Result: \(2x^2 + 4x + 12\)
Distractor Alert: Option A (\(-12x + 2\)) occurs when students fail to negate the \(-8x\) and \(-5\). Option D misses the constant term sign flip.
TSI Math Solutions Guide • Algebraic Reasoning Page 1 of 2
Teacher Guide Solutions: Functions, Modeling & Geometry (Q5 - Q10)
Section Benchmarks & Misconceptions
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Q5: Function Notation Ans: C (\(28\))
\(f(x) = 2x^2 - 3x + 1\), find \(f(-3)\)
\(f(-3) = 2(-3)^2 - 3(-3) + 1\)
\(= 2(9) - (-9) + 1\)
\(= 18 + 9 + 1 = 28\)
Trap: Squaring \(-3\) without parentheses yields \(-9\), leading to \(-18 + 9 + 1 = -8\).
Q6: Linear Model Ans: B (\(60h+45=255\))
\(\$45\) fixed fee, \(\$60/\text{hr}\), total \(\$255\)
Total = (Hourly Rate \(\times h\)) + Fee
\(\text{Total} = 60h + 45\)
\(60h + 45 = 255 \implies h = 3.5\text{ hrs}\)
Trap: Attaching \(h\) to the one-time diagnostic fee gives option A (\(45h + 60\)).
Q7: Perpendicular Lines Ans: A (\(-2\))
Line: \(3x - 6y = 18\)
\(-6y = -3x + 18 \implies y = \frac{1}{2}x - 3\)
Original slope \(m_1 = \frac{1}{2}\)
Perpendicular: \(m_\perp = -\frac{1}{m_1} = -2\)
Trap: Option C is parallel slope (\(\frac{1}{2}\)). Option B is negative but not reciprocal.
Q8: Rectangle Area Ans: B (\(140\text{ m}^2\))
\(l = w + 4\), Perimeter = \(48\text{ m}\)
\(2(w + 4 + w) = 48 \implies 4w + 8 = 48\)
\(4w = 40 \implies w = 10\text{ m}, l = 14\text{ m}\)
\(\text{Area} = l \times w = 14 \times 10 = 140\text{ m}^2\)
Trap: Option C (\(144\)) comes from confusing perimeter with a square (\(12 \times 12\)).
Q9: Cylinder Volume Ans: C (\(90\pi\))
\(r = 3\text{ ft}, h = 10\text{ ft}\)
\(V = \pi r^2 h\)
\(V = \pi (3)^2 (10)\)
\(V = \pi (9)(10) = 90\pi\text{ ft}^3\)
Trap: Forgetting to square radius yields \(30\pi\) (A). Squaring height yields \(180\pi\).
Q10: Ladder Application Ans: C (\(12\text{ ft}\))
\(\text{hypotenuse} = 13\), \(\text{leg} = 5\)
\(a^2 + 5^2 = 13^2 \implies a^2 + 25 = 169\)
\(a^2 = 169 - 25 = 144\)
\(a = \sqrt{144} = 12\text{ ft}\)
Trap: Adding squares instead of subtracting (\(169 + 25 = 194\)) yields option D (\(\sqrt{194}\)).
TSI 2.0 College Placement Diagnostic Guide Texas Higher Education Coordinating Board Standards
Score 8 - 10 / 10
College Ready (CRC 950+ equivalent). Ready for credit-bearing college algebra without corequisite.
Score 5 - 7 / 10
Borderline College Ready (CRC 940-949). Recommend corequisite support or targeted module review.
Score < 5 / 10
Developmental Placement needed. Route to TSI Diagnostic Test; focus on basic linear equations and arithmetic.
