Provincial Finalist Exam for 6th Class Students Do not turn the page until you are instructed to do so. Answer each question in the box provided next to the question on this sheet. Only one answer should be given unless the question states otherwise. There is no need to explain your answer or show your work. You may use a separate piece of paper if you need more space to complete your rough work. You will have 40 minutes to complete 8 problems of varying difficulty. You may not leave until the exam has finished. USE BLOCK CAPITAL LETTERS Name: ____________________ Student ID: ____________________ School: ____________________ County: ____________________ THIS IS ON YOUR BADGE 1. A train left Belfast at 3:45pm. It arrived in Dublin 2 hours and 38 minutes later. What time did it arrive in Dublin? 2. What is the sum of the first ten prime numbers minus the sum of the first four square numbers? Final answer: 3. Final answer: The area of a rectangle is 112cm2. The length is 9cm longer than the breadth. Find the length of the rectangle. Final answer: √ 2 2 θ is an angle √ such√that sin θ = √ 3/3, then 8 sin θ + 7 cos θ equals . 5 b. 4 3 c. 5 3 d. 10 3/3 e. 22/3 he perimeter square is equal the circumference a fcircle C.of tWhich of 1the 4. of How many ofof area the t1hree digit nto umbers that can be mof ade rom all he digits , 3 and 5 ollowing numbers is closest area ofoC? (When they ato re the used only nce each) are prime? . 1 b. 1.1 c. 1.2 d. 1.3 e. 1.4 olve the following equation. 2 log10 (x) + log10 (x + 4) = log10 (4) + log10 (x) + log10 (x + 1). √ √ . x = 1 b. x = 2 c. x = 10 d. x = 3 + 10 e. x = 5 et L be the line that is tangent to the circle (x − 7)2 + (y − 4)2 = 25 at the point (3, 7). The ne L intersects the y-axis at the point (0, b). What is b? . −2 b. e. 9 0 c. 3 d. 5 A swimming pool has an input pump for filling the pool and an output pump for emptying the ool. The pool ainnswer: 3 hours, input pump can fill the Final and the output pump can drain the pool in hours. As you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. At midnight, you awake to find the pool half empty. Immediately, you turn on the input pump, but ou are sleepy and forget to turn oﬀ the output pump. At what time will the pool become full? . 1:30 am 5. b. We 2:45kam c. 3:30 am d.f t3:45 e. f4:30 now that each one o he dam isplayed ive cam ards (shown face up) has a number on one side and a letter on the other side. We know that each one of the displayed five cards (shown face up) has a number on one side nd a letter on the other side. S 3 H 3 8 onsider the assertion: ‘If a card has an S on one side, then it has a 3 on the other side.’ Let m Consider the athat ssertion: If a card has aover n S oin n oorder ne side, then it that has athe 3 oassertion n the other e the least number of cards you ‘need to turn to prove is side.’ Let m be t he l east n umber o f c ards t hat y ou n eed t o t urn o ver i n o rder t o p rove t hat t he assertion rue. Determine m. . 1 b. 2 c. is 3 true. d. D 4 etermine e. 5 m. Wile E. Coyote and Road Runner have a 100-mile race. Road Runner runs 10 miles per hour aster than Wile E. Coyote and finishes 1 hour ahead of Wile E. Coyote. How fast does Road (in miles per hour)? Runner √ run √ √ . 5 + 5 41 b. 37 c. 110 d. 120 e. 30 + 37 2n n or how many positive integers n is 22 < 1010 ? . 1 b. 2 c. 3 d. 4 e. An infinite number of n onsider the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. For every subset A of S, John computes the sum of ll elements in A and writes the result on the blackboard. Mary then computes the sum of all he numbers that John wrote on the board. The final result is equal to . 11385 b. 11430 c. 11475 d. 11500 e. 11520 he integers from 2 to 1000 are written on the blackboard. The students in school play the ollowing game. Each student in turn picks a number on the blackboard and erases it together Final answer: ith all of its multiples. The game ends when only primes are left written on the board. What the smallest number of students that need to play before the game ends? . 11 b. 31 c. 51 d. 71 e. 91 6. Which number should replce the question mark? Final answer: 7. Jane is about to travel by bus, and she knows that she must have the exact fare. She is not sure what this is, but she knows that it is greater than €1 and less than €3. What is the minimum number of coins she must carry to be sure of carrying the correct fare? (assume that the available coins are 1 cent, 2 cent , 5 cent , 10 cent,20 cent, 50 cent , €1 and €2) Final answer: 8. How many sets of 2 or more consecutive whole numbers(starting at 0) sum up to 15? Final answer:

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