SAT Math – Practice Set

If $3(x – 4) = 2x + 5$, what is the value of $x$?

A line in the $xy$-plane passes through the points $(2, 5)$ and $(6, 13)$.(a) Find the slope of the line.(b) Find the $y$-intercept of the line.

The system $2x + 3y = 12$ and $x – y = 1$ has solution $(x, y)$. What is the value of $xy$?

A phone plan costs $\$20$ per month plus $\$0.05$ per text message. Write an inequality for the number of texts $t$ that keeps the monthly cost at most $\$35$, and find the greatest possible value of $t$.

After a $20$ percent reduction, a jacket costs $\$48$. What was the original price, in dollars?

The mean of five numbers is $12$. When a sixth number is included, the mean of the six numbers is $14$. What is the sixth number?

A survey of $40$ students recorded year group and whether the student plays a school sport. $24$ students play a sport, of whom $15$ are juniors. $10$ juniors do not play a sport. If a junior is chosen at random, what is the probability that the student plays a sport?

The function $f$ is defined by $f(x) = 2x^2 – 12x + 7$. What are the coordinates of the vertex of the graph of $y = f(x)$?

A town’s population is $5000$ and grows by $4$ percent each year.(a) Write a function $P(t)$ for the population after $t$ years.(b) To the nearest whole number, what is the population after $10$ years?

What value of $x$ satisfies $\dfrac{2}{x + 1} = \dfrac{3}{x + 4}$?

The equation $x^2 + y^2 – 6x + 4y = 12$ represents a circle in the $xy$-plane.(a) Find the coordinates of the centre.(b) Find the radius.

In right triangle $ABC$, angle $C = 90^\circ$ and $\sin A = \dfrac{3}{5}$.(a) Find $\tan A$.(b) Triangle $DEF$ is similar to triangle $ABC$ with $DE = 3 \times AB$. What is $\sin D$, where $D$ corresponds to $A$?(c) A cylinder has radius $3$ and height $10$. Find its volume in terms of $\pi$.