Answers

1. In the standard (x,y) coordinate plane, the graph
     (x-5)² + (y -6)² = 9 is a circle. What is the area
     enclosed by this circle?

A = ¶r²
radius is 3 then area is  ¶(3)²= 9¶

2. If one leg of a right triangle is 7 inches long, and
     the other leg is 24 inches long, how many inches
     long is the triangle's hypotenuse?

7² + 24² = c²
49 + 576 =  c²
625 =  c²
25 = c
 

3. In ΔABC, if angle A and angle B are acute
     angles, and sin A = 5/13, what is the value of
    cos A?

sinA is opp/hyp and cos is adj/hyp

4. Which of the following is divisible by 3 (with no
     remainder)?

    a. 2,725    b. 4,210    c. 4,482    d. 6,203

c. 4,482
because if the sum of the digits are divisible by 3 then the number is divisible by 3: 4+4+8+2 = 18

5. The triangle below is isosceles and is drawn to
     scale. Angles L and N are congruent. What is the
     measure of angle M?

180 - (22+22) = 136

6. When graphed in the (x,y) coordinate plane, at
     what point do the lines x + y = 5 and y = 7
     intersect?

x + 7 = 5
x = -2
intersects at (-2,7)

7. What is the slope of the line 4y = -3x + 16?

y = -¾ + 4
slope is -¾

8. What is the largest possible product for 2 even
     integers whose sum is 34?

x + x = 34
2x = 34
x = 17 then the two even numbers would
be 16 and 18.
16 x 18 = 288

9. John tried to compute the average of his 7 test
     scores. He mistakenly divided the correct sum of
     all his test scores by 6, which yields 84. What is
     John's correct average test score?

84 x 6 = 504
504 ÷ 7 = 72

10. In the figure, lines m and n are parallel with t as
     the transversal. What is the sum of the angles x and
     y?

180-45 = 135 = y
x =45 because corresponding angles are congruent.
therefore x + y = 180.

11. What is the value of 2x² - 3x - 4 when x = -2?

2(-2)² - 3(-2) - 4 = 10

12. In the following equation, what is the solution for
     x in terms of a?
                            2x + 3 = 2a + 4

2x = 2a + 4 - 3
2x = 2a + 1

13. Which of the following is equivalent to:
        4(3x - 1) < 7x + 2(x + 4)

12x - 4 < 7x + 2x + 8
12x - 4 < 9x + 8
3x < 12
x < 4

14. In the figure below, what is the value of sin a.

15. If the length of AC is 8 units, the length of BD is
     7 units, and the length of AD is 12 units, what is
     the length of AB?