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?
Answer: 5/3

2.) How many degrees is 1 \frac{1}{5} of a revolution?
Answer: 432°

3.) What is the vertex of the parabola with equation y = x^2 + 2x + 3?
Answer: (-1, 2)

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

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.
Answer: -1/2 

7.) What is the domain of \ln(x - x^2)?
Answer: (0, 1)

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

9.) What is the x-intercept of f(x) = log(x-1)
Answer: 2

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

11.) What is the range of y = 2x - 7x^2?
Answer: (-∞, 1/7)

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.
Answer: 6

2.) Find the value of a if the line ax + 2y = 1 is perpendicular to 3x – 6y = 7.
Answer: 4

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

4.) If sec θ = -13/5 and sin θ < 0, find the value of tan θ.
Answer: 12/5

5.) Assuming that p and q are the roots of 3x^2 - 2x + 4 = 0, what is p^2 + q^2?
Answer: -20/9

6.) Find the solutions of (\log_2 x)^2 - \log_2 x^3 = 4.
Answer: 16, 1/2

1-minute question (5 points each)

1.) How many multiples of 3 are there between 5 and 200?
Answer: 65

2.) Given that tan θ = -2, find the value of sin 2θ.
Answer: -4/5

3.) Solve: 4^{x - x^2} = \sqrt{2}
Answer: 1/2

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.
Answer: √2+ π/2

5.) Find the remainder when y = 1 + 3x^2 + 5x^5 + \cdots + 11x^{11} + 13x^{13} is divided by x-1?
Answer: 49

6.) Find the real roots of x^4 - 2x^3 + x^2 - 8x - 12 = 0 given that 2i is one root.
Answer: -1, 3

Clincher Question

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

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?

Answer: 13

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

  1. PLEASE SHARE ME THE 2015 MMC GRADE 10 ELIMNATION QUSTIONS WITH ANSWERS

  2. Tyeng says:

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

  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

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