Question

please tell me proven math difficult questions

Answer 1

download them from Google:)

Answer 2

The 13 Hardest SAT Math Questions
Now that you’re sure you should be attempting these questions, let’s dive right in! We've curated 13 of the most difficult SAT Math questions for you to try below, along with walkthroughs of how to get the answer (if you're stumped).



No Calculator SAT Math Questions
Question 1
C=
5
9
(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only



ANSWER EXPLANATION:Think of the equation as an equation for a line

y=mx+b

where in this case

C=
5
9
(F−32)

or

C=
5
9
F−
5
9
(32)

You can see the slope of the graph is
5
9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5
9
of 1 degree Celsius.

C=
5
9
(F)

C=
5
9
(1)=
5
9

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9
5
degrees Fahrenheit.

C=
5
9
(F)

1=
5
9
(F)

(F)=
9
5

Since
9
5
= 1.8, statement II is true.

The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of
5
9
degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

C=
5
9
(F)

C=
5
9
(
5
9
)

C=
25
81
(whichis≠1)

An increase of
5
9
degree Fahrenheit leads to an increase of
25
81
, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.



Question 2
The equation
24x2+25x−47
ax−2
=−8x−3−
53
ax−2
is true for all values of x≠
2
a
, where a is a constant.

What is the value of a?

A) -16
B) -3
C) 3
D) 16



ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.

The final answer is B.



Question 3
If 3x−y=12, what is the value of
8x
2y
?

A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.



ANSWER EXPLANATION: One approach is to express

8x
2y

so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of
8x
2y
gives

(23)x
2y

which can be rewritten

23x
2y

Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that

8x
2y
=212

The final answer is A.



Question 4
8−i
3−2i

If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: i=√−1)



ANSWER EXPLANATION: To rewrite
8−i
3−2i
in the standard form a+bi, you need to multiply the numerator and denominator of
8−i
3−2i
by the conjugate, 3+2i. This equals

(
8−i
3−2i
)(
3+2i
3+2i
)=
24+16i−3+(−i)(2i)
(32)+(2i)2

Since i2=−1, this last fraction can be reduced simplified to

24+16i−3i+2
9−(−4)
=
26+13i
13

which simplifies further to 2+i. Therefore, when
8−i
3−2i
is rewritten in the standard form a + bi, the value of a is 2.

The final answer is A.



Question 5
In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is
1
3
the length of the corresponding side of triangle ABC. What is the value of sinF?



ANSWER EXPLANATION: Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem,

AB=√202−162=√400−256=√144=12

Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle∠F equals the measure of angle∠C. Therefore, sinF=sinC. From the side lengths of triangle ABC,

sinF=
oppositeside
hypotenuse
=
AB
AC
=
12
20
=
3
5

Therefore, sinF=
3
5
.

The final answer is
3
5
or 0.6.