Friday, May 28, 2021

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)



While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


16. If rx - st = r, which expression represents x?

(1) (r + st) / r
(2) r / (r + st)
(3) r / (r - st)
(4) (r - st) / r

Answer: (1) (r + st) / r
Use inverse operations isolate x:

rx - st = r
rx = r + st
x = (r + st) / r





17. What is the solution of the equation (x + 2) / 2 = 4 / x?

(1) 1 and -8
(2) 2 and -4
(3) -1 and 8
(4) -2 and 4

Answer: (2) 2 and -4
Cross-multiply and solve the quadratic equation:

(x + 2) / 2 = 4 / x
x(x + 2) = (2)(4)
x2 + 2x = 8
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x + 4 = 0 OR x - 2 = 0
x = -4 or x = 2

Or you could have substituted the values in the choices into the original equation and checked which ones made a true statement.

(1 + 2) / 2 ?= 4 / 1
3/2 =/= 4 (No need to check -8)

(2 + 2) / 2 ?= 4 / 2
4/2 = 4/2 (YES!)

(-4 + 2) / 2 ?= 4 / -4
-2 / 2 ?= 4 / -4
-1 = -1 (YES!)



18.Which type of function is graphed below?


(1) linear
(2) quadratic
(3) expotential
(4) absoulte value

Answer: (3) expotential
Linear is a straight line. A quadratic function would go up toward infinity on both sides, down on both sides, but not to the left. An absolute value function is V shaped.

Exponetial functions go almost horizontal on end, and ever-upward on the other.





19. What is the slope of the line represented by the equation 4x + 3y = 12?

(1) 4/3
(2) 3/4
(3) -3/4
(4) -4/3

Answer: (4) -4/3
If you didn't know that the slope of a line in Standard Form (Ax + By = C) is -A/B, then you could have found the answer by converting the equation to slope-intercept form:

4x + 3y = 12
3y = -4x + 12
y = (-4/3)x + 12/3




20. The diagram below shows the graph of which inequality?


(1) y > x - 1
(2) y > x - 1
(3) y < x - 1
(4) y < x - 1

Answer: (4) y < x - 1
It has a solid line which is shaded below. That makes it equal and less than.



More to come. Comments and questions welcome.

More STAAR problems.

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