2017 Grade 9 Math Challenge – Division Finals Team Orals with answer key

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 [? ?????? ????]
1.) What value of ? will make x^2 - 14x + c a perfect square trinomial?

2.) Solve for ? in the quadratic equation x^2 + x - 6 = 0

3.) What is the sum of the roots of 2x^2 + 6x + 1 = 0?

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

5.) Simplify the expression \sqrt {49x^7}

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 (2? + 2)° and (2? – 2)°. Find x.

8.) If x^{0.123} = 4 , what is 1 more than x^{0.246} ?

9.) If ?: ? = 2: 1 and ?: ? = 2: 1, find the ratio ?: ?

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 y = x^2 - 4x + 5

30 – Second Questions [? ?????? ????]

1.) Simplify: 4 \sqrt{20} - 2 \sqrt{45}

2.) If 9x + 19 = (x + 3)^2

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 x^2 + kx + 9k = 0 has no real roots.

5.) Isosceles trapezoid ???? has parallel bases ?? and ??, and the diagonals intersect at ?. If ?? = 8, ?? = 3? – 1, ?? = 5? – 2, how long (in units) is ???

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

1 – Minute Questions [? ?????? ????]

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

2.) Solve for ? in the equation \sqrt {x} + 2 = \sqrt{2x - 1}

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

4.) Fencing material that is 400 ? 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 ? which satisfies (2x + 1)^2 + 3x \geq 2(x + 1)^2 + 1

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

Tiebreaker

1.) Find the smallest positive integer solution of ?2 – 3? – 10 ≥ 0

2.) Rationalize the denominator of \dfrac {1 + \sqrt{5}}{3- \sqrt{5}}

3.) If ? and ? are the roots of 2x^2 - 7x + 4 = 0 , find the value of r^2 + s^2

Do-or-Die

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

Answer Key

15 – Second Questions [? ?????? ????]
1.) 49
2.) x = -3, 2
3.) -3
4.) y = 4
5.) 7x^3\sqrt{x}
6.) 16 m^2
7.) 45
8.) 17
9.) 4 : 1
10.) \sqrt{5} cm
11.) (2, 1)

30 – Second Questions [? ?????? ????]
1.) 2 \sqrt{2}
2.) x = -2, 5
3.) 6, 21
4.) 0, 36
5.) 13 units
6.) 15 cm

1 – Minute Questions [? ?????? ????]
1.) \dfrac {32}{3}
2.) x = 25
3.)
4.) 100m, 200m
5.) \dfrac {1}{2}
6.) 20 cm

Tiebreaker
1.) 5
2.) 2 + \sqrt{5}
3.) \dfrac {33}{4}

Do-or-Die
1.) 5

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