2022 Anhui Matriculation Examination Mathematics Paper Analysis

Original Link #

31#

First, we need to know that A∪B is the union, which means the content that is present in both set A and set B (if both sets contain 1, then we only write it once).
Therefore, the answer is: C. {-1,0,1,2,3}

32#

For absolute value inequalities, we need to know that for greater than, we take both sides, and for less than, we take the middle, as shown in the figure. This question is greater than, so we take both sides. We can treat it as x+1≥2 and x+1≤2, solving gives: x≥1, x≤-3, represented as the solution set {x|x≤-3 or x≥1}.
Therefore, the answer is: A. {x|x≤-3 or x≥1}

33#

First, we need to know that in the Cartesian coordinate system, angles start from the positive x-axis. So for a 230° angle, as shown in the figure. This means that adding or subtracting any multiple of 360° from 230° will yield the same terminal side. After repeatedly adding or subtracting 360°, we find: 230° + 2×360° = 950°, thus option D is correct.
Therefore, the answer is: D. 950°

34#

There are a total of 6 balls, with 1 red ball (1/6 probability), 2 yellow balls (the probability of red or yellow balls is 1/2, which means 3 balls, and since there is 1 red ball, there are 3-1=2 yellow balls), and 3 white balls.
Therefore, the answer is: C. 2

35#

We need this formula:

\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha}

\sin \alpha = \pm \sqrt{1 - \cos^2 \alpha}

From this, we can derive:

\cos \alpha = \pm \sqrt{1 - (\frac{3}{5})^2}

\cos \alpha = \frac{4}{5}

\cos^2 \alpha = \frac{16}{25}

We also need this formula:

\cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha

\sin^2 \alpha = (\frac{3}{5})^2

\sin^2 \alpha = \frac{9}{25}

So,

\cos 2\alpha = \frac{16}{25} - \frac{9}{25}

\cos 2\alpha = \frac{7}{25}

Therefore, the answer is: A.

36#

First, we need to know that subtracting a vector is the same as adding the opposite vector. Then, we draw a diagram, and from the diagram, it is a continuous vector, so connecting the head and tail gives the answer (the vector marked in red).

Therefore, the answer is: A.

37#

Pure formula question (Mathematics Book Volume 1, Page 84)

Standard equation:

y^2 = 2px

Directrix equation:

x = -\frac{p}{2}

So p = 2. Substituting gives x = -1.

Therefore, the answer is: B. x = -1

38#

If x = 2, then -1 < x ≤ 3. This holds, so it is a sufficient condition.
If -1 < x ≤ 3, then x = 2. This does not hold, so it is not a necessary condition.
Combining these, it is a sufficient but not necessary condition. Since there is no option for sufficient but not necessary, we choose sufficient condition.
Therefore, the answer is: A. Sufficient condition

39#

We need to know the following formulas are equivalent:

f(x) = (x-1)^2

f(x) = \sqrt{x-1}

We know that after taking the square root, it must be a positive integer, so we can take values from 1 to positive infinity.
Therefore, the answer is: D. [1, +∞)

40#

As shown in the figure, drawing a perpendicular line can split into a 30° right triangle and a 45° isosceles triangle, and we can solve it using the trigonometric functions of the right triangle.

Therefore, the answer is: A.

41#

We need to know that adding logarithms with the same base means multiplication, and subtracting means division:

\log_a 3 + \log_a 4 = \log_a (3 \times 4)

\log_a 3 - \log_a 4 = \log_a \left(\frac{3}{4}\right)

The question just nests them:

\log_a 3 + \log_a 3 = \log_a9 = 2a

\log_a 9 + \log_a 5 = \log_a45 = 2a+b

Therefore, the answer is: C. 2a+b

42#

We need to know that the intercept is the point where it intersects the x-axis, which is y = 0, so x = 4.
Therefore, the answer is: B. 4

43#

Substituting special values can solve the problem; we need to take positive and negative sizes and exclude them one by one.
Moreover, option D also has the usual formula:

a^2 + b^2 \geq 2ab

Therefore, the answer is: D.

44#

We need to know that

T = \frac{2\pi}{\Omega}

This Ω is the coefficient in front of x, and the question asks us to find 3. We analyze one by one:
A is 1, B is 2, C is 2, D is 3.
Therefore, the answer is: D.

45#

Triangular prism (black frame) example diagram.

First, calculate the surface area:

\frac{1}{2} \times 1 \times \frac{1}{2} = \frac{1}{4}

Then calculate the volume:

\frac{1}{4} \times 1 = \frac{1}{4}

Therefore, the answer is: C.

46#

You can just guess 1, 2, 4, 8.
Therefore, the answer is: B.

47#

We need to know that left addition and right subtraction (for x), and upper addition and lower subtraction (for the whole).
The question requires us to move to the right, so it is to subtract from x:

y = \sin\left(3\left(x - \frac{\pi}{12}\right) + \frac{\pi}{4}\right)

y = \sin3x

To add:
If this question is downward:

y = \sin\left(3x + \frac{\pi}{4}\right) - \frac{\pi}{12}

Therefore, the answer is: A. y = sin3x

48#

We need to know that letting X and Y be 0 gives the coordinates of the center of the circle:

(x + 1)^2 + (y - 1)^2 = 2

To make X zero, it is -1 + 1 = 0, so x = -1.
To make Y zero, it is 1 + -1 = 0, so y = 1.
Thus, (-1, 1) is the center of the circle. This question then becomes the distance from a point to a line, for which we need a formula. A, B, and C are the coefficients in front of x, y, and the constant term respectively:

d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}

Substituting and calculating gives:
d = 2

Therefore, the answer is: B. 2

49#

Skip, just look at the diagram.

50#

We need to know that when the base is greater than 1, it is an increasing function, and the larger the exponent, the larger the result.
When the base is less than 1, it is a decreasing function, and the larger the exponent, the smaller the result.
It is easy to see that D is correct.
Therefore, the answer is: D.

51#

You can just guess 3, 6, 9, 12.
Therefore, the answer is: B.

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