# 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 $n$ if $27.63%$ 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 when $P(x) = 27x^3 + 81x^2 + 5x + 20$ 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 $C$.

### 8 responses to “2018 Grade 10 Math Challenge Questions 1-25”

1. Elena Banares

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

2. Nelia

Do you have an answer key for this? Thanks

3. Precious Angel Oares

key to correction pleaseeee

4. Lincoln Line

Do you have an answer key for this? At least answer key?

5. bobowaya

Answers?

6. ella C. armayan

Do you have an answer key for this please.Thank you

7. Belle

Can we ask for an answers key po please

8. johnN_69

bonak solution please?