SAT Math Readiness Diagnostic Prototype Instructor Review

Instructor review preview. Items are eligible for offline Canvas payload export only when deterministic checks, GPT-5.5 item review, and GPT-5.5 visual review gates pass. Current draft source item count: 36.

Offline review artifact only. No Canvas upload, LMS mutation, scoring action, or source item status change happens from this page.

Source policy: official-source research, original items only, offline Canvas payloads only. Timing note: this preview is the 60-minute scaled MVP form based on a 70-minute target assessment structure.

Review Dashboard

This instructor preview is offline-only. It supports content review, answer-key checks, distractor feedback review, and public-safety review before any Canvas export.

Domains

Advanced Math: 13
Algebra: 13
Geometry and Trigonometry: 5
Problem-Solving and Data Analysis: 5

Item Types

multiple_choice: 27
numeric_student_produced_response: 9

Difficulty

easy: 12
hard: 10
medium: 14

Review Status

draft: 36

Item Navigation

Module 1

ITEM-001 ITEM-002 ITEM-003 ITEM-004 ITEM-005 ITEM-006 ITEM-007 ITEM-008 ITEM-009 ITEM-010 ITEM-011 ITEM-012 ITEM-013 ITEM-014 ITEM-015 ITEM-016 ITEM-017 ITEM-018

Module 2

ITEM-019 ITEM-020 ITEM-021 ITEM-022 ITEM-023 ITEM-024 ITEM-025 ITEM-026 ITEM-027 ITEM-028 ITEM-029 ITEM-030 ITEM-031 ITEM-032 ITEM-033 ITEM-034 ITEM-035 ITEM-036

Module 1

Time: 30 minutes. Items: 18.

Draft review status shown per item.

Module 1 | Question 1 of 18 | Algebra

ITEM-001

If 3x + 5 = 20, what is the value of x?

Select one answer. A5 B15 C253 D-5

Instructor Review Details Answer A | Review status draft | Answer Feedback | easy

Correct answer: A

Explanation: Subtract 5 from both sides to get 3x = 15, then divide by 3 to get x = 5.

Subdomain: Linear equations in one variable

Difficulty: easy

Review status: draft

Misconception tags: inverse-operation error, sign error

Remediation tag: linear-equation-solving

Answer Feedback

B: This subtracts 5 but does not divide by 3.
C: This adds 5 instead of subtracting 5 before dividing.
D: This uses the opposite sign after solving.

Module 1 | Question 2 of 18 | Algebra

ITEM-002

The equation 2y - 4x = 10 represents a line. What is the slope of the line?

Select one answer. A2 B-2 C4 D5

Instructor Review Details Answer A | Review status draft | Answer Feedback | easy

Correct answer: A

Explanation: Rewrite as 2y = 4x + 10, then y = 2x + 5. The slope is 2.

Subdomain: Linear equations in two variables

Difficulty: easy

Review status: draft

Misconception tags: slope-intercept confusion, coefficient scaling error

Remediation tag: linear-equation-slope

Answer Feedback

B: This keeps the sign from -4x instead of solving for y.
C: This uses the coefficient of x before dividing by 2.
D: This identifies the y-intercept, not the slope.

Module 1 | Question 3 of 18 | Problem-Solving and Data Analysis

ITEM-003

A train travels 144 miles in 3 hours at a constant speed. What is the speed, in miles per hour?

Select one answer. A36 B48 C141 D432

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: Divide miles by hours: 144 / 3 = 48 miles per hour.

Subdomain: Ratios, rates, proportional relationships, and units

Difficulty: easy

Review status: draft

Misconception tags: unit-rate error

Remediation tag: unit-rate-reasoning

Answer Feedback

A: This divides by 4 rather than by the 3 hours given.
C: This subtracts the time from the distance.
D: This multiplies distance by time instead of dividing.

Module 1 | Question 4 of 18 | Geometry and Trigonometry

ITEM-004

A triangle has base 14 units and height 9 units. What is its area, in square units?

Select one answer. A23 B63 C126 D196

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: Triangle area is (12)bh = (12)(14)(9) = 63.

Subdomain: Area and volume formulas

Difficulty: easy

Review status: draft

Misconception tags: formula selection error

Remediation tag: triangle-area

Answer Feedback

A: This adds the base and height instead of using area.
C: This multiplies base by height but omits the factor of 12.
D: This squares the base instead of using both dimensions.

Module 1 | Question 5 of 18 | Algebra

ITEM-005

Which inequality is equivalent to 5 - 2x > 13?

