A) \( x = 4 \) [A]
B) \( x = 6 \) [E]
C) \( x = 1.5 \) [L]
D) \( x = 3 \) [K]
CARD A3 • Exponent Laws Algebraic
Simplify completely for all non-zero values of \( x \) and \( y \):
\( \frac{(3x^3 y^{-2})^2 \cdot (2x^4 y^3)}{6x^2 y^{-1}} \)
Equivalent expression:
A) \( 3x^8 \) [C]
B) \( 3x^8 y^2 \) [D]
C) \( x^7 y^{-1} \) [P]
D) \( 6x^5 y \) [S]
CARD A4 • Rational Equations Algebraic
Solve the rational equation for all valid real values of \( x \):
\( \frac{4}{x-3} - \frac{2}{x} = \frac{14}{x(x-3)} \)
Check for extraneous solutions:
A) \( x = 3 \) [B]
B) \( x = 4 \) [O]
C) \( x = 5 \) [U]
D) No solution [N]
CARD A5 • Functions Algebraic
Given \( f(x) = 2x^2 - 3x + 1 \) and \( g(x) = 3x - 4 \):
Evaluate composite function: \( f(g(2)) \)
Resulting value:
A) 3 [T]
B) 5 [S]
C) 7 [H]
D) 15 [W]
CARD A6 • Inequalities Algebraic
Production constraints for posters (\( x \)) and brochures (\( y \)):
\( 4x + 6y \le 240 \) and \( x \ge 30 \)
Maximum possible value of \( y \):
A) 15 [Z]
B) 20 [X]
C) 25 [Y]
D) 40 [J]
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What is the vehicle's speed in miles per hour?
A) 40 mph [BP-A]
B) 45 mph [BP-B]
C) 50 mph [BP-C]
D) 55 mph [BP-D]
CARD G2 • Percent Discounts Quantitative
A graphing calculator has an original retail price of $120. It is placed on sale at 20% off. A student then applies a store membership coupon for an additional 15% off the discounted sale price.
Sale = \( 120 \times (1 - 0.20) \) → Final = \( \text{Sale} \times (1 - 0.15) \)
What is the final price paid before tax?
A) $78.00 [BP-K]
B) $81.60 [BP-L]
C) $84.00 [BP-M]
D) $86.40 [BP-N]
CARD G3 • Right Triangle Trig Geometric
A 13-foot extension ladder leans against a vertical brick wall. The base of the ladder is placed 5 feet away from the wall on level ground.
Hypotenuse = 13 ft | Adjacent = 5 ft | Wall height = \( h \)
What is the exact value of \( \sin(\theta) \), where \( \theta \) is the ground angle?
A) \( \frac{5}{13} \) [BP-Q]
B) \( \frac{12}{13} \) [BP-R]
C) \( \frac{5}{12} \) [BP-S]
D) \( \frac{12}{5} \) [BP-T]
CARD G4 • Sector Area Geometric
A circular courtyard has a radius of 12 meters. A landscaping section occupies a sector with a central angle of \( 45^\circ \).
\( \text{Area}_{\text{sector}} = \left(\frac{45^\circ}{360^\circ}\right) \pi (12)^2 \)
What is the exact area of the sector in \( \text{m}^2 \)?
A) \( 16\pi \text{ m}^2 \) [BP-U]
B) \( 18\pi \text{ m}^2 \) [BP-V]
C) \( 24\pi \text{ m}^2 \) [BP-W]
D) \( 36\pi \text{ m}^2 \) [BP-X]
CARD G5 • Volume & Density Geometric
A solid metal cylinder has a radius of 3 cm and a height of 10 cm. The density of the metal alloy is \( 8.5 \text{ g/cm}^3 \).
\( V = \pi r^2 h = \pi (3)^2 (10) \) | \( \text{Mass} = \text{Density} \times V \)
What is the total mass of the cylinder in grams?
A) \( 255\pi \text{ g} \) [BP-E]
B) \( 510\pi \text{ g} \) [BP-F]
C) \( 765\pi \text{ g} \) [BP-G]
D) \( 850\pi \text{ g} \) [BP-H]
CARD G6 • Perpendicular Lines Geometric
What is the equation of the line that is perpendicular to the line \( 2x - 3y = 9 \) and passes through the point \( (4, -1) \)?
