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?
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ISEE Middle Level Quantitative Reasoning Quiz
Practice Function Rules And Output in ISEE Middle Level Quantitative Reasoning with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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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?
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 Quantitative Reasoning.
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.
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?
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.
Commission rule: c=3s+10. Find c when s=6.
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.
Commission rule: c=5s−2. Find c when s=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 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.
Car distance rule: d=30t. Find d when t=4.
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.
Discount rule: y=10x−5. Find y when x=4.
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.
Car distance rule: d=40t+5. Find d when t=2.
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.
Store cost rule: y=6x+1. Find y when x=3.
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.
Store total cost: y=4x+2. Find y when x=5.
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.
A car travels at constant speed: d=50t. Find d when t=3.
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.
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?
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).
A function (h(a, b)) is defined by the rule (h(a, b) = 3a - b^2). What is the value of (h(4, -3))?
Explanation: The correct answer is 3. Substitute (a=4) and (b=-3) into the function rule: (h(4, -3) = 3(4) - (-3)^2). Following the order of operations, calculate the exponent first: ((-3)^2 = (-3) \times (-3) = 9). Then, do the multiplication: (3(4) = 12). Finally, perform the subtraction: (12 - 9 = 3).
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?
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.
A function (k(x)) gives the next term in a sequence and is defined by (k(x) = 3x - 5). If the first term of the sequence is 4, what is the fourth term?
Explanation: The correct answer is 43. This requires applying the function repeatedly. The first term is 4. The second term is (k(4) = 3(4) - 5 = 12 - 5 = 7). The third term is (k(7) = 3(7) - 5 = 21 - 5 = 16). The fourth term is (k(16) = 3(16) - 5 = 48 - 5 = 43).
The (n)-th term of a sequence is determined by the function (T(n) = n^2 - 2n + 5). What is the 8th term in this sequence?
Explanation: The correct answer is 53. To find the 8th term, substitute (n=8) into the function: (T(8) = 8^2 - 2(8) + 5). Following the order of operations, first calculate the exponent: (8^2 = 64). Then, perform the multiplication: (2(8) = 16). The expression becomes (64 - 16 + 5). Now, perform subtraction and addition from left to right: (64 - 16 = 48), and (48 + 5 = 53).
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?
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.
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?
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).
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?
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).
A function (f(x)) is defined as (f(x) = 2(x - 3)^2 + 5). What is the output for an input of 1?
Explanation: The correct answer is 13. To find the output, substitute (x = 1) into the function: (f(1) = 2(1 - 3)^2 + 5). According to the order of operations, evaluate the expression in the parentheses first: (1 - 3 = -2). The function becomes (f(1) = 2(-2)^2 + 5). Next, evaluate the exponent: ((-2)^2 = 4). The function is now (f(1) = 2(4) + 5). Then, perform the multiplication: (2(4) = 8). Finally, perform the addition: (8 + 5 = 13).
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?
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.
The value (V) of a collectible item after (t) years is modeled by the function (V(t) = 50(1.1)^t). What is the value of the item after 3 years, rounded to the nearest dollar?
Explanation: The correct answer is 67. Substitute \(t=3\) into the function: \(V(3) = 50(1.1)^3\). First, calculate \((1.1)^3\): \(1.1 \times 1.1 = 1.21\), and \(1.21 \times 1.1 = 1.331\). Now, multiply this by 50: \(50 \times 1.331 = 66.55\). Rounded to the nearest dollar, the value is 67.