Mixed SAT-Level Review — Algebra, Modelling, Stats & Geometry

Practice Questions

Level 1: Easy (Foundational)

1. Solve $2x + 7 = 21$.
   A) $5$
   B) $6$
   C) $7$
   D) $14$
2. A triangle has angles $50^\circ$ and $60^\circ$. Determine the exact third angle.
   A) $60^\circ$
   B) $70^\circ$
   C) $80^\circ$
   D) $90^\circ$
3. What is the mean of $\{4, 6, 8, 10\}$?
   A) $6$
   B) $7$
   C) $8$
   D) $28$
4. Determine $\sqrt{81}$. (SPR)

Level 2: Medium (Standard)

1. A cone has base radius $3$ and height $4$. Determine the exact volume.
   A) $4\pi$
   B) $9\pi$
   C) $12\pi$
   D) $36\pi$
2. A bag has $2$ red, $3$ blue, $5$ green marbles. Determine the exact probability of drawing a blue.
   A) $\tfrac{1}{10}$
   B) $\tfrac{3}{10}$
   C) $\tfrac{5}{10}$
   D) $\tfrac{3}{5}$
3. The exponential $y = 100 \cdot 0.8^{t}$ models decay. Determine the exact value of $y$ at $t = 2$.
   A) $64$
   B) $72$
   C) $80$
   D) $100$
4. A car depreciates $15\%$ each year from $\$20{,}000$. Determine the exact value, in dollars, after $2$ years. (SPR)

Level 3: Hard (Advanced)

1. For what $k$ does $x^2 - 6x + k = 0$ have exactly one real root?
   A) $-9$
   B) $3$
   C) $9$
   D) $36$
2. A trapezium has parallel sides $6$ and $10$ and height $4$. Determine the exact area.
   A) $24$
   B) $32$
   C) $40$
   D) $60$
3. The vectors $\mathbf{u} = (2, k)$ and $\mathbf{v} = (3, -4)$ are perpendicular. Determine the exact value of $k$.
   A) $\tfrac{3}{2}$
   B) $\tfrac{4}{3}$
   C) $\tfrac{3}{4}$
   D) $2$
4. A savings account of $\$1000$ earns $5\%$ compound interest annually. Determine, to the nearest whole dollar, the balance after $10$ years. (SPR)