SAT Sample Math Test: No-Calculator Questions

By Geraldine Woods, Ron Woldoff

The no-calculator section of the new SAT Mathematics test contains questions that are more concept-based than arithmetic-based; however, they are no less challenging. You’ll be tackling 20 questions in 25 minutes: fifteen multiple choice, and five with grid-in answers.

The following sample questions are similar to what you will find on the SAT.

Sample Questions

You can use these formulas to solve the following questions.

image0.png

  1. In the xycoordinate plane, what is the area of the rectangle with opposite vertices at (–3, –1) and (3, 1)?

    (A) 3

    (B) 6

    (C) 9

    (D) 12

    image1.png

  2. In the figure above, ABCD is a square and points B, C, and O lie on the graph of

    image2.png

    where k is a constant. If the area of the square is 36, what is the value of k?

    (A) 1.5

    (B) 3

    (C) 4.5

    (D) 6

  3. The price of a television was first decreased by 10 percent and then increased by 20 percent. The final price was what percent of the initial price?

    (A) 88%

    (B) 90%

    (C) 98%

    (D) 108%

  4. The first term of a sequence is –1. If each term after the first is the product of –3 and the preceding term, what is the fourth term of the sequence?

    (A) –27

    (B) –9

    (C) 9

    (D) 27

Answers and Explanations

  1. D. Sketch out this problem to help you solve it:

    image3.png

    The length of the rectangle is 6, and the height is 2. The area of a rectangle is length times width, so the area of this rectangle is

    image4.png

  2. A. The key to this problem is paying attention to the fact that the figure is a square. Knowing that the area is 36, you can immediately deduce that the length of a side of the square is 6 because

    image5.png

    You also know that the length of half the side of the square is 3. That means that the (x, y) coordinates of point C will be (3, 6).

    You can then plug those coordinates into the equation

    image6.png

    and solve for k:

    image7.png

  3. D. Whenever you’re working on percentage problems, it’s a great idea to assume that the starting price is $100. So if the TV cost $100 to start, and then the price was decreased by 10 percent ($10), the reduced price is $90. You add 20 percent on to 90 by finding 20 percent of 90 and adding it to $90:

    image8.png

    It’s easy to see that $108 is 108 percent of $100:

    image9.png

  4. D. For this problem, it’s a good idea to just calculate each of the terms. You know that the first term is –1. To get the second term, multiply –1 by –3:

    image10.png

    To get the third term, multiply the second term by –3:

    image11.png

    For the fourth term, multiply the third term by –3:

    image12.png

    Therefore, the fourth term is 27, Choice (D).