Select one answer. Ax > -4 Bx < -4 Cx > 4 Dx < 4

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: Subtract 5 to get -2x > 8. Dividing by -2 reverses the inequality, so x < -4.

Subdomain: Linear inequalities in one or two variables

Difficulty: easy

Review status: draft

Misconception tags: inequality reversal error, sign error

Remediation tag: linear-inequality-solving

Answer Feedback

A: This does not reverse the inequality when dividing by -2.
C: This misses both the negative value and the inequality reversal.
D: This reverses the inequality but loses the negative value.

Module 1 | Question 6 of 18 | Advanced Math

ITEM-006

For x not equal to 3, which expression is equivalent to (x² - 9)/(x - 3)?

Select one answer. Ax - 3 Bx + 3 Cx² + 3 D1/(x + 3)

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: Factor x² - 9 as (x - 3)(x + 3). Cancel x - 3 to get x + 3.

Subdomain: Equivalent expressions

Difficulty: easy

Review status: draft

Misconception tags: factoring error, rational-expression error

Remediation tag: equivalent-expressions

Answer Feedback

A: This cancels the wrong factor after factoring the numerator.
C: This does not factor the difference of squares.
D: This reverses the simplified expression.

Module 1 | Question 7 of 18 | Algebra

ITEM-007

If x + y = 11 and x - y = 3, what is the value of x?

Select one answer. A4 B7 C8 D14

Instructor Review Details Answer B | Review status draft | Answer Feedback | medium

Correct answer: B

Explanation: Add the equations to get 2x = 14, so x = 7.

Subdomain: Systems of two linear equations in two variables

Difficulty: medium

Review status: draft

Misconception tags: system-elimination error

Remediation tag: systems-linear

Answer Feedback

A: This is the value of y, not x.
C: This comes from subtracting equations incorrectly.
D: This adds the equations but does not divide by 2.

Module 1 | Question 8 of 18 | Advanced Math

ITEM-008

If f(x) = x² - 4x, what is f(6)?

Select one answer. A4 B12 C20 D36

Instructor Review Details Answer B | Review status draft | Answer Feedback | medium

Correct answer: B

Explanation: Substitute x = 6: f(6) = 6² - 4(6) = 36 - 24 = 12.

Subdomain: Nonlinear functions

Difficulty: medium

Review status: draft

Misconception tags: function-substitution error, order-of-operations error

Remediation tag: function-evaluation

Answer Feedback

A: This computes (6 - 4)² instead of substituting 6 into both terms of x² - 4x.
C: This uses 6² - 4 instead of 6² - 4(6).
D: This evaluates only 6².

Module 1 | Question 9 of 18 | Problem-Solving and Data Analysis

ITEM-009

A price of $80 is increased by 15%. What is the new price?

Select one answer. A$12 B$68 C$92 D$95

Instructor Review Details Answer C | Review status draft | Answer Feedback | medium

Correct answer: C

Explanation: The increase is 0.15(80) = 12, so the new price is 80 + 12 = 92.

Subdomain: Percentages

Difficulty: medium

Review status: draft

Misconception tags: percent-base error

Remediation tag: percent-change

Answer Feedback

A: This finds only the amount of increase.
B: This subtracts the increase instead of adding it.
D: This adds 15 dollars instead of 15 percent.

Module 1 | Question 10 of 18 | Algebra

ITEM-010

The line y = 3x - 7 passes through the point (k, 8). What is the value of k?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 5 | Review status draft | Answer Feedback | medium

Correct answer: 5

Explanation: Substitute y = 8: 8 = 3k - 7, so 15 = 3k and k = 5.

Subdomain: Linear functions

Difficulty: medium

Review status: draft

Misconception tags: linear-function-substitution error

Remediation tag: linear-function-input

Answer Feedback

Accepted answer rules: exact=5

Module 1 | Question 11 of 18 | Advanced Math

ITEM-011

What is the smaller solution to x² - 5x + 6 = 0?

Select one answer. A1 B2 C3 D6

Instructor Review Details Answer B | Review status draft | Answer Feedback | medium

Correct answer: B

Explanation: Factor as (x - 2)(x - 3) = 0. The solutions are 2 and 3, so the smaller solution is 2.

Subdomain: Nonlinear equations in one variable

Difficulty: medium

Review status: draft

Misconception tags: factoring error, solution-selection error

Remediation tag: quadratic-solving

Answer Feedback

A: This chooses a factor of 6 but does not check that the two factors add to 5.
C: This is a solution, but it is the larger solution.
D: This is the product of the two solutions, not a solution.

