Math Questions for SAT Prep.
Calculator: Not Permitted.
Line straight ell is graphed in the xy-plane below.
If line straight ell is translated up 5 units and right 7 units, then what is the slope of the new line?
Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope is -3/2
The mean number of students per classroom, y, at Central High School can be estimated using the equation y=0.8636x+27.227. where x represents the number of years since 2004 and x ≤ 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
Choice D is correct. When an equation is written in the form y=mx +b, the coefficient of the x-term (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).
If 2/(a-1)=4/y where y ≠1, what is y in terms of
Choice A is correct. Multiplying both sides of the equation by the denominators of the rational expressions in the equation gives 2y=4a-4 The student should then divide both sides by 2 to isolate the y variable, yielding the equation y=2a-2.
if y=x^3 +2x+5 and z= x^2 + 7x+1, what is 2y+z in terms of x?
2x^3 + x^2 + 11x +11
Substituting the expressions equivalent to y and z into 2y +z results in the expression
2(x^3 +2x +5) +x^2+ 7x +1. The student must apply the distributive property to multiply
x^3 +2x +5 by 2
and then combine the like terms in the expression.
where a>0 and x>0, which of the following equations gives a in terms of x?
There are multiple ways to approach this problem, but all require an understanding of the properties of exponents. The student may rewrite the equation as 1/(a^0.5)=x
and then proceed to solve for a first by squaring both sides, which gives
(1/a)=x^2 and then multiplying both sides by a to find 1=a(x^2).Finally, dividing both sides by x^2 isolates the desired variable.
The graph of the eqution is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?
Which of the following is equal to (14-2i)(7+12i)? (Note i=(-1)^0.5)
Choice D is correct. Applying the distributive property to multiply the binomials yields the expression 98+168i - 14i - 24(i^2)
The note in the stem of the question reminds students that i=(-1)^0.5 therefore i^2 = -1.
Substituting this value into the expression gives the student 98+168i-14i - (-24). and combining like terms results in 122+154i.
In the equation above, what is the value of k?
Based on the system of equations above, what is the value of the product xy?
There are several solution methods possible, but all involve persevering in solving for the two variables and calculating the product. For example, combining like terms in the first equation yields 4x - 4y = 7 and then multiplying that by 2 gives 8x -8y-14. When this transformed equation is added to the second given equation, the y-terms are eliminated, leaving an equation in just one variable:
9x = 18 ,or x =2.
Substituting 2 for x in the second equation (one could use either to solve) yields
2+8y =4 , which gives y =1 /4. Finally, the product xy is 2 * 1/4 =1/2.
if 0.5x+(1/3)y=4, what is the value of 3x+2y?
A student may find the solution to this problem by noticing the structure of the given equation and seeing that multiplying both sides of the equation 0.5x +(1/3)y =4 by 6 to clear fractions from the equation yields 3x +2 y =24.
Which of the following is equal to sin(π/5)?
In the system of linear equations above, a is a constant. If the system has no solution, what is the value of a ?
Anise needs to complete a printing job using both of the printers in her office. One of the printers is twice as fast as the other, and together the printers can complete the job in 5 hours. The equation above represents the situation described. Which of the following describes what the expression 1/x represents in this equation?
The semicircle above has a radius of r inches, and chord CD is parallel to the diameter AB. If the length of CD is (2/3) of the length of AB what is the distance between the chord and the diameter in terms of r?
Choice D is correct. This represents the length of the distance between the chord and the diameter, using a radius of the circle to create a triangle, and then the Pythagorean theorem to solve correctly:(r^2)=(x^2)+((2r/3)^2) where r represents the radius of the circle and x represents the distance between the chord and the diameter.
Choice A is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have tried to use the circumference formula to determine the distance rather than making use of the radius of the circle to create a triangle.
Choice B is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have tried to use the circumference formula to determine the distance rather than making use of the radius of the circle to create a triangle.
Choice C is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have made a triangle within the circle, using a radius to connect the chord and the diameter, but then may have mistaken the triangle for a 45-45-90 triangle and tried to use this relationship to determine the distance.
It is given that sinx= a, where x is the radian measure of an angle and π/2
The equation of a circle in the xy-plane is shown above. What is the diameter of the circle?
Completing the square yields the equation (x-3)^2 +(y+4)^2 = 169.
the standard form of an equation of the circle. Understanding this form results in the equation r^2=169, which when solved for r gives the value of the radius as 13. The diameter is twice the value of the radius; therefore, the diameter is 26.