# 2018 Grade 10 Math Challenge Elimination Level Questions – Part 1

This is the 2018 Grade 10 Math Challenge Elimination Level Questions – Part 1 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

Give all fractions and ratios in lowest terms and all expressions in expanded form.

1.) Ten percent of 450 is 20% of what number?

2.) Let r and s be the roots of $x^2 - 9x + 7 = 0$. Find r + s + rs.

3.) How many integers between 60 and 600 are divisible by 7?

4.) Simplify: $\dfrac{8!}{6!}$

5.) If A = {2, 3, 5, 7}, B = {2, 4, 6, 8, 10}, and C = {3, 6, 9}, find $(A \bigcup B) \bigcap C.$

6.) If the first two terms of an arithmetic sequence are 3 and 7, find the 10th term.

7.) If the 1st and 5th terms of an arithmetic sequence are -5 and 7 respectively, find the sum of the first 21 terms.

8.) The 1st and 6th terms of a geometric sequence are 4 and $-\dfrac{1}{8}$ respectively. Find the 4th term.

9.) Three numbers form an arithmetic sequence with common difference 15. If the first is increased by 3, and the third by 21, a geometric sequence will be formed. Find the first number of the arithmetic sequence.

10.) Find the sum of the infinite geometric series 9 – 6 + 4 – 8/3 + … .

11.) An infinite geometric series with sum 12 has first term 8. Find the first term of this series that is less than 1.

12.) In a sequence $\{a_n\}, a_n = 2n + 2^n.$ Find $a_5 - a_2.$

13.) If $P(x^3) = 4x^9 - 7x^6 + 2x^3 + 27,$ find P(x).

14.) Find the remainder when $P(x) = 2x^3 + 5x^2 - 3x + 4$ is divided by x + 2.

15.) What is the coefficient of x in the quotient when $p(x) = 4x^3 - 17x^2 + 8x + 11$ is divided by x – 3.

16.) Find the constant k if x– 2 is a factor of $f(x) = 3x^4 - kx^3 + kx^2 - 13x + 6.$

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

18.) If p(x) is a 3rd degree polynomial and p(-2) = p(2) = p(1) = 0, and p(1) = – 18, find p(3).

19.) Find the polynomial smallest possible degree and all of whose coefficients are integers, with the leading coefficient positive and as small as possible, if it has $\sqrt{2}$ and 2 as zeros.

20.) Two lines, with slopes 3 and -4, intersect at a point P on the y-axis. If their x-intercepts are 14 units apart, find the distance of P from the origin.

21.) The midpoint of P(7, -1) and R is Q(10.5, 2). Find the coordinate of R.

22.) Find the radius of the circle with center (-3, 5) and which passes through the origin.

23.) Find the center of the circle with equation $x^2 + y^2 + 8x - 14y + 60 = 0.$

24.) Give the equation (in center-radius form) of the circle having as a diameter the segment with endpoints (-2, 10) and (4, 2).

25.) Find the coordinates of the point of the y-axis having the same distance from (-8, 7) as from (-4, 1).

Answer key:

1.) 225
2.) 16
3.) 17
4.) 56
5.) {3, 6}
6.) 39
7.) 525
8.) $-\dfrac{1}{2}$
9.) 3
10.) $\dfrac{27}{5}$
11.) $\dfrac{8}{9}$
12.) 34
13.) $4x^3 - 7x^2 + 2x + 27$
14.) 6
15.) -5
16.) 7
17.) $\dfrac{1}{2}$
18.) 60
19.) $x^3 - 2x^2 - 2x + 4$
20.) 24
21.) (14, 5)
22.) $\sqrt{34}$
23.) (-4, 7)
24.) $(x - 1)^2 + (y - 6)^2 = 25$
25.) (0, 8)

View Part 2 here:2018 Grade 10 Math Challenge Elimination Level Questions – Part 2

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