2014 Grade 7 Math Challenge – Elimination Round with answer key – Part I

Below are the 2014 Grade 7 Math Challenge – Elimination Round questions and answers – Part I. More reviewers can be found on the Past Tests and All Posts pages.

1.) Simplify:
\dfrac {6}{5} \times \dfrac {1}{4} + 2 \div \dfrac {5}{2}

2.) Simplify:
\dfrac{\dfrac{2}{3} - \dfrac{5}{4}}{\dfrac{1}{2} + \dfrac{4}{3}}

3.) Write in scientific notation:
\dfrac {7}{12500000}

4.) Simplify:
2 - \left( 1 + \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} \right)

5.) Julie’s average for the first four tests is 88.5 If she wants an average of at least 90 in the five tests, what score must she get in her last test?



6.) Alma walks 4.5 kilometers in one hour. What is her speed in meters per minute?

7.) The grade 6 pupils of a school are divided equally into Team A and Team B. The ratio of the number of boys to the number of girls in Team A is 2 : 1 and in Team B it is 4 : 11. What is the ratio of the number of boys to the number of girls in grade 6?

8.) A dress is marked with a 12% discount. If the dress is marked at Php 1188, how much was it before the discount was applied.

9.) Simplify:
\left ( 2 - \dfrac{3}{2}\right)^2 -\left ( 2 + \dfrac{3}{2}\right)^2

10.) What is the product of three consecutive odd integers if the middle integer is n?

11.) What number is exactly midway between \dfrac{3}{2} and -9?

12.) The price of a pencil is p pesos and a notebook costs Php 12 more than a pencil. How much do 3 pencils and 2 notebooks cost?

13.) Compute:
\left( 1 - \dfrac{2}{3} \right)\left( 1 + \dfrac{2}{3} \right)\left( 1 + \dfrac{4}{9} \right)

14.) Subtract 2a - 4b + 9c from the sum 3a + 5b - 3c and a - b + 7c

15.) If x is twice as far from 5 as it is from -7, what are the possible values of x?

16.) What must be added to the product of 3x + 1 and $latex2x – 5 $ to obtain 4x^2 - 5x - 6 ?

17.) Let A be the set of all positive even integers less than 10, B the set of all prime numbers less than 10, and C the set of all one-digit numbers which are NOT multiples of 3. Find C - (A \cup B).

18.) In a triangle, the second angle is twice the first angle and the third angle is 12 degrees less than 5 times the first angle. What is the measure of the largest angle?

19.) The universal set U be the set of positive integers less than 20, A the set of odd integers, B the set of perfect squares and C the set of multiples of 3. Determine C - (A \cap B)

20.) In a class of 35 students, 10 speak Ilocano, 18 speak Bicolano, 16 speak Cebuano, 5 speak both Bicolano and Ilocano, 2 speak both Ilocano and Cebuano, 9 speak both Bicolano and Cebuano, and 2 speak all three languages. How many students do not speak any of the three languages?

21.) Simplify: 2(5)^2 - 6(-2)^3 + (3 - 7)^3.

22.) How many different lengths of diagonals does a regular decagon have?

23.) Give the solution set for 3[7 – 2(7x – 4)] = -42x + 45.

24.) Paul is 20 years older than Jason. In 12 years, Paul will be twice as old as Jason will be then. How old is Paul now?

25.) Karen jogs every morning while Roy cycles on the same route. If Roy’s speed is three times that of Karen and Roy starts 2 hours after Karen, how long does Roy cycle before he overtakes Karen?

Answer key:

1.) \dfrac{11}{10}
2.) -\dfrac{7}{22}
3.) 5.6 \times 10^{-7}
4.) \dfrac{1}{16}
5.) at least 96
6.) 75 m/min
7.) 7 : 8
8.) Php 1, 350
9.) -12
10.) n^3 - 4n
11.) -\dfrac{15}{4}
12.) 5p + 24
13.) \dfrac{65}{81}
14.) 2a + 8b - 5c
15.) -3 or -19
16.) -2x^2 + 8x - 1
17.) (1)
18.) 108^\circ
19.) (9)
20.) 5
21.) 34
22.) 4
23.) set of real numbers \mathbb{R}
24.) 28
25.) 1 hour

View Part II here: 2014 Grade 7 Math Challenge – Elimination Round with answer key – Part II

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