Module 1 | Question 12 of 18 | Geometry and Trigonometry

ITEM-012

A right triangle has legs of lengths 9 and 12. What is the length of the hypotenuse?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 15 | Review status draft | Answer Feedback | medium

Correct answer: 15

Explanation: Use a² + b² = c²: 9² + 12² = 81 + 144 = 225, so c = 15.

Subdomain: Right triangles and trigonometry

Difficulty: medium

Review status: draft

Misconception tags: pythagorean-theorem error

Remediation tag: right-triangle-length

Answer Feedback

Accepted answer rules: exact=15

Module 1 | Question 13 of 18 | Algebra

ITEM-013

A line passes through (2, 7) and (5, 19). What is the slope of the line?

Select one answer. A3 B4 C6 D12

Instructor Review Details Answer B | Review status draft | Answer Feedback | medium

Correct answer: B

Explanation: The slope is (19 - 7)/(5 - 2) = 123 = 4.

Subdomain: Linear functions

Difficulty: medium

Review status: draft

Misconception tags: slope formula error

Remediation tag: slope-from-points

Answer Feedback

A: This is the change in x, not the slope.
C: This divides the change in y by 2 instead of the change in x.
D: This is the change in y, not the slope.

Module 1 | Question 14 of 18 | Advanced Math

ITEM-014

If h(x) = 2x² + 3x - 5, which expression is equivalent to h(x + 1) - h(x)?

Select one answer. A4x + 5 B4x + 1 C2x + 3 D2x² + 7x

Instructor Review Details Answer A | Review status draft | Answer Feedback | hard

Correct answer: A

Explanation: h(x + 1) = 2(x + 1)² + 3(x + 1) - 5 = 2x² + 7x. Subtracting h(x) gives 4x + 5.

Subdomain: Nonlinear functions

Difficulty: hard

Review status: draft

Misconception tags: function-composition error, expansion error

Remediation tag: symbolic-function-comparison

Answer Feedback

B: This expands h(x + 1) with an incorrect constant term.
C: This treats the change in 2x² as 2x and includes only the +3 from the linear term.
D: This computes h(x + 1) but does not subtract h(x).

Module 1 | Question 15 of 18 | Problem-Solving and Data Analysis

ITEM-015

Six numbers have a mean of 18. When the largest number is removed, the mean of the remaining five numbers is 16. What is the largest number?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 28 | Review status draft | Answer Feedback | hard

Correct answer: 28

Explanation: The six numbers have total 6*18 = 108. The remaining five numbers have total 5*16 = 80. The removed largest number is 108 - 80 = 28.

Subdomain: One-variable data distributions

Difficulty: hard

Review status: draft

Misconception tags: mean-total error, removed-value error

Remediation tag: mean-change-removed-value

Answer Feedback

Accepted answer rules: exact=28

Module 1 | Question 16 of 18 | Algebra

ITEM-016

For what value of a is a(2x - 3) = 10x - 15 true for all values of x?

Select one answer. A3 B5 C10 D15

Instructor Review Details Answer B | Review status draft | Answer Feedback | hard

Correct answer: B

Explanation: Distribute to get 2ax - 3a. Matching 10x - 15 requires 2a = 10 and -3a = -15, so a = 5.

Subdomain: Linear equations in one variable

Difficulty: hard

Review status: draft

Misconception tags: distribution error, coefficient-matching error

Remediation tag: equivalent-linear-expressions

Answer Feedback

A: This matches the constant inside the parentheses, not the distributed expression.
C: This matches the coefficient of x before accounting for 2x.
D: This matches the constant term without considering the sign and factor.

Module 1 | Question 17 of 18 | Advanced Math

ITEM-017

If √(3x + 1) = 5, what is the value of x?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 8 | Review status draft | Answer Feedback | hard

Correct answer: 8

Explanation: Square both sides to get 3x + 1 = 25. Then 3x = 24, so x = 8.

Subdomain: Nonlinear equations in one variable

Difficulty: hard

Review status: draft

Misconception tags: radical-equation error

Remediation tag: radical-equation-solving

Answer Feedback

Accepted answer rules: exact=8

Module 1 | Question 18 of 18 | Advanced Math

ITEM-018

For which values of x is the expression 1/(x² - 4x) undefined?

