Test (No calculator) - 1 - SAT MCQ

Since k = 3, one can substitute 3 for k in the equation Multiplying both sides of  gives x -1 = 9 and then adding 1 to both sides of x- 1 = 9 gives x = 10.
Choices A, B, and C are incorrect because the result of subtracting 1 from the value and dividing by 3 is not the given value of k, which is 3.

To calculate (7 + 3i) + (-8 + 9i), add the real parts of each complex number, 7 + (-8) = -1, and then add the imaginary parts, 3i + 9i = 12i. The result is -1 + 12i.
Choices B, C, and D are incorrect and likely result from common errors that arise when adding complex numbers. For example, choice B is the result of adding 3i and -9i, and choice C is the result of adding 7 and 8.

The total number of text messages sent by Armand can be found by multiplying his rate of texting, in number of text messages sent per hour, by the total number of hours he spent sending them; that is m texts/hour * 5 hours = 5 m texts. Similarly, the total number of text messages sent by Tyrone is his hourly rate of texting multiplied by the 4 hours he spent texting: p texts/hour * 4 hours = 4p texts. The total number of text messages sent by Armand and Tyrone is the sum of the total number of messages sent by Armand and the total number of messages sent by Tyrone: 5 m + 4p.
Choice A is incorrect and arises from adding the coefficients and multiplying the variables of 5 m and 4p. Choice B is incorrect and is the result of multiplying 5 m and 4p. The total number of messages sent by Armand and Tyrone should be the sum of 5 m and 4p, not the product of these terms. Choice D is incorrect because it multiplies Armand’s number of hours spent texting by Tyrone’s hourly rate of texting, and vice versa. This mix-up results in an expression that does not equal the total number of messages sent by Armand and Tyrone.

The value 108 in the equation is the value of P in P = 108 - 23d when d = 0. When d = 0, Kathy has worked 0 days that week. In other words, 108 is the number of phones left before Kathy has started work for the week. Therefore, the meaning of the value 108 in the equation is that Kathy starts each week with 108 phones to fix.
Choice A is incorrect because Kathy will complete the repairs when P = 0. Since P = 108 - 23d, this will occur when 0 = 108-  23d or when d = 108/23, not when d = 108. Therefore, the value 108 in the equation does not represent the number of days it will take Kathy to complete the repairs. Choices C and D are incorrect because the number 23 in P = 108 - 23d indicates that the number of phones left will decrease by 23 for each increase in the value of d byl;in other words, Kathy is repairing phones at a rate of 23 per day, not 108 per hour (choice C) or 108 per day (choice D).

Only like terms, with the same variables and exponents, can be combined to determine the answer as shown here:
(x²y - 3y² + 5xy²) - {-x²y + 3xy² - 3y²)
= (x²y - (-x²y)) + (-3y² - (-3y²)) + (5xy² - 3xy²)
= 2x²y + 0 + 2xy²
= 2x²y + 2xy²
Choices A, B, and D are incorrect and are the result of common calculation errors or of incorrectly combining like and unlike terms.

In the equation h = 3a + 28.6, if a, the age of the boy, increases by 1, then h becomes h = 3(a +1) + 28.6 = 3a + 3 + 28.6 = (3 a + 28.6) + 3. Therefore, the model estimates that the boy’s height increases by 3 inches each year.
Alternatively: The height, h, is a linear function of the age, a, of the boy. The coefficient 3 can be interpreted as the rate of change of the function; in this case, the rate of change can be described as a change of 3 inches in height for every additional year in age.
Choices B, C, and D are incorrect and are likely the result of dividing 28.6 by 5, 3, and 2, respectively. The number 28.6 is the estimated height, in inches, of a newborn boy. However, dividing 28.6 by 5, 3, or 2 has no meaning in the context of this question.

Since the right-hand side of the equation is P times the expression multiplying both
sides of the equation by the reciprocal of this expression results in 
Choice A is incorrect and is the result of multiplying both sides of the equation by the rational expression  rather than by the reciprocal of this expression  Choices C and D are incorrect and are likely the result of errors while trying to solve for P.

Adding x and 19 to both sides of 2y- x = -19 gives x = 2y + 19. Then, substituting 2y + 19 for x in3x + 4y = -23 gives 3(2y + 19) + 4y = -23. This last equation is equivalent to 10y + 57 = -23. Solving 10y + 57 = -23 gives y = -8. Finally, substituting -8 for y in 2y- x = -19 gives 2(-8) - x = -19, or x = 3. Therefore, the solution (x, y) to the given system of equations is (3, -8).
Choices A, C, and D are incorrect because when the given values of x and y are substituted in 2y- x = -19, the value of the left side of the equation does not equal -19.

Since g is an even function, g (-4) = g(4) = 8.
Alternatively: First find the value of a, and then find g(-4).
Since g(4) = 8, substituting 4 for x and 8 for g(x) gives 8 = a(4)² + 24 = 16a + 24. Solving this last equation gives a = -1. Thus g(x) = -x² + 24, from which it follows that g (-4) = -(-4)² + 24; g (-4) = -16 + 24; and g (-4) = 8.
Choices B, C, and D are incorrect because g is a function and there can only be one value of (g -4).