Slope of original line: \( m = \frac{2}{3} \) → Perpendicular slope: \( m_{\perp} = -\frac{3}{2} \)
Equation of the perpendicular line:
A) \( y = -\frac{3}{2}x + 5 \) [BP-1]
B) \( y = -\frac{3}{2}x - 5 \) [BP-2]
C) \( y = \frac{2}{3}x - \frac{11}{3} \) [BP-3]
D) \( y = -\frac{2}{3}x + \frac{5}{3} \) [BP-4]
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What % of STEM students had an internship?
A) 30% [DT-A]
B) 60% [DT-B]
C) 75% [DT-C]
D) 80% [DT-D]
CARD D2 • Conditional Chance Probability
At a high school clinic, 150 athletes were screened. 90 play contact sports. Of those 90, 27 have suffered a sprain. Among non-contact athletes, 12 suffered a sprain.
Given athlete plays contact sports, find \( P(\text{Sprain}) \)
What is the conditional probability?
A) \( \frac{9}{50} \) [DT-E]
B) \( \frac{3}{10} \) [DT-F]
C) \( \frac{13}{50} \) [DT-G]
D) \( \frac{9}{13} \) [DT-H]
CARD D3 • Center & Spread Statistics
A dataset consists of 7 exam scores:
74, 76, 80, 82, 85, 88, 95
If an outlier score of 15 is mistakenly entered into the dataset, which statement correctly describes the effect?
A) The mean decreases significantly, while the median remains nearly unchanged. [DT-J]
B) The median decreases significantly, while the mean remains unchanged. [DT-K]
C) Both mean and median decrease by the exact same amount. [DT-L]
CARD D4 • Box Plots & IQR Statistics
The five-number summary for Math Placement scores of 120 college freshmen is:
Min = 32 | \( Q_1 = 54 \) | Med = 68 | \( Q_3 = 84 \) | Max = 98
What is the Interquartile Range (IQR)?
A) 14 [DT-M]
B) 30 [DT-N]
C) 36 [DT-P]
D) 66 [DT-Q]
CARD D5 • Compound Events Probability
A pouch contains 6 blue tokens, 4 red tokens, and 2 gold tokens. Two tokens are drawn at random without replacement.
Total = 12 → \( P(\text{Blue}_1 \text{ and } \text{Blue}_2) = \frac{6}{12} \times \frac{5}{11} \)
What is the probability both are blue?
A) \( \frac{5}{22} \) [DT-R]
B) \( \frac{1}{4} \) [DT-S]
C) \( \frac{15}{66} \) [DT-T]
D) \( \frac{5}{24} \) [DT-U]
CARD D6 • Normal Distribution Statistics
Scores on a statewide algebra readiness exam are normally distributed with a mean of \( \mu = 500 \) and standard deviation of \( \sigma = 50 \).
Range: 450 to 600 → \( (\mu - 1\sigma) \) to \( (\mu + 2\sigma) \)
Using the Empirical Rule, what % scored in this range?
A) 68.0% [DT-V]
B) 81.5% [DT-W]
C) 84.0% [DT-X]
D) 95.0% [DT-Y]
TSIA2 Station Manipulatives • Print on cardstock for best durability 6 Chance Tiles Complete
TSIA2 Station Facilitation Blueprint • Page 1 of 2 Full Worked Solutions & Answer Keys on Page 2 →
Proctor Master Key
All 18 Station Tasks
STATION 1: ALGEBRA VAULT SOLUTIONS Vault Word: [M-A-C-O-T-X] / TOMCAT anagram
A1: Linear Systems → B (50) [M]
\( s = 140 - a \). Substitute: \( 12a + 8(140 - a) = 1320 \implies 4a + 1120 = 1320 \implies 4a = 200 \implies a = 50 \). Adult tickets = 50.
A2: Quadratic Roots → A (x = 4) [A]
Factor: \( (2x + 3)(x - 4) = 0 \). Roots are \( x = -\frac{3}{2} \) and \( x = 4 \). Question specifies positive root: \( x = 4 \).
A3: Exponent Laws → A (\(3x^8\)) [C]
Numerator: \( (9x^6 y^{-4})(2x^4 y^3) = 18x^{10}y^{-1} \). Divide by \( 6x^2 y^{-1} \): \( \frac{18}{6}x^{10-2}y^{-1-(-1)} = 3x^8 y^0 = 3x^8 \).