Select one answer. A0 only B4 only C0 and 4 D-4 and 4

Instructor Review Details Answer C | Review status draft | Answer Feedback | hard

Correct answer: C

Explanation: The denominator factors as x(x - 4). It is zero at x = 0 and x = 4.

Subdomain: Equivalent expressions

Difficulty: hard

Review status: draft

Misconception tags: domain restriction error, factoring error

Remediation tag: rational-expression-domain

Answer Feedback

A: This finds one zero of the denominator but misses x = 4.
B: This finds one zero of the denominator but misses x = 0.
D: This factors x² - 4x as if it were a difference of squares.

Module 2

Time: 30 minutes. Items: 18.

Draft review status shown per item.

Module 2 | Question 1 of 18 | Algebra

ITEM-019

If 4x - 9 = 2x + 7, what is the value of x?

Select one answer. A2 B4 C8 D16

Instructor Review Details Answer C | Review status draft | Answer Feedback | easy

Correct answer: C

Explanation: Subtract 2x from both sides to get 2x - 9 = 7. Add 9 to get 2x = 16, so x = 8.

Subdomain: Linear equations in one variable

Difficulty: easy

Review status: draft

Misconception tags: inverse-operation error

Remediation tag: linear-equation-solving

Answer Feedback

A: This divides the constant difference by the wrong coefficient.
B: This treats the right side as 7 and ignores the 2x term before solving.
D: This finds 2x but does not divide by 2.

Module 2 | Question 2 of 18 | Advanced Math

ITEM-020

Which expression is equivalent to (2x³)(3x²)?

Select one answer. A5x⁵ B6x⁵ C6x⁶ D12x⁵

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: Multiply coefficients and add exponents on like bases: 2*3*x³⁺² = 6x⁵.

Subdomain: Equivalent expressions

Difficulty: easy

Review status: draft

Misconception tags: exponent-rule error, coefficient operation error

Remediation tag: exponent-rules

Answer Feedback

A: This adds the coefficients instead of multiplying them.
C: This multiplies the exponents instead of adding them.
D: This multiplies the coefficients by an extra factor of 2.

Module 2 | Question 3 of 18 | Problem-Solving and Data Analysis

ITEM-021

A bag contains 5 red tiles, 3 blue tiles, and 2 green tiles. If one tile is selected at random, what is the probability that it is not blue?

Select one answer. A310 B710 C27 D73

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: There are 10 tiles total and 7 are not blue, so the probability is 710.

Subdomain: Probability and conditional probability

Difficulty: easy

Review status: draft

Misconception tags: probability complement error

Remediation tag: basic-probability

Answer Feedback

A: This is the probability of blue, not not blue.
C: This compares green tiles to non-blue tiles.
D: This reverses favorable and total counts.

Module 2 | Question 4 of 18 | Geometry and Trigonometry

ITEM-022

Two angles of a triangle measure 42 degrees and 68 degrees. What is the measure, in degrees, of the third angle?

Select one answer. A70 B90 C110 D138

Instructor Review Details Answer A | Review status draft | Answer Feedback | easy

Correct answer: A

Explanation: The angles in a triangle sum to 180 degrees. The third angle is 180 - 42 - 68 = 70.

Subdomain: Lines, angles, and triangles

Difficulty: easy

Review status: draft

Misconception tags: angle-sum error

Remediation tag: triangle-angle-sum

Answer Feedback

B: This assumes the triangle is right without evidence.
C: This adds the two given angles.
D: This subtracts one given angle from 180 but ignores the other.

Module 2 | Question 5 of 18 | Algebra

ITEM-023

What is the y-intercept of the line 3x + 2y = 12?

Select one answer. A2 B3 C4 D6

Instructor Review Details Answer D | Review status draft | Answer Feedback | easy

Correct answer: D

Explanation: Set x = 0 to find the y-intercept: 2y = 12, so y = 6.

Subdomain: Linear equations in two variables

Difficulty: easy

Review status: draft

Misconception tags: intercept confusion

Remediation tag: linear-intercepts

Answer Feedback

A: This uses the coefficient of y, not the intercept.
B: This uses the coefficient of x, not the intercept.
C: This is the x-intercept.

Module 2 | Question 6 of 18 | Advanced Math

ITEM-024

The function q(x) = (x - 4)² + 7 is graphed in the xy-plane. What is the vertex of the graph?

Select one answer. A(-4, 7) B(4, 7) C(7, 4) D(4, -7)

Instructor Review Details Answer B | Review status draft | Answer Feedback | easy

Correct answer: B

Explanation: A quadratic in vertex form (x - h)² + k has vertex (h, k), so the vertex is (4, 7).

