Below are the 2017 MTAP Grade 9 Math Challenge Division Finals Team Orals questions and answers. Solutions will be posted later. More reviewers can be found on the **Past Tests** and **All Posts** pages.

**15 – Second Questions [𝟐 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉]**

1.) What value of 𝑐 will make a perfect square trinomial?

2.) Solve for 𝑥 in the quadratic equation

3.) What is the sum of the roots of ?

4.) Suppose 𝑦 varies directly as 𝑥. If 𝑥 = 6, then 𝑦 = 12. If 𝑥 = 2, find 𝑦.

5.) Simplify the expression

6.) The diagonals of a rhombus are 4 cm and 8 cm. Find the area of the rhombus.

7.) In a parallelogram, two adjacent angles have measures (2𝑥 + 2)° and (2𝑥 – 2)°. Find *x*.

8.) If , what is 1 more than ?

9.) If 𝑎: 𝑏 = 2: 1 and 𝑏: 𝑐 = 2: 1, find the ratio 𝑎: 𝑐

10.) How long is the hypotenuse of a right triangle if its two legs are 1 cm and 2 cm?

11.) Find the vertex of the graph of

**30 – Second Questions [𝟑 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉]**

1.) Simplify:

2.) If

3.) In a triangle, a line parallel to the base divides one side into segments 4 and 14 units long. If the other side has length 27, how long (in units) is each segment formed when the line divides this side?

4.) Find the range of values of has no real roots.

5.) Isosceles trapezoid 𝐴𝐵𝐶𝐷 has parallel bases 𝐴𝐵 and 𝐶𝐷, and the diagonals intersect at 𝐸. If 𝐴𝐸 = 8, 𝐵𝐸 = 3𝑥 – 1, 𝐶𝐸 = 5𝑥 – 2, how long (in units) is 𝐷𝐸?

6.) The diagonals of a rhombus are 18 𝑐𝑚 and 24 𝑐𝑚. Find the length of each side.

**1 – Minute Questions [𝟓 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉] **

1.) Triangle 𝐴𝐵𝐶 has a right angle at 𝐵. Let 𝐷 be the foot of the altitude from 𝐵 to AC. If 𝐴𝐵 = 10 and 𝐴𝐷 = 6, find the length (in units) of 𝐶𝐷.

2.) Solve for 𝑥 in the equation

3.) Suppose 𝑧 varies directly as the cube of 𝑥 and inversely as 𝑦. If 𝑧 = 6 when 𝑥 = . Find 𝑧 when 𝑥 = 3 and 𝑦 = 6.

4.) Fencing material that is 400 𝑚 long is used to enclose 3 sides of a rectangular lot. What are the dimensions of such lot with the largest possible area?

5.) Find the smallest possible values of 𝑥 which satisfies

6.) The shortest sides of two similar triangles are 5 𝑐𝑚 and 7 𝑐𝑚. If the sum of their perimeters is 48 𝑐𝑚, find the perimeter of the smaller triangle.

Tiebreaker

1.) Find the smallest positive integer solution of 𝑥2 – 3𝑥 – 10 ≥ 0

2.) Rationalize the denominator of

3.) If 𝑟 and 𝑠 are the roots of , find the value of

Do-or-Die

1.) In a right triangle, the two legs have lengths 𝑎 and 𝑎 + 7𝑑, while the hypotenuse has length 𝑎 + 8𝑑, find the value of ?

Answer Key

**15 – Second Questions [𝟐 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉]**

1.) 49

2.) x = -3, 2

3.) -3

4.) y = 4

5.)

6.)

7.) 45

8.) 17

9.) 4 : 1

10.)

11.) (2, 1)

**30 – Second Questions [𝟑 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉]**

1.)

2.) x = -2, 5

3.) 6, 21

4.) 0, 36

5.) 13 units

6.) 15 cm

**1 – Minute Questions [𝟓 𝒑𝒐𝒊𝒏𝒕𝒔 𝒆𝒂𝒄𝒉] **

1.)

2.) x = 25

3.)

4.) 100m, 200m

5.)

6.) 20 cm

Tiebreaker

1.) 5

2.)

3.)

Do-or-Die

1.) 5