A4: Rational Eq → B (x = 4) [O]
Multiply LCD \( x(x-3) \): \( 4x - 2(x-3) = 14 \implies 2x + 6 = 14 \implies 2x = 8 \implies x = 4 \). Valid since \( x \ne 0, 3 \).
A5: Functions → A (3) [T]
Evaluate inner: \( g(2) = 3(2) - 4 = 2 \). Evaluate outer: \( f(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3 \).
A6: Inequalities → B (20) [X]
Set \( x = 30 \) for max \( y \): \( 4(30) + 6y \le 240 \implies 120 + 6y \le 240 \implies 6y \le 120 \implies y \le 20 \). Max = 20.
STATION 2: DIMENSION SHIFT SOLUTIONS Blueprint Codes: BP-B, BP-L, BP-R, BP-V, BP-G, BP-1
G1: Rates → B (45 mph) [BP-B]
\( \frac{66 \text{ ft}}{\text{sec}} \times \frac{3600 \text{ sec}}{\text{hr}} = 237,600 \text{ ft/hr} \). Divide by \( 5,280 = 45 \text{ mph} \).
G2: Percents → B ($81.60) [BP-L]
Sale price: \( 120 \times 0.80 = \$96.00 \). Apply coupon: \( 96 \times 0.85 = \$81.60 \). (Trap: don't subtract 35% directly!).
G3: Trig → B (12/13) [BP-R]
Opposite height: \( \sqrt{13^2 - 5^2} = \sqrt{144} = 12 \text{ ft} \). By definition, \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{12}{13} \).
G4: Sectors → B (\(18\pi\)) [BP-V]
\( A = \frac{45}{360}\pi (12^2) = \frac{1}{8}(144\pi) = 18\pi \text{ m}^2 \). Central angle fraction is \( \frac{1}{8} \).
G5: Density → C (\(765\pi\)) [BP-G]
Volume: \( \pi (3^2)(10) = 90\pi \text{ cm}^3 \). Mass = \( \text{Density} \times V = 8.5 \times 90\pi = 765\pi \text{ g} \).
G6: Slopes → A (\(y=-\frac{3}{2}x+5\)) [BP-1]
Slope is \( \frac{2}{3} \implies m_{\perp} = -\frac{3}{2} \). Equation: \( y - (-1) = -\frac{3}{2}(x - 4) \implies y = -\frac{3}{2}x + 5 \).
STATION 3: CHANCE MATRIX SOLUTIONS Data Tiles: DT-C, DT-F, DT-J, DT-N, DT-R, DT-W
D1: Tables → C (75%) [DT-C]
Condition: among STEM students (total = 80). STEM with internship = 60. \( \frac{60}{80} = \frac{3}{4} = 75\% \).
D2: Conditional → B (3/10) [DT-F]
Given contact sports (total = 90). Contact with sprain = 27. Probability = \( \frac{27}{90} = \frac{3}{10} \).
D3: Outlier → A (Mean drops) [DT-J]
Mean is sensitive to outliers and drops heavily; median is resistant to extreme values and shifts by only 1 point.
D4: Box Plot → B (IQR = 30) [DT-N]
\( \text{IQR} = Q_3 - Q_1 = 84 - 54 = 30 \). (Trap: 66 is the overall full range \( \text{Max} - \text{Min} \)).
D5: Compound → A (5/22) [DT-R]
Without replacement: \( P(\text{B}_1) = \frac{6}{12} \). \( P(\text{B}_2 | \text{B}_1) = \frac{5}{11} \). Product: \( \frac{6}{12} \times \frac{5}{11} = \frac{5}{22} \).
D6: Normal Dist → B (81.5%) [DT-W]
\( 450 = \mu - 1\sigma \), \( 600 = \mu + 2\sigma \). Area = \( 34\% + 34\% + 13.5\% = 81.5\% \) by Empirical Rule.
Common TSIA2 Traps & Targeted Interventions
Additive Discounts: Remind students that successive discounts cannot be added (20% + 15% \(\ne\) 35%). Apply each sequentially.
Extraneous Roots: Emphasize checking denominator zeroes in rational equations; answers that make denominator zero are invalid.
Conditional Denominators: Train students to underline "given that" and cross out all non-qualifying rows/columns immediately.
TSIA2 Master Proctor Solutions • Confirmed 100% Accurate Benchmark: College Readiness Classification (CRC 950+)
