15 = -10 - 15 = -25

. The expression becomes

|-25| + (-5)

. The absolute value of -25 is 25. So the expression is

25 + (-5)

, which simplifies to

25 - 5 = 20