SAT Math practice questions

Question 1 — Linear functions (easy)

If $f(x) = 3x - 4$, what is the value of $f(5)$?

1. $3$
2. $11$
3. $19$
4. $1$

Answer: B. Substituting $x = 5$ gives $f(5) = 3(5) - 4 = 15 - 4 = 11$.

Question 2 — Systems of 2 linear equations in 2 variables (medium)

A theater sold $40$ tickets for a play. Adult tickets cost $10$ dollars each, student tickets cost $6$ dollars each, and ticket sales totaled $336$ dollars. How many adult tickets were sold?

1. $16$
2. $20$
3. $24$
4. $36$

Answer: C. For adult tickets $a$ and student tickets $s$, $a+s=40$ and $10a+6s=336$. Solving gives $a=24$ and $s=16$.

Question 3 — Equivalent expressions (medium)

Which expression is equivalent to $(2x-3)^2 - (x-3)(x+3)$?

1. $3x^2 - 12x + 18$
2. $3x^2 + 18$
3. $3x^2 - 12x$
4. $3x^2 - 6x$

Answer: A. $(2x-3)^2 = 4x^2 - 12x + 9$ and $(x-3)(x+3) = x^2 - 9$; subtracting gives $3x^2 - 12x + 18$.

Question 4 — Nonlinear functions (hard)

The function $m(t) = 240(0.5)^{t/8}$ gives the mass, in grams, of a radioactive sample $t$ days after it was first measured. Which of the following is the best interpretation of the number $8$ in this context?

1. The mass of the sample decreases by $8$ grams each day.
2. The mass of the sample halves every $8$ days.
3. The initial mass of the sample is $8$ grams.
4. The mass of the sample halves $8$ times each day.

Answer: B. Each time $t$ increases by $8$, the exponent $t/8$ increases by $1$, multiplying the mass by one additional factor of $0.5$.

Question 5 — Percentages (easy)

After a $20\%$ discount, the sale price of a jacket is $48$ dollars. What was the original price of the jacket, in dollars?

1. $38.40$
2. $57.60$
3. $68$
4. $60$

Answer: D. A $20\%$ discount leaves $80\%$ of the original price $p$, so $0.8p = 48$ and $p = 60$.

Question 6 — Probability and conditional probability (medium)

The table below shows the number of students in two clubs at a school, by grade.

If a student is selected at random from the robotics club, what is the probability that the student is in Grade 11?

1. $\dfrac{7}{20}$
2. $\dfrac{11}{25}$
3. $\dfrac{7}{10}$
4. $\dfrac{14}{25}$

Answer: D. The condition restricts the sample space to the $50$ robotics students, of whom $28$ are in Grade 11: $28/50 = 14/25$.

Question 7 — Circles (medium)

The graph of $x^2 + y^2 - 6x + 4y - 12 = 0$ in the $xy$-plane is a circle. What is the radius of the circle?

1. $5$
2. $\sqrt{12}$
3. $25$
4. $10$

Answer: A. Completing the square gives $(x-3)^2 + (y+2)^2 = 12 + 9 + 4 = 25$, so the radius is $\sqrt{25} = 5$.

Question 8 — Right triangles and trigonometry (medium)

In right triangle $ABC$, angle $C$ is the right angle, and $\sin A = \dfrac{3}{5}$. If the hypotenuse has length $40$, what is the length of the side opposite angle $A$?

1. $24$
2. $30$
3. $32$
4. $\dfrac{200}{3}$

Answer: A. Sine is opposite over hypotenuse, so the opposite side is $\sin A \times 40 = \dfrac{3}{5}(40) = 24$.