# 2015 Grade 10 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 10 MTAP Math Challenge Division Oral Competition questions with answers.

Note: I will fix the latex equations later.

15-second question (2 points each)

1.) What is the y-intercept of 2x + 3y = 5?

2.) How many degrees is $1 \frac{1}{5}$ of a revolution?

3.) What is the vertex of the parabola with equation $y = x^2 + 2x + 3$?

4.) Find the value of $\log_{\sqrt{2}} \sqrt[3]{2}$

5.) What’s the exact value of sin (29π/4)?
Answer: $\frac{-\sqrt{2}}{2}$

6.) Find the value of $a$ so that $8^3 + 1$ is divisible by $x - a$.

7.) What is the domain of $\ln(x - x^2)$?

8.) If the sequence 1, 2/3, x is harmonic, find the value of x.

9.) What is the x-intercept of f(x) = log(x-1)

10.) The system 2x + 2y = 1 and 3x + 3y = a has infinitely many solutions for which value of a?

11.) What is the range of $y = 2x - 7x^2$?

30-second question (3 points each)

1.) Find the area of the triangle in the first quadrant bounded by the line x/3 + y/4 = 1.

2.) Find the value of a if the line ax + 2y = 1 is perpendicular to 3x – 6y = 7.

3.) Find the value of $a$ so that the domain and range of $f(x) = \frac{ax + 1}{2x - 3}$ are identical sets.

4.) If sec θ = -13/5 and sin θ < 0, find the value of tan θ.

5.) Assuming that $p$ and $q$ are the roots of $3x^2 - 2x + 4 = 0$, what is $p^2 + q^2$?

6.) Find the solutions of $(\log_2 x)^2 - \log_2 x^3 = 4$.

1-minute question (5 points each)

1.) How many multiples of 3 are there between 5 and 200?

2.) Given that tan θ = -2, find the value of sin 2θ.

3.) Solve: $4^{x - x^2} = \sqrt{2}$

4.) Find the perimeter of the region in Quadrant I that is bounded by the circle $x^2 + y^2 = 1$ and the line $x + y = 1$.

5.) Find the remainder when $y = 1 + 3x^2 + 5x^5 + \cdots + 11x^{11} + 13x^{13}$ is divided by $x-1$?

6.) Find the real roots of $x^4 - 2x^3 + x^2 - 8x - 12 = 0$ given that $2i$ is one root.

Clincher Question

1.) If secθ = 5, find the value of cos(π – θ).

2.) What is the inverse of f(x) = (2x + 3)/(5x-1)?
Answer: y = (x + 3)/(5x – 2)

3.) x is directly proportional to y and inversely proportional to the square of z. What happens to x if y and z are both doubled?
Answer: halved or divided by 2

Do or Die Question

What is the next term in the arithmetic sequence x + 1, 2x – 3, x + 5?

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### 10 Responses to 2015 Grade 10 MTAP Math Challenge – Division Orals

• wow, so demanding

• i dont have a copy of the 2014 orals, but i do have a copy of an oral if you know what i mean 😉

2. Tyeng says:

hi…do you have a copy of the 2014 orals? tnx ahead…

• i dont have a copy of the 2014 orals, but i do have a copy of an oral if you know what i mean 😉

3. gomezjoemar says:

why is it there there is not grade 7 for oral 2015 please who can help us thank you very much for your generosity!

4. Lambda Jose says:

Can I get a copy of the solutions? Thanks, in advance

5. John Romar says:

Do you have the 2016 mtap grade 10 orals