2013 Grade 7 Math Challenge – Elimination Round with answer key – Part I

Below are the 2013 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: $\left (2 - \dfrac {1}{2} \right) + \left (3 - \dfrac {1}{3} \right) + \left (4 - \dfrac {1}{4} \right)$

2.) Let $A = (a, b, c, d, e), B = (a, e, i, o ,u), C = (e, f, g, h, i).$ Find $(A \cap B ) \cup (B \cap C)$.

3.) Write $\dfrac {1}{50000000}$ in scientific notation.

4.) Nonoy left Butuan City to drive to Cagayan de Oro City at 6:15 PM and arrive 9:15 PM. If he averaged 80 kph and stopped 30 minutes for dinner, approximately how far is Cagayan de Oro from Butuan?

5.) Simplify: $\left (1 - \dfrac {1}{2} \right)^2 - \left (1 + \dfrac {1}{2} \right)^2$

6.) Let the universal set U be (1, 2, 3, … 20). If S = (2, 4, 6, 8, 10, 12), E = (3, 6, 9, 12, 15, 18), and T = (15, 16, 17, 18, 20) , find $(S \cup E \cup T)$

7.) What is the product of two consecutive odd integers if the larger number is 3a – 4?

8.) Two angles are supplementary. One angle is $24^\circ$ less than thrice the other. What is the complement of the smaller angle?

9.) Simplify: $\dfrac { \dfrac {2}{3} + \dfrac {5}{6} } { \dfrac {4}{5} - \dfrac {1}{3} }$

10.) Let the universal set U be the set of all prime numbers less than 20, A = (x | x is a prime factor of 210), B = (x | x is a prime number greater than 10), and C = (3, 19). Find $A' \cap (B \cap C)'$.

11.) Kristine receives a basic monthly salary of Php 18, 000 plus a commission of 12% on her total sales. In her recent monthly payday, she received Php 21, 000. How much was her total sales last month?

12.) Simplify: $(x + 1)(x - 2) - (x + 2)(x - 3) + (x + 3)(x - 4) - (x + 4)(x - 5)$.

13.) How many two-digit prime numbers are there whose units digit is greater than its tens digit?

14.) Nila is now x years old. Three years ago, her brother Ricky was twice as old as she. Write Ricky’s age 10 years from now in terms of x.

15.) In the Math Department of a school, 10 teachers have Yahoo! accounts, 13 have Gmail accounts, and 6 have both accounts. How many teachers in the department have accounts, and 6 have both accounts. How many teachers in the epartment have Yahoo! or Gmail accounts?

16.) Together, Pearl and Harvey are going to visit their their aunt on Sunday. If Pearl visit their aunt every 6 days, while Harvey every 8 days, on what day will they visit their aunt together again?

17.) What should be added to $(x - 3)(x + 2)$ to get $(x - 4)^2$?

18.) Simplify. $\sqrt {|1.8 \times 10^4 - 2.55 \times 10^4| + 6.9 \times 10^3}$.

19.) In a triangle, one angle is twice the second, and the third angle is $20^\circ$ less than the second. What is the measure of largest angle?

20.) It costs (x + 3) pesos per square foot to paint a wall. If the wall stands (4x + 3) ft high and (7x – 2)ft long, how much does it cost to paint the wall?

21.) In a class of 40 students, 27 like Math and 25 like Filipino. At most how many students do not like at least one of these subjects?

22.) How many four-digit numbers are multiples of 9?

23.) Manuel can walk from his house to his school at a rate of 5.4 kph, and back at the rate of 3.6 kph. What is his average speed for the entire walk in meters per second?

24.) A polynomial has quotient $(x^2 - 3x)$ and remainder $(x^2 - 1)$ when divided by $(x^2 - 1)$. What is the polynomial?

25.) Aldo cut a long piece of bamboo into four pieces. The second piece was one-third of the first piece, the third piece was one-third of the second, and finally the fourth piece was one-third of the third. If the smallest piece was 2 dm, how long was the bamboo before before it was cut?

1.) $\dfrac {95}{12}$
2.) (a, e, i)
3.) $2 \times 10^-8$
4.) 200 km
5.) -2
6.) (1, 5, 7, 11, 13, 14, 19)
7.) $9a^2 - 30a + 24$
8.) $39^\circ$
9.) $\dfrac {45}{14}$
10.) (11, 13, 17)
11.) Php 25 000
12.) 12
13.) 11
14.) 2x + 7
15.) 17
16.) Wednesday
17.) -7x + 22
18.) 120
19.) $100^\circ$
20.) $28x^3 + 97x^2 + 33x - 18$
21.) 28
22.) 1000
23.) 1.25
24.) $x^5 - 3x^4 + 3x - 1$
25.) 80 dm

View Part II here: 2013 Grade 7 Math Challenge – Elimination Round with answer key – Part II

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