Mathematics Diagnostic Tests

Convexity definition

“1” is the answer.

The slope of the line that passes through any two of the collinear points A(-1, h), B(3, 2), and C(7, 3) should be the same.

First, let’s determine the line’s slope as it passes through points A and B:

Slope of AB=y2-y1/x2-x1 =2-h/3-(-1)=2-h/4

Let’s now determine the line’s slope as it passes through points B and C:

Slope of BC =y2-y1/x2-x1=3-2/7-3=1/4

Any two pairs of points should have the same slope because the points are collinear. Consequently:

2-h /4 = 1/4

Finding h by solving this equation:

2-h=1

-h=1-2

h=1

h-1

Thus, h 1. This corresponds to the response given.

The right choice is pi/2.

We can figure it out as follows:

If we enter θ=12, we obtain

(Cotπ2)4+(Cotπ2)²=(Cosecπ2)4-(Cosecπ2)2

1 + 0 = 0 + 0 = 1-1

0=0

Therefore, when θ = n/2, the given identity is true.

THE RIGHT ANSWER (C)

The number of students who study Arabic and Turkish is denoted by x.

18 students study nothing, 126 students study only Arabic, and 248 students study only Turkish.

All of these added together must equal 360. 248-x+x+126-x+18=360

x=32

C is the right response. Venn is being tested by this question.

A finite geometric series’ sum (S_n) can be found using the following formula:

S_n = a_1 (1 – r^n) / (1 – r)

where:

The first term is a_1.
R is the standard ratio.
The number of terms is n.