Mixed SAT-Level Review 2 — Applied Modelling Sprint

Practice Questions

Level 1: Easy (Foundational)

1. Simplify: $\tfrac{8x^2}{4x}$ for $x \ne 0$.
   A) $2x$
   B) $\tfrac{1}{2}x$
   C) $4x$
   D) $2x^2$
2. A rectangle has length $10$ and width $6$. Determine the exact perimeter.
   A) $16$
   B) $26$
   C) $32$
   D) $60$
3. The median of $\{1, 3, 3, 5, 7, 9, 11\}$ is:
   A) $3$
   B) $5$
   C) $7$
   D) $9$
4. Determine $2^{10}$. (SPR)

Level 2: Medium (Standard)

1. A car accelerates from $0$ to $30$ m/s in $12$ s. Determine, to $2$ s.f., the acceleration in m/s².
   A) $1.5$
   B) $2.0$
   C) $2.5$
   D) $3.0$
2. Two events $A, B$ have $P(A)=0.5$, $P(B)=0.4$, $P(A \cap B) = 0.2$. Determine $P(A \cup B)$.
   A) $0.6$
   B) $0.7$
   C) $0.8$
   D) $0.9$
3. If $f(x) = 3x^2 - 2$, determine $f(3)$.
   A) $16$
   B) $19$
   C) $25$
   D) $27$
4. A pyramid has square base side $6$ and vertical height $8$. Determine the exact volume. (SPR)

Level 3: Hard (Advanced)

1. A best-fit line has equation $y = 0.6x + 5$. Determine the predicted $y$ at $x = 25$.
   A) $17$
   B) $18$
   C) $20$
   D) $22$
2. A binomial random variable $X \sim B(20, 0.4)$. Determine the exact expected value.
   A) $4$
   B) $6$
   C) $8$
   D) $10$
3. A cylinder has volume $V = \pi r^2 h$. If $V = 100\pi$ and $r = 5$, determine the exact height.
   A) $2$
   B) $4$
   C) $5$
   D) $10$
4. A dataset has values $\{10, 12, 14, 16, 18\}$. Determine the exact standard deviation (population, $\sigma$). (SPR)