Subdomain: Nonlinear functions

Difficulty: easy

Review status: draft

Misconception tags: vertex-form error

Remediation tag: quadratic-vertex-form

Answer Feedback

A: This uses the sign inside the parentheses without reversing it.
C: This switches the x- and y-coordinates.
D: This changes the sign of the vertical shift.

Module 2 | Question 7 of 18 | Algebra

ITEM-025

A line is parallel to y = -3x + 2. What is the slope of the line?

Select one answer. A-3 B-13 C13 D2

Instructor Review Details Answer A | Review status draft | Answer Feedback | medium

Correct answer: A

Explanation: Parallel lines have the same slope. The slope of y = -3x + 2 is -3.

Subdomain: Linear functions

Difficulty: medium

Review status: draft

Misconception tags: parallel-slope error

Remediation tag: linear-slope-relationships

Answer Feedback

B: This uses the negative reciprocal, which applies to perpendicular lines.
C: This uses the reciprocal and changes the sign.
D: This identifies the y-intercept of the given line.

Module 2 | Question 8 of 18 | Advanced Math

ITEM-026

If 2^{x + 1} = 32, what is the value of x?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 4 | Review status draft | Answer Feedback | medium

Correct answer: 4

Explanation: Since 32 = 2⁵, x + 1 = 5 and x = 4.

Subdomain: Nonlinear equations in one variable

Difficulty: medium

Review status: draft

Misconception tags: exponent-equation error

Remediation tag: exponential-equation-solving

Answer Feedback

Accepted answer rules: exact=4

Module 2 | Question 9 of 18 | Geometry and Trigonometry

ITEM-027

Two similar triangles have corresponding side lengths in the ratio 3:5. If the area of the smaller triangle is 36 square units, what is the area of the larger triangle?

Select one answer. A60 B144 C100 D180

Instructor Review Details Answer C | Review status draft | Answer Feedback | medium

Correct answer: C

Explanation: Area scales by the square of the side scale factor. The larger area is 36*(53)² = 36*(259) = 100.

Subdomain: Lines, angles, and triangles

Difficulty: medium

Review status: draft

Misconception tags: scale-factor error

Remediation tag: similar-figure-area

Answer Feedback

A: This scales area by the side-length ratio instead of the square of the ratio.
B: This treats the side scale factor as 2 instead of 53, then squares that incorrect factor.
D: This multiplies by 5 instead of using the squared scale factor.

Module 2 | Question 10 of 18 | Algebra

ITEM-028

If 0.25x + 6 = 18, what is the value of x?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 48 | Review status draft | Answer Feedback | medium

Correct answer: 48

Explanation: Subtract 6 to get 0.25x = 12. Since 0.25 = 14, x = 48.

Subdomain: Linear equations in one variable

Difficulty: medium

Review status: draft

Misconception tags: decimal-coefficient error

Remediation tag: linear-equation-decimals

Answer Feedback

Accepted answer rules: exact=48

Module 2 | Question 11 of 18 | Advanced Math

ITEM-029

Which expression is equivalent to x² + 7x + 10?

Select one answer. A(x + 5)(x + 2) B(x - 5)(x - 2) C(x + 10)(x + 1) D(x + 7)(x + 10)

Instructor Review Details Answer A | Review status draft | Answer Feedback | medium

Correct answer: A

Explanation: Find two numbers that multiply to 10 and add to 7: 5 and 2. The factorization is (x + 5)(x + 2).

Subdomain: Equivalent expressions

Difficulty: medium

Review status: draft

Misconception tags: factoring error

Remediation tag: quadratic-factoring

Answer Feedback

B: This gives the correct factors with incorrect signs.
C: This has the right product but the middle term would be 11x.
D: This uses the coefficient and constant as factors directly.

Module 2 | Question 12 of 18 | Problem-Solving and Data Analysis

ITEM-030

Thirty percent of n is 45. What is the value of n?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 150 | Review status draft | Answer Feedback | medium

Correct answer: 150

Explanation: Set 0.30n = 45. Dividing by 0.30 gives n = 150.

Subdomain: Percentages

Difficulty: medium

Review status: draft

Misconception tags: percent-base error

Remediation tag: percent-whole-from-part

Answer Feedback

Accepted answer rules: exact=150

Module 2 | Question 13 of 18 | Algebra

ITEM-031

A service charge is modeled by C = 25 + 8h, where C is the total cost in dollars for h hours. What does 8 represent in this model?

