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 . Find *r* + *s* + *rs*.

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

4.) Simplify:

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

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 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 Find

13.) If find *P*(*x*).

14.) Find the remainder when is divided by *x* + 2.

15.) What is the coefficient of *x* in the quotient when is divided by *x* – 3.

16.) Find the constant *k* if *x*– 2 is a factor of

17.) Find the largest root *x* of

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 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

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.)

9.) 3

10.)

11.)

12.) 34

13.)

14.) 6

15.) -5

16.) 7

17.)

18.) 60

19.)

20.) 24

21.) (14, 5)

22.)

23.) (-4, 7)

24.)

25.) (0, 8)

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