SAT Math: Challenging Problems #4

Here are another five problems in our series of challenging SAT Math problems.  Give them a try, and as always, let me know if you have any questions.  Answers are located at the bottom of the page.

1)  The line m contains the point (4, 10) and the vertex of the parabola y = 3(x – 1)2 + 4.  Another point on the line is (a, b).  Which of the following points must also be on line m?

(A)  (a + 1, b + 3)
(B)  (a + 5, b + 10)
(C)  (a – 2, b + 3)
(D)  (a – 4, b – 6)
(E)  (a +2, b + 8)

2)  A regular polygon is covered by a piece of paper so that only one of its interior angles is visible.  You are able to determine that the interior angle is four times as large as the exterior angle.  How many sides does the polygon have?

Challenge 4-2(A)  8
(B)  9
(C)  10
(D)  11
(E)  12

3)  In the diagram below, the function graphed is f(x) = 2x3 + kx.  The rectangle ABCD has a perimeter of 136 units.  What is the value of k?

Challenge 4-3Note:  Horizontal & Vertical Scales are Different

(A)  – 24
(B)  -12
(C)  8
(D)  12
(E)  24

4)  The rectangle in the figure below is inscribed in a circle with an area of 40 pi.  If the length of the rectangle is three times its width, what is the area, in square units, of the rectangle?

Challenge 4-4
(A)  12
(B)  36
(C)  48
(D)  108
(E)  192

5)  The distance between the point (x, 3x) and the point (5, 10) is 5 units.  What is one possible value of x?

Note:  This is a “grid-in” problem.  You need to provide your own answer.

If you have questions about these problems or anything else to do with the SAT, leave a comment below or send me an email at .


1)  (B)
2)  (C)
3)  (A)
4)  (C)
5)  2 or 5

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