This is the 2007 Grade 6 MTAP Regional Individual Finals with answers. Please comment if you find any error.
I. Solve each item and write the answer on the blank before the number. [ 2 points each]. Use π= 3.14
1.) A typist can type an average of 85 words in 2 minutes. At this rate, how long would it take to type a term paper of about 1232 words if a 5-minute allowance is given for change of paper? Give the answer to the nearest minute.
Answer: 34 minutes
2.) The base of isosceles triangle ABC is 3 cm less than a leg. If the perimeter is 42 cm and the altitude to the base is 12 1/5cm, what is its area?
Answer: 73.2 sq. cm.
3.) The outer dimensions of a picture frame are 36 cm by 24 cm. If the frame is uniformly 3 cm around a picture, what is the area of the picture?
Answer: 540 sq. cm.
4.) A park is 115 m long and 95 m wide. How many times must a jogger go around the park completely to make sure he has run at least 5 kilometers?
5.) A job can be done by 30 men in 35 days. After 10 days, 5 men left. How long will the remaining men finish the job?
6.) A car travels 140 km in 3.5 hours and a train travels 30 km in 50 min. Find the ratio of the speed of the car to that of the train.
7.) A hectare of riceland yields an average of 75 cavans per harvest. At that rate about how many cavans, to the nearest cavan, is the yield per harvest of a field 275 m by 250 m.
Answer: 516 cavans
8.) A piece of rope 165 m long is cut into 3 pieces in the ratio 1/2 : 1/3 : 5/(12 ). How long is the longest piece?
Answer: The givens are wrong because ½ + 1/3 + 5/12 is greater than 1.
9.) Electric posts are 50 m apart. How many posts are needed from town A to town B which are 2.6 km apart if the first post is at A and the last post is at B?
Solution: If you have 50 meters, you have 2 posts. For 100m, you have 3 posts. For 150m, you have 4 posts. So, n/50 + 1 posts. So, 2600/50 + 1 = 52 + 1 = 53 posts.
10.) A salesman has a basic salary of P4,500 and a commission of 5% on all sales above P50,000. What were his total sales in a month when he earned P13,177.50?
Solution: The salesman’s commission is 13,177.50 – 4500.00 = 8677.50.
The amount which is 8677.50 is 5% of his commission above 50,000.00
To know his actual sale, we multiply the 5% amount to 20 to make it 100%.
That is, 8677.50 x 20 = 173 550.00. This is above 50,000, so we still have to add 50 000.00.
Therefore, the total sales is 173 550.00 + 50 000.00 = 223 550.00
Answer: Php223 550.00
11.) How many cubic meters of soil will be needed to raise a circular plot of radius 7 m and height 1.2 dm?
Answer: 18.46 cu. m.
12.) What is the remainder when 330 is divided by 4?
13.) If 6401 ÷ N gives a quotient of 74 and a remainder of 37, what is N?
14.) PQ is a straight line. If ∠b = 3 ∠a – 15o, find ∠b.
Answer: 131.25 degrees
15.) A can 2 ½ dm long and 2 ½ dm wide and 4 dm high is full of oil. How many 250 ml of oil can be filled from it?
II. Solve on scratch paper. Then, write a neat and complete solution on the given space. Label all parts of the answer. [3 points each]
1.) A lounge needs 72 m of carpet, 5/4m wide to cover it. How many meters of carpet, 3/2m wide will cover the same lounge?
Answer: This problem is vague and poorly worded.
2.) A boy cycles a certain distance for 42 minutes at 10 km/hr. If he tries to cover the same distance in 35 minutes, what must be his speed?
3.) A wooden cube is of side 12 cm. Find the volume of the largest sphere that can be cut from it. [Use π= 3.14]
4.) How many degrees is the smaller angle between the hands of a clock at 1:40?
Answer: 220 degrees
5.) A class of 33 students counted off from 1 to 33. Each student who counted a multiple of 3 stood UP. Then, the students who remained seated counted off again from 1 and those who counted a multiple of 3 stood UP. The procedure was repeated. How many students remained seated after the 3rd standing UP?
III. Solve on scratch paper. Then, write a neat and complete solution on the given space. Label all parts of the answer. [5 points each]
1.) A machine can cap 1,800 bottles in one hour; another can cap 1,700 bottles an hour. There are 20,000 bottles to be capped. How long will it take the 2 machines to do the capping together?
Answer: 5 hours 42.9 min
2.) City A is 625 km from City B. Greg left City A at 6:30 A.M. at 100 km/h for City B. Fifteen minutes later, Rey left City B for City A at 80 km/h. At what time will Greg and Rey meet assuming they are using the same road?
Answer: 3 1/3 hrs or 3 hours 20 min
3.) In one year, the gross income of a company was P16,500,000, which after the payment of all working expenses including salaries, left a balance of P625,000. The next year, the gross income increased by 10% and the working expenses increased by 12%. What balance remained?
Answer: This problem was poorly worded. The working expenses from the previous year is around 96%, so you cannot increase 12%.