cueprepThe hardest SAT Math questions, solved
Try each one, then see the answer, why the other choices miss, and the full solution.
30% of every Math skill free on the 3-day trial. No card.
Area and volume · Question 1 of 5
In a lab, a solid cylindrical block of growth medium shown has a base radius of cm and a height of cm. A conical cavity with the same base radius and the same height as the cylinder, with its apex at the center of the cylinder's base, is scooped out of the block. What is the volume, in cubic centimeters, of the growth medium that remains?
Linear inequalities in 1 or 2 variables · Question 2 of 5
A lab measures the heights of seedlings in a tray. Four of them measure , , , and cm. The tray is acceptable only if the mean height of all seedlings is at least cm and at most cm. What is the greatest possible height, in centimeters, of the fifth seedling?
Nonlinear equations and nonlinear systems · Question 3 of 5
The fuel cost, in dollars, for a single ferry crossing is modeled by , where is the ferry's average speed in knots. What is the sum of all speeds at which the fuel cost equals ?
Systems of 2 linear equations in 2 variables · Question 4 of 5
The graph shows the two lines given by the equations and . If is the solution to this system, what is the value of ?
Area and volume · Question 5 of 5
A lemonade stand pours from a cylindrical pitcher with a radius of centimeters and a height of centimeters into cylindrical cups, each with a radius of centimeters and a height of centimeters. The stand earns profit only on completely filled cups. If the full pitcher is poured out, filling as many cups as possible, how many completely filled cups can be poured from one full pitcher?
Frequently Asked Questions
What are the hardest SAT Math questions?
The ones in the harder second Math module. They tend to stack two or three steps, hide the equation you need inside a word problem, or ask for a value in a form you have to rearrange to see.
How do you get better at hard SAT Math questions?
Work them one skill at a time and read the explanation for every miss, including why your wrong answer looked right. A miss you understand rarely repeats.
Can Desmos help on hard SAT Math questions?
Often. Graphing both sides of an equation and reading where they cross, or fitting a regression with ~, turns a lot of hard algebra into a few keystrokes. Desmos is built into Bluebook for every Math question.
Make hard questions routine
30% of every Math skill free on the 3-day trial. No card.