2018 Grade 10 Math Challenge Questions 1-25

This is the 2018 MTAP Grade 10 Math Challenge questions 1 to 25. Questions  26 to 50 (including the pdf of Questions 1-50) can be found here. Solutions and answers will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Questions

1.) The average of a number and \sqrt{7} + \sqrt{5} is \sqrt{7} - \sqrt{5}. Find the number.

2.) Find n if27.63% of 349 is $latex  2.763%4 of n.

3.) Simplify:

\dfrac{101!}{99!}.

4.) If 3^n = 90, find the integer closest to n.

5.) Find the largest positive integer n such that  (n - 18)^{4036} \leq 99^{2018}.

6.) How many integers between 60 and 600(inclusive) are divisible by 2 or by 3? 

7.) How many positive factors does the product of 3 different prime numbers have?

8.) A triangle has area 30 sq cm, and two sides are 5 cm and 12 cm long. How long is the third side?

9.) If 𝐴 = {all prime numbers between 1 and 100}, 𝐵 = {2,4,6,…,98,100}, and 𝐶 = {3,6,9, … , 96, 99}, how many elements does (𝐴 ∪ 𝐵) ∩ 𝐶 have?

10.) Find the perimeter of a regular hexagon inscribed inside a circle whose area is 49 \pi sq cm.

11.) Sets A and B are subsets of a set having 20 elements. If set A has 134 elements, at least how many elements should set B have to guarantee that A and B are not disjoint?

12.) If the 2nd and 5th terms of an arithmetic sequence are -2 and 7, respectively, Find the 101st term.

13) Find the sum of the first 71 terms of the arithmetic sequence above.

14.) Find k such that k - 2, 2k + 2, and 10k + 2 are consecutive terms of a geometric sequence.

15.) Three numbers form an arithmetic sequence with common difference 15. If the first is doubled, the second is unchanged, and the third is increased by 21, a geometric sequence will be formed. Find the first number of the geometric sequence.

16.) The sum of an infinite geometric series have sum 14. If their squares have sum \frac{196}{3} , find the sum of their cubes.

17.) A sequence a_n has first two terms a_1 = 3 and a_2 = 2. For every 𝑛 ≥ 3,  a_n is the sum of all the preceding terms of the sequence. Find a_{12}

18.) Let r and s be the roots of x^2 - 9x + 7. Find $latex (r+1)(s + 1)

19.) If P(x + 2) = 3x^2 + 5x + 4, find P(x).

20.) Find the remainder whenP(x) = 27x^3 + 81x^2 + 5x + 20 is divided by x + 3.

21.) Find the constant term of the quotient when p(x) = 6x^4 - 8x^3 + x^2 + 9x + 7 is divided by x + \frac{2}{3}.

22.) Find the constant k if x + 3 is a factor of f(x) = 2x^4 - 8x^3 + (k^2 + 1)x^2 + kx + 15.

23.) Find the largest real root x of 2x^3 - 5x^2 - 2x + 2 = 0.

24.0 If  p(x) is a 3rd degree polynomial,  p(\frac{5}{3}) =  p(4) = p(-5) = 0, and p(0) = -200, find p(2).

25.) The midpoint o f P(1,2) and A is Q; the midpoint of P and C is S; the midpoint of Q and S is R(5, 1.5). Find the coordinates of B, the midpoint of A and C.

3 responses to “2018 Grade 10 Math Challenge Questions 1-25

  1. DO YOU HAVE AN ANSWER KEY FOR THIS? Thank you. 🙂

  2. Do you have an answer key for this? Thanks

  3. Precious Angel Oares

    key to correction pleaseeee

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