key to correction g7

MATH QUIZ (Individual-Written) Contestant’s Code Number: KEY TO CORRECTION

GRADE 7

SCORE

Category B:

2016 DIVISION FESTIVAL OF TALENTS

General Instruction: Write your final answer on the space provided before each item. Part I. No solution is required for this part of the quiz. Two points will be given for every correct answer. 8 16 0 (zero)

1. Let 𝐴 = {1, 5, 6}. How many subsets does set A have? 2. 𝐶 is the set of all prime numbers less than 50. What is the cardinality of set 𝐶? 3. Let 𝑈 be the set of integers. If 𝐴 = {𝑥 |𝑥 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟}, and 𝐵 = {𝑥 |𝑥 𝑖𝑠 𝑎 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟}, what is(are) the element(s) of (𝐴 ∪ 𝐵)′? U

For items 4 to 5 refer to the Venn diagram at the right showing the number of elements in each set. 20

24 40 222 -6 𝒙𝟐 + 𝟖 = (𝒙 − 𝟓)𝟐 or 𝟐 𝟏 𝟐 𝒙 + 𝟖 = (𝒙 − 𝟓)𝟐 𝟐

C 4 3 1

D 5

4. What is the cardinality of the set, (𝐵 ∪ 𝐷 )′? 5. How many elements does (𝐵′ ∩ 𝐶)′ have? 6. What number should be added to the product of 8 and -16 to get a sum of 94? 7. When a number is multiplied by -2, the product is the same as (−6) + 18. What is the number? 8. Write as a mathematical sentence: Eight more than half the square of a number is the square of the quantity of five less than the number. 9. What property of equality is applied in the equation below?

△ (⋄ + ⋆ −⨀) =△⋄ + △⋆ − △ ⨀

Distributive Property 18 and 19

B 13 A 1

10. Between which two integers can you find 2√85?

Part II. Each question is worth a maximum of three points. Solutions are needed to earn partial scores. Write your solutions on the spaces provided after each item. 1. Of the 49 students of Grade 7 – Matinambuligon, 18 like Science, 8 like 19 English, and 21 like Math. If half of those who like Science also like Math and all who like English also like Math but dislike Science, how many of the students do not like any of the three subjects? 1 point 2 points

10 years

2. Carol is five times as old as her brother. She will be three times as old as her brother in two years. How old is Carol now? 1 point

𝒂 𝒄

The solution shows that there are 9 students who like both Science and Math. Contestant determined that 30 students like at least one subject mentioned.

The correct equation, 5𝑥 + 2 = 3(𝑥 + 2) or a variation of this is determined.

𝑎𝑏 2𝑐 3 3. Simplify (√ 3 2 ) 𝑎 𝑏 𝑐

−1

.

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (INDIVIDUAL-WRITTEN) GRADE

7

1 point

𝟓𝒙𝟒 − 𝟗𝒙𝟑 + 𝟏𝟑𝒙𝟐 −𝟗𝒙 + 𝟏𝟗

4. Give the sum of the expressions 𝑥 4 − 3𝑥 3 + 5𝑥 2 − 7𝑥 + 9 and 8𝑥 2 − 6𝑥 3 + 4𝑥 4 − 2𝑥 + 10. 2 points

𝒓 ≤ −𝟐𝟐

𝑐2

Radicand is simplified to 𝑎2

Just one of the terms is incorrect.

5. Solve the inequality: 2𝑟 − 32 ≥ 4𝑟 + 12 1 point

The answer provided is 𝑟 ≥ −22

Part III. Each question is worth a maximum of five points. Solutions are needed to earn partial scores. Write your solutions on the spaces provided after each item. 1. What should be multiplied to 𝑥 2 + 8𝑥 − 1 to get a polynomial equal 𝟐𝒙 + 𝟏 to the sum of 𝑥 3 + 10𝑥 2 + 6𝑥 and 𝑥 3 + 7𝑥 2 − 1 2 points 3 points

0.162 (liters)

2. Dexter is creating a new secret formula. An 82 centiliter-solution of this new formula contains 78 000 microliters of chemical X, 532 milliliters of chemical Y, 0.48 deciliters of chemical Z. The rest of the solution is water. How many liters of water is in the solution? 2 points 3 points

42

The sum of the last two polynomials is determined and correct, 2𝑥 3 + 17𝑥 2 + 6𝑥 − 1 The sum is divided by the other polynomial. This is evident in the solution.

All of the given measures have been converted correctly into liters: 0.82 liters, 0.078 liters, 0.532 liters, 0.048 liters. The sum of the other components of the formula is correct: 0.658

3. Jay and Kaye have marbles. If Jay gives Kaye three of his marbles, they will have the same number of marbles but if Kaye gives four of her marbles to Jay, she will then be left with half as many as Jay’s marbles. How many marbles do they have in total? 2 points 3 points 4 points

Student determined the correct set of equations. This can be any of the following, or a variation, 𝑦−3 =𝑥+3 𝑦=𝑥+6 { { 𝑜𝑟 𝑦 = 2𝑥 − 12 𝑦 + 4 = 2(𝑥 − 4) Either Jay’s marbles, 24 or Kaye’s marbles, 18 is correct. Both Jay’s and Kaye’s number of marbles are correct but their sum is not given or is incorrect.

2016 DIVISION FESTIVAL OF TALENTS - MATH QUIZ (INDIVIDUAL-WRITTEN) GRADE

7