Mixed SAT-Level Review 2 — Full-Domain Sprint

Practice Questions

Level 1: Easy (Foundational)

1. If $3x + 5 = 20$, determine the exact value of $x$.
   A) $3$
   B) $5$
   C) $\tfrac{15}{3}$
   D) $\tfrac{25}{3}$
2. A circle has radius $5$. Determine the exact area.
   A) $10\pi$
   B) $25\pi$
   C) $50\pi$
   D) $100\pi$
3. What is the median of $\{2, 5, 7, 10, 12\}$?
   A) $5$
   B) $7$
   C) $10$
   D) $36/5$
4. Determine $\sqrt{144}$. (SPR)

Level 2: Medium (Standard)

1. Solve $x^2 - 5x + 6 = 0$. Which is the sum of the roots?
   A) $5$
   B) $6$
   C) $-5$
   D) $-6$
2. A right triangle has legs $5$ and $12$. Determine the exact length of the hypotenuse.
   A) $13$
   B) $17$
   C) $\sqrt{60}$
   D) $\sqrt{119}$
3. A jar holds $6$ red, $3$ blue, $1$ green ball. Determine the exact probability of drawing a red ball.
   A) $\tfrac{1}{10}$
   B) $\tfrac{3}{10}$
   C) $\tfrac{6}{10}$
   D) $\tfrac{9}{10}$
4. The line through $(1,2)$ and $(4,11)$ has slope $m$. Determine the exact value of $m$. (SPR)

Level 3: Hard (Advanced)

1. For what value of $k$ does $y = x^2 - 4x + k$ touch the $x$-axis at exactly one point?
   A) $1$
   B) $2$
   C) $3$
   D) $4$
2. Vectors $\mathbf{u}=(3,4)$ and $\mathbf{v}=(a,-3)$ are perpendicular. Determine the exact value of $a$.
   A) $3$
   B) $4$
   C) $\tfrac{9}{4}$
   D) $\tfrac{4}{3}$
3. An investment of $\$1000$ grows by a compounded $6\%$ annually. Determine the exact balance after $2$ years.
   A) $\$1060$
   B) $\$1120$
   C) $\$1123.60$
   D) $\$1136$
4. Determine the exact value of $\sin(30^\circ) + \cos(60^\circ)$. (SPR)