Sat Math Medium Practice Quiz With Answer Key Page 15
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16SAT Math Medium Practice Quiz Answers
5. 100
(Estimated Difficulty Level: 3)
9. E
(Estimated Difficulty Level: 3+)
The angles x
, y
, and 70
make a straight angle: they
◦
◦
◦
First, note that AE = 4 and ED = 4. (Hint: fill in
2
must add to 180
. Since y = x
, we know that x +
◦
the diagram with information that you are given or can
2
2
x
+ 70 = 180, so that x
+ x
110 = 0. Factoring the
figure out.) When a 120
angle is used in a triangle, it
◦
left side of the equation gives: (x
10)(x + 11) = 0, so
is often a clue that a 30-60-90 triangle (shown on the
that either x = 10 or x =
11. We only want positive
first page of each SAT math section) is involved in the
angles, so x = 10 and the answer is y = 100. Did you
question. If you draw a line from E perpendicular to
answer too quickly by saying 10? Oops! Before you
the bottom side of the square, you should see that two
answer a math question, always reread it to be sure you
of these special triangles are formed, as shown in the
are answering what it is asking for.
figure below.
If factoring is not your thing, you could try plugging
in real numbers for x until the angles add up to 180
.
◦
E
Remember that no question on the SAT requires you
to have a calculator, so x won’t be something like 8.4 if
4
4
60
◦
60
◦
you have to square it like you do here.
30
◦
30
◦
√
√
A
D
2
3
2
3
Using the 30-60-90 triangle figure given to you (even
6. 4
(Estimated Difficulty Level: 3)
better, know it from memory), the side opposite the
30
angle is 2, and the side opposite the 60
angle is
◦
◦
2
√
√
√
√
The area of the square is s
, and the perimeter is 4s.
2
3. Then, the side of the square is 2
3 + 2
3 = 4
3
√
Since we are told that these two quantities are equal,
2
so that the area of the square is (4
3)
= 48.
2
s
= 4s, so that s = 4.
7. 6
(Estimated Difficulty Level: 3)
10. C
(Estimated Difficulty Level: 3)
Suppose that the length of one edge of the cube is equal
To find the area of the shaded region, we need to find
3
to x. Then, the volume of the cube is x
. There are six
the area of the large circle and subtract the area of the
faces on the cube, and each face is a square with side
small circle. The diameter of the large circle is 3, so
2
of length x. So, the total area of the faces is 6x
. Since
2
its area is π(3/2)
= 9π/4. The diameter of the small
3
2
the volume equals the area, x
= 6x
, making x = 6.
2
circle is 1, so its area is π(1/2)
= π/4. The area of the
shaded region is then 9π/4
π/4 = 8π/4 = 2π.
8. D
(Estimated Difficulty Level: 3)
The phrase “intersects the x-axis at x = b” is code
(sometimes called “math-speak”) for “goes through the
point (b, 0)”. If a line goes through a point, the point
satisfies the equation of the line. Plugging x = b and
y = 0 into the equation gives 3b = 72, or b = 24.
pg. 15
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