SAT Math Problems
QUESTIONS WITH
DETAILED ANSWERS
If the difference of two numbers is greater than the sum of the numbers, which of the following must be
true? - Answer: (a) Neither number is negative
(b) At least one number is negative
(c) Exactly one number is negative
(d) Both numbers are negative
(e) None of these statements must be true
A rectangle has a perimeter equal to the circumference of a circle of radius 3. If the width of the
rectangle is 3 what is the length? - Answer: (a) 3π-3 (b) 4.5π-3 (c) 6π-6 (d) 9π-3 (e) 9π-6
In the figure above, BC is equal to BE If R represents the perimeter of rectangle ABCD, and T represents
the perimeter of CBE, what is the value of R-T? - Answer: (a) 2 (b) 8 (c) 20 (d) 12-4√(2) (e) It cannot be
determined.
Two cylindrical tanks have the same height, but the radius of one tank equals the diameter of the other.
If the volume of the larger is k% more than the volume of the smaller, k= - Answer: (a) 50 (b) 100 (c) 200
(d) 300 (e) 400
If F(x)=3x+8, for what value of a is f(a)=a - Answer: (a) -4 (b) -2 (c) -3/8 (d) 0 (e) 3/8
The measures of the three angles of a triangle are in the ratio of 5:5:10, and the length of the longest
side is 10. From this information, which of the following can be determined. - Answer: I. The area of the
triangle
II. The perimeter of the triangle.
III. The length of each of the three altitudes. Solving for product of quadratic - Answer: c/a
, Solving for sum of quadratic - Answer: -b/a
Vertex Point (keyword maximum/minimum of quadratic) - Answer: -b/2a
Quadratic Formula - Answer: x = -b ± √(b² - 4ac)/2a
No solution for linear equation - Answer: Same slope but don't intersect
How to solve for x-int in linear equation - Answer: set y to 0
infinite solutions to linear equation - Answer: lines are the same
Convex (geometry term meaning) - Answer: All interior angles are less than 180 degrees
Concave (geometry term meaning) - Answer: All interior angles are greater than 180 degrees
Density - Answer: mass/volume
Discriminant quadratic - Answer: b^2-4ac
Discriminant quadratic (2 solutions) - Answer: b^2-4ac= positive value
Discriminant quadratic (1 solution) - Answer: b^2-4ac= 0
Discriminant quadratic (no solution) - Answer: b^2-4ac= negative value
Quadratic Vertex Form - Answer: y=a(x-h)^2+k, (h,k) = center, a+/a-= parabola facing up or down
QUESTIONS WITH
DETAILED ANSWERS
If the difference of two numbers is greater than the sum of the numbers, which of the following must be
true? - Answer: (a) Neither number is negative
(b) At least one number is negative
(c) Exactly one number is negative
(d) Both numbers are negative
(e) None of these statements must be true
A rectangle has a perimeter equal to the circumference of a circle of radius 3. If the width of the
rectangle is 3 what is the length? - Answer: (a) 3π-3 (b) 4.5π-3 (c) 6π-6 (d) 9π-3 (e) 9π-6
In the figure above, BC is equal to BE If R represents the perimeter of rectangle ABCD, and T represents
the perimeter of CBE, what is the value of R-T? - Answer: (a) 2 (b) 8 (c) 20 (d) 12-4√(2) (e) It cannot be
determined.
Two cylindrical tanks have the same height, but the radius of one tank equals the diameter of the other.
If the volume of the larger is k% more than the volume of the smaller, k= - Answer: (a) 50 (b) 100 (c) 200
(d) 300 (e) 400
If F(x)=3x+8, for what value of a is f(a)=a - Answer: (a) -4 (b) -2 (c) -3/8 (d) 0 (e) 3/8
The measures of the three angles of a triangle are in the ratio of 5:5:10, and the length of the longest
side is 10. From this information, which of the following can be determined. - Answer: I. The area of the
triangle
II. The perimeter of the triangle.
III. The length of each of the three altitudes. Solving for product of quadratic - Answer: c/a
, Solving for sum of quadratic - Answer: -b/a
Vertex Point (keyword maximum/minimum of quadratic) - Answer: -b/2a
Quadratic Formula - Answer: x = -b ± √(b² - 4ac)/2a
No solution for linear equation - Answer: Same slope but don't intersect
How to solve for x-int in linear equation - Answer: set y to 0
infinite solutions to linear equation - Answer: lines are the same
Convex (geometry term meaning) - Answer: All interior angles are less than 180 degrees
Concave (geometry term meaning) - Answer: All interior angles are greater than 180 degrees
Density - Answer: mass/volume
Discriminant quadratic - Answer: b^2-4ac
Discriminant quadratic (2 solutions) - Answer: b^2-4ac= positive value
Discriminant quadratic (1 solution) - Answer: b^2-4ac= 0
Discriminant quadratic (no solution) - Answer: b^2-4ac= negative value
Quadratic Vertex Form - Answer: y=a(x-h)^2+k, (h,k) = center, a+/a-= parabola facing up or down