Select one answer. AThe fixed cost before any hours are added BThe number of hours purchased CThe cost per hour DThe total cost for 8 hours

Instructor Review Details Answer C | Review status draft | Answer Feedback | medium

Correct answer: C

Explanation: In C = 25 + 8h, the coefficient of h is the rate of change, so the cost is 8 dollars per hour.

Subdomain: Linear functions

Difficulty: medium

Review status: draft

Misconception tags: linear-model interpretation error

Remediation tag: linear-model-rate

Answer Feedback

A: The fixed cost is the constant 25.
B: The variable h represents the number of hours.
D: The coefficient 8 is a rate, not a total for 8 hours.

Module 2 | Question 14 of 18 | Advanced Math

ITEM-032

What are the solutions to |x - 2| = 5?

Select one answer. A-3 and 7 B3 and 7 C-7 and 3 D7 only

Instructor Review Details Answer A | Review status draft | Answer Feedback | hard

Correct answer: A

Explanation: The equation means x - 2 = 5 or x - 2 = -5, so x = 7 or x = -3.

Subdomain: Nonlinear equations in one variable

Difficulty: hard

Review status: draft

Misconception tags: absolute-value branch error

Remediation tag: absolute-value-equations

Answer Feedback

B: This solves x - 2 = 5 but handles the negative case incorrectly.
C: This changes the sign of the wrong term.
D: This includes only the positive-distance solution.

Module 2 | Question 15 of 18 | Geometry and Trigonometry

ITEM-033

In a right triangle, sin(θ) = 35 and the hypotenuse has length 20. What is the length of the leg adjacent to θ?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 16 | Review status draft | Answer Feedback | hard

Correct answer: 16

Explanation: If sin(θ) = 35, the opposite leg and hypotenuse are in the ratio 3:5. With hypotenuse 20, the scale factor is 4, so the opposite leg is 12. The adjacent leg is √(20² - 12²) = √(256) = 16.

Subdomain: Right triangles and trigonometry

Difficulty: hard

Review status: draft

Misconception tags: trig-ratio error, pythagorean-theorem error

Remediation tag: right-triangle-trigonometry

Answer Feedback

Accepted answer rules: exact=16

Module 2 | Question 16 of 18 | Algebra

ITEM-034

Which inequality is equivalent to 2(x - 3) ≤ 10?

Select one answer. Ax ≤ 2 Bx ≤ 8 Cx ≥ 8 Dx ≤ 13

Instructor Review Details Answer B | Review status draft | Answer Feedback | hard

Correct answer: B

Explanation: Distribute or divide by 2: x - 3 ≤ 5, so x ≤ 8.

Subdomain: Linear inequalities in one or two variables

Difficulty: hard

Review status: draft

Misconception tags: inequality solving error

Remediation tag: linear-inequality-solving

Answer Feedback

A: This subtracts 6 from 10 after distributing instead of adding 6.
C: This reverses the inequality even though division is by a positive number.
D: This ignores the factor of 2 and solves x - 3 ≤ 10 before adding 3.

Module 2 | Question 17 of 18 | Advanced Math

ITEM-035

If f(x) = x² + 2 and g(x) = 3x - 1, what is f(g(2))?

Response: Enter a numeric value. Equivalent fractions or decimals may be accepted when mathematically equal.

Instructor Review Details Answer 27 | Review status draft | Answer Feedback | hard

Correct answer: 27

Explanation: First find g(2) = 3(2) - 1 = 5. Then f(5) = 5² + 2 = 27.

Subdomain: Nonlinear functions

Difficulty: hard

Review status: draft

Misconception tags: function-composition error

Remediation tag: function-composition

Answer Feedback

Accepted answer rules: exact=27

Module 2 | Question 18 of 18 | Advanced Math

ITEM-036

If (x + 2)/(x - 1) = 3 and x is not equal to 1, what is the value of x?

Select one answer. A25 B52 C-52 D5

Instructor Review Details Answer B | Review status draft | Answer Feedback | hard

Correct answer: B

Explanation: Multiply by x - 1: x + 2 = 3x - 3. Then 5 = 2x, so x = 52.

Subdomain: Nonlinear equations in one variable

Difficulty: hard

Review status: draft

Misconception tags: rational-equation error

Remediation tag: rational-equation-solving

Answer Feedback

A: This reverses the final division step and divides 2 by 5 instead of 5 by 2.
C: This changes the sign when moving terms after clearing the denominator.
D: This finds the numerator difference but does not divide by 2.