The sat math section 5 ppsx

12. a. This problem is difficult if you make it diffi￾cult, but it’s easy if you make it easy. The eas￾iest way to do this problem is to calculate the

mean, median, and mode for the data set.

Remember:

■ The mean is the same as the average.

■ The median is the middle number of

data. First, you must order the num￾bers from least to greatest.

■ The mode is the most frequently

occurring number.

So, the mean equals:

5+7+6

5

+5+7 = 6

The median, if found by rearranging

the numbers in the data set as shown, is {5, 5,

6, 7, 7}. Therefore, the median is 6.

The mode is the most frequently occur￾ring number. In this data set, there are two

numbers that appear most frequently: {5, 7}.

Now, inspect the answers.

You will quickly see that choice a is cor￾rect: The mean = median, because 6 = 6.

13. c. You have to figure out if

XY and

YZ are per￾pendicular. The key thing to remember here is

that perpendicular lines intersect to form right

angles. If you can find a right angle at the

point that

XY and

YZ intersect, then you know

that the two segments are perpendicular.

In Figure 1, if

XY and

YZ are perpendi￾cular, then ΔXYZ is a right triangle because it

contains a right angle at Y.

In ΔXYZ, you are given three sides. If

ΔXYZ is a right triangle, then the Pythago￾rean theorem should hold true for these

three sides.

(Leg 1)2 + (Leg 2)2 = (Hypotenuse)2

(6)2 + (8)2 = (10)2

Note: 10 is the hypotenuse because it is

across from the largest angle of the triangle.

36 + 64 = 100

100 = 100

ΔXYZ is a right triangle and, likewise,

XY is perpendicular to

YZ because the

Pythagorean theorem is true for Figure 1.

In Figure 2, you are given the two

angles of ΔXYZ. If a third angle measures

90°, then ∠Y is a right triangle. Thus, XY is

perpendicular to YZ.

m∠X + m∠Y + m∠Z = 180°, since

the sum of the angles of a triangle = 180.

25° + x + 65° = 180°

90° + x = 180°

Therefore, x = 90°. ∠Y is a right angle

and XY is perpendicular to YZ.

Thus, XY is perpendicular to YZ in

both figures. The answer is choice c.

14. d. The first thing that you should realize is that

x and y are both greater than 0, but less than

1. So, x and y are going to be between 0 and 1

on the number line.

Next, you see the formula for d; d = x – y.

To solve for d, you must substitute a

value in for x and y. However, you do not have

a value. You should recognize however that x

is less than y. Thus, whatever value you choose

for x, the answer for d is going to be negative.

Therefore, the answer is choice d.

15. a. This question involves calculating distance.

The pieces of information that you are given

or have to calculate are rate of speed and time.

The formula for distance (with these

specific given pieces of information) is:

Distance = Rate × Time

The first step is to calculate the rate

traveled at by the car.

Solving for rate, you have

Rate =

D

T

is

i

t

m

an

e

ce =

1

2

10

ho

m

u

i

r

le

s s

= 55 mph

Now, all you have to do is substitute

into the formula above using the rate you

just solved for.

–THE SAT MATH SECTION–

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