Tip #17 to Get a Top SAT Math Score
The SAT does not ask you to memorize any formulas. That's right, no memorizing. Actually, they do expect you to know perimeter formulas, but only a total jackass doesn't know these. I'm kidding; the perimeter of any shape is found by adding up the lengths of the sides. But any other formula that you need for area or volume is shown in the info box at the beginning of each math section. The box tells you:
For area and volume on the SAT, these are all the formulas that you'll need. Now, let's practice using them.
Let's look at this question:
In the figure above, the perimeter of the square BCDF is 12 and the perimeter of the rectangle ACEG is 30. If AB and DE are each positive integers, what is one positive value of the area of the rectangle ACEG?
Solution: Since the perimeter of square BCDF is 12, each side must be 12 ÷ 4 = 3; and since the perimeter of rectangle ACEG is 30, AB + DE = 15 – 3 – 3 = 9. So AB and DE can be any 2 integers that add up to 9, for example, 1 and 8; and AC and CE would each be 3 units longer, 4 and 11. There are four such possibilities for the area of ACEG:
4 × 11 = 44, 5 × 10 = 50, 6 × 9 = 54, 7 × 8 = 56. Any one of these is a correct answer.
Correct answers: 44, 50, 54, or 56
- If the square and the rectangle above have equal perimeters, what is the length of ?
- For the circles above, the diameter of circle A is 10, and the radius of circle B is half the diameter of circle A. What is the area of circle B ?
Note: Figure not drawn to scale.
- The three–dimensional figure pictured above has square and triangular faces. If each square face has area m and each triangular face has area n, what is the total surface area of the figure in terms of m and n ?
- m + n
- 2(m + n)
- 3m + 2n
- 3m + 3n
- The figure above shows the dimensions of a children's stacking block that is composed of rectangular solids. What is the volume of the block?
- A The perimeter of the rectangle is 7 + 7 + 3 + 3 = 20. Since the square has four equal sides and its perimeter is also 20, each side must be 20 ÷ 4 = 5.
- B Since the radius of circle B is half the diameter of circle A, it must be 5. Therefore, the area of circle B is a = πr2 = π(52) = 25π.
- C The surface area equals the addition of the faces. There are three square faces (area = m) and two triangular faces (area = n), so the total surface area = 3m + 2n.
- C Since volume = length × width × height, just determine the volume for each part of the block. The smaller part = 5 × 1 × 1 = 5, and the larger part = 5 × 3 × 1 = 15. So the volume of the whole block = 5 + 15 = 20.
Go to: Tip #18
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