2016 Grade 10 Math Challenge Elimination Level Questions with Answers – Part 1

This is the 2016 Grade 10 Math Challenge Elimination Level Questions with Answers – 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.

1.) Find the value of \sqrt{x + \sqrt{14 - x}} when x = -2.

2.) Find the area of the triangle formed by the coordinate axes and the line 3x + 2y = 6.

3.) A sequence is defined by a_n = 3(a_{n-1} + 2) for n\geq 2, where a_1 = 1. What is a_4?

4.) Christa leaves Town A. After traveling 12 km, she reaches Town B at 2:00 P.M. Then she drove at a constant speed and passes Town C, 40 km from Town B, at 2:50 P.M. Find the function d(t) that models the distance (in km) she has traveled from Town A t minutes after 2:00 P.M.

5.) What is the largest negative integer that satisfies the inequality |3x + 2| > 4?

6.) A person has two parents, four grandparents, eight grand-parents, and so on. How many ancestors does a person have 10 generations back?

7.) In \triangle ABC, \angle B is twice \angle A, and \angle C is three times as large as \angle B. Find \angle C.

8.) If -3 \leq x \leq 0, find the minimum value of f(x) = x^2 + 4x.

9.) The 9th and the 11th term of an arithmetic sequence are 28 and 45, respectively. What is the 12th term?

10.) Perform the indicated operation, and simplify: \dfrac{2}{x} + \dfrac{3}{x - 1} - \dfrac{4}{x^2 - x}.

11.) Find the range of the function f(x) = |2x + 1|.

12.) Find the value of [x - (x - x^{-1})^{-1}]^{-1}.

13.) Find the equation (in the form ax + by = c) of the line through the point (5, 2) that is parallel to the line 4x + 6y + 5 = 0

14.) In \triangle ABC, \angle B = 90^\circ, \angle ABC = 28^\circ, and D is the midpoint of AC. What is \angle BDC?

15.) Find all solutions of the system:
2x + y = 1
3x + 4y = 14

16.) If f(2x - 1) = x, what is f(2)?

17.) What is the quotient when 3x^5 + 5x^4 - 4x^3 + 7x + 3 is divided by x + 2?

18.) A man is walking away from a lamppost with a light source 6 meters above the ground. The man is 2 meters tall. How long is his shadow when he is 110 meters from the lamppost?

19.) Find the length of the shorter segment made on side of AB of \triangle ABC by the bisector of \angle C, if AB = 20, AC = 12, and BC = 18 cm.

20.) How many different three-digit numbers less than 300 can be formed with the digits 1,2,3 and 5 if repetition of digits is not allowed?

21.) Factor completely the expression x^3 - 7x + 6.

22.) An integer between 1 and 10000 inclusive is selected at random. What is the probability

23.) If a chord 24 cm long is 5 cm from the center of a circle, how long is a chord 10 cm from the center?

24.) Pipes are being stored in a pile with 25 pipes in the rest layer, 24 in the second, and so on. If there are 12 layers, how many pipes does the pile contain?

25.) Find the solution set of the inequality x^2 < 5x - 6.

Answer key:

1.) \sqrt{2}
2.) 3 units²
3.) 105
4.) d(t) = \dfrac{14}{25}t + 12
5.) -3
6.) 2046
7.) 120°
8.) -2
9.) \dfrac{107}{2}
10.) \dfrac{5x - 6}{x^2 - x}
11.) [0, \infty]
12.) \dfrac{3}{4}
13.) 2x + 3y = 16
14.) 124^\circ
15.) x = -2, y = 5
16.) \dfrac{3}{2}
17.) 3x^4 - x^3 - 2x^2 + 4x - 1
18.) 55 m
19.) 8 cm
20.) 12
21.) (x - 1)(x - 2)(x + 3)
22.) \dfrac{49}{5000}
23.) 2 \sqrt{69} cm
24.) 234
25.) 2 < x < 3

View Part 2 here: 2016 Grade 10 Math Challenge Elimination Level Questions with Answers – Part 2

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