If you chose (A) you may have subtracted the y-values from the x-values.
If you chose (E) you may have divided run by rise.
If you chose (D) you may have done both these things.
If you chose (B), you may have forgotten the rules for exponents in denominators.
(B) is incorrect because two different $x$-values must correspond to two different $y$-values.
(C) and (D) are incorrect because even though one of them must be false, it is impossible to know which one without more information (answer (C) would be true if the function’s slope was negative; answer (D) if the slope was positive).
(E) is incorrect because we know nothing about the function’s $x$-intercepts.
Instead, you can use your knowledge of numbers to find which statement is true. (A) is false if $a=b=1$. (C) and (D) are also false when $a=b=1$. (E) is false when $a=1$ and $b=2$, for example.
If you got (A), you found the negative slope but forgot to take the reciprocal.
If you got (C), you took the reciprocal of the entire line equation.
If you got (D), you took the reciprocal of the slope but forgot to change the sign.
If you chose (E), you may have thought that the a’s wouldn’t cancel out.
If you got (A) or (C), you forgot that the floor function will round any value to the nearest integer smaller than the value itself: 2.28 will become 2.
If you got (E), you may have taken the floor of $x$ instead of the floor of $x+1$.
If you chose (A), you forgot to shift the graph upwards and selected the range of the function y = 3 sin (2x – π).
If you chose (C), you may have confused the vertical shift and the amplitude.
If you chose (E), you picked the domain of the function.
(B) is incorrect because $f$ dips below -18 between $x=0$ and $x=2$.
(C) is incorrect because $f$ rises above -18 between $x=-18$ and $x=0$.
(D) is incorrect because $f$ is increasing over this entire range, meaning $f(x)$ gets larger as $x$ gets larger.
(E) is incorrect because $f$ is decreasing between $x=-2$ and $x=1$.
y ≐ 344
y' = 2y – x
Now, you want to find out when x = x’ and when y = y’:
If you chose (B), you solved for y and stopped there.
Set A is perfectly symmetrical about its mean of zero, so multiplying all its elements by 2 will not change the mean. Since the mean is zero, and all the other elements are multiplied by a factor of 2, the distance from the mean in B is twice the distance of the elements in set A. You can refer to the equation for standard deviation, where you can see that this multiplier will first be squared and then square rooted. Therefore, the standard deviation of B will be two times the standard deviation of A.
(A) and (B) are incorrect because the mean of A is the same as the mean of B, because they are both 0.
(C) is incorrect because the range of A is half the range of B (20 vs. 40).
(D) is incorrect because the standard deviation of B is exactly two times that of A.
If you got (B), you probably forgot to multiply $g(6)$ by 2.
If you got (E), you multiplied the $g(6)$ by 4 instead of by 2.
If you got (C), you probably reversed the matrix’s columns and rows.
(A) is incorrect because this polynomial has degree 1+3=4.
(B) is incorrect because this polynomial has degree 1+5=6.
(C) is incorrect because this polynomial has degree 14.
(E) is incorrect because this polynomial has degree 2+2+4.
(A) is incorrect because 3 is a factor of 240 but 32 = 9 is not.
(B) is incorrect because 11 is a factor but 121 is not.
(C) is incorrect because 3 is a factor but 9 is not.
(D) is incorrect because 3 is a factor but 9 is not.
To decide whether the exponent should be n or n – 1, you can plug in a value for n. For example, when n = 2, a2 = –3, so the exponent should be 1, meaning that n – 1 (and not n) is correct.
If you got (E), you forgot that –25i2 = –25(–1) = +25, so you thought the last two binomials multiplied to zero.
Since only a = 6 is an answer choice, the answer is (D).
(A) is incorrect because this will make the expression equal to 0.
You can see that (B) is incorrect because if b = –1 and a = 2 then the expression is equal to ⅓ > 0.
(C) is incorrect because if a = –2 and b = 1 then the expression is again equal to ⅓ > 0.
(D) is incorrect because of either of the examples above.
The other answer options are incorrect because the cosine of two times them is not equal to ½.
If you got (D) or (E), you were trying to set the entire function equal to zero.
If you mistakenly include the values π ≤ t ≤ 2π, you will get a complete circle, or answer choice (A).