Free SAT Math Student Produced Answers with Solutions
Sample 1

A set of 12 Math questions, with detailed solutions similar to the questions in the SAT math test where students have to produce the answer.

  1. Which positive number is equal to the quarter of its cube root?

  2. What is the diameter of the circle whose area and perimeter have the same value?

  3. John can read 15 pages of a book every 20 minutes. Linda can read 20 pages of the same book every 16 minutes. How many minutes are needed so that John and Linda read a total of 100 pages together?

  4. In the figure below, ABCD is a square. M is the midpoint of AD and N is the midpoint of BC. What is the ratio of the area of the square to ABCD to the area of triangle MNO?

  5. The remainder of the division of x by 3 is 1 and the remainder of the division of y by 3 is 3. What is the remainder of the division of 2x + 3y by 3?

  6. Find the smallest positive integer so that when it is divided by 5 the remainder is 4 and when it is divided by 6 the remainder is 5.

  7. 1 liter of water is poured into a cylindrical container of radius 10 cm. How high in cm will the water rise?

  8. In the figure below, AB is tangent to a circle with diameter BC. Find the length of segment AD.

    sat question - rigth similar triangle.


  9. If the length of AB is 1/3 of the length of BO, what is the length of cord MN of the circle with center O and a radius of 5 cm?

    sat question - cord of circles.


  10. Lines m and n are parallel and lines k, n and J all intersect at the same point O. Find the size of angle x.

    sat question - parallel lines and intersects.


  11. Points A, B, C and D are on a circle (concyclic points). BE cuts the circle at C and the segments CD and DE have the same length. Find the size of angle CED.

    sat question - Concyclic points.


  12. Points A, B, C and D are on a circle (concyclic points). BE cuts the circle at C and the segments CD and DE have the same length. Find the size of angle CED.

    sat question - triangle within rectangle.


  13. In the figure below, the circle of radius R is inscribed inside a equilateral triangle of side x. Find R in terms of x.

    sat question - inscribed circle within a triangle.


  14. In the figure below, the circle of radius R circumscribes an equilateral triangle of side x. Find x in terms of R.

    sat question - circle circumscribes a triangle.


  15. In the figure below, a small circle is inscribed within an equilateral triangle and a larger circle circumscribes the same triangle. Find the ratio of the area of the larger circle to that of the smaller circle.

    sat question - Large circle circumscribes a triangle and another is inscribed.




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