Sat Math Medium Practice Quiz With Answer Key Page 12
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16SAT Math Medium Practice Quiz Answers
6. E
(Estimated Difficulty Level: 3)
9. A
(Estimated Difficulty Level: 3+)
To find x, we need to square both sides of the equation:
Subtract x/2 from both sides of the equation to get
2
√
√
√
2/x = x/2. Cross-multiplying, you should get x
= 4
√
√
√
√
2
2
(
x)
= (
a +
b)
= (
a +
b)(
a +
b).
so that x = 2 or x =
2, which makes answer E the
correct one.
Now “FOIL” the right-hand side to get
If you got stuck on the algebra, you also could have
√
√
√
√
2
2
x = (
a)
+ 2
a
b + (
b)
used the answers by plugging them in for x until the
equation worked.
so that
√
√
√
x = a + 2
a
b + b = a + b + 2
ab.
Did you fall for answer D? Sorry about that.
7. 8
(Estimated Difficulty Level: 3)
3
Did you notice that there are four 4
terms on the left
3
side of the equation? So the left side is just 4(4
) =
10. A
(Estimated Difficulty Level: 3)
4
2
4
8
4
= (2
)
= 2
, which means that x = 8.
For the SAT, it is really useful to know the difference of
If manipulating exponents isn’t your thing, you could
2
2
two squares: x
y
= (x + y)(x
y). Here, the second
also use your calculator: figure out the left hand side
2
equation is: y = (2m + 1)(2m
1) = 4m
1. Since
(256), and then try various numbers for x until you get
2
x = 4m
, the correct answer is y = x
1.
256.
You could also plug in real numbers by making up a
number for m. For example, if m = 1, then x = 4 and
y = 3 so that y = x
1.
8. C
(Estimated Difficulty Level: 3)
Convert the phrase “x is y% of z” into an equation:
11. D
(Estimated Difficulty Level: 3+)
y
It is good to know some fraction-to-decimal conversions
x =
· z.
100
for the SAT: 1/2 = 0.5, 1/3 = 0.33, 1/4 = 0.25, and
1/5 = 0.2. So, the equation is really:
Now, solve this equation for y by multiplying both sides
by 100 and then dividing both sides by z. You should
x
y
+
= 18
find that y = 100x/z, which makes answer C correct.
1/2
1/5
You could also plug in some easy numbers for y and z
or
to determine x, and then see which of the answers is
2x + 5y = 18.
equal to the value you used for y.
Now, try working with the answers by plugging them
in for x: you are looking for a corresponding y value
that is a positive integer. (With a calculator, you can
probably skip rewriting the equation and go directly to
plugging in the answers for x.) Only x = 4 and y = 2
can work, so answer D is correct.
pg. 12
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