Entrance Test Math 10 [PDF]

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Torch of Life Academy Entrance Test Mathematics Grade 10 --------------------------------------------------------------------------------------------------------------------------------Instructions: 1. Read the questions carefully. 2. Ask the proctor for any inquiry. 3. Use black or blue ink in shading the answer sheet. 4. Do not write anything on the questionnaire.



4



1.



2.



2 Which of the following is equivalent to   ? 3 8 A. C. 81 16 B. D. 81



On five successive days, a delivery boy from a water company listed the distance he traveled to different provinces. These are 50 km, 90 km, 100 km, 50 km and 60 km. If his delivery van averages 10 km for each 1 liter of gas used, how many liters of gas did he use during these five days? A. 30 liters



3.



1 8



3 8



C.



3 4



D.



1 4



B. 3



C. 4



D. 5



B. 19 feet



C. 20 feet



D. 24 feet



B. 91



C. 94



D. 95



What is the value of 3ab  x 2 y if a = 4, b = 5, y = x3 and x = 2? A. 18



8.



B.



The top 5 board passers had the following scores taken at random; 91, 95, 90, 88 and 94. What is the median of these scores? A. 90



7.



D. 45 liters



A flagpole casts a shadow of 16 feet. At the same time, a pole of 9 feet high casts a shadow of 6 feet. What is the height of the flagpole, in feet? A. 18 feet



6.



C. 40 liters



For which value of x is the inequality 2x > 9 true? A. 2



5.



B. 35 liters



One half of the students at the University of the Philippines ride a jeepney in going to school. One fourth of the remainder goes to school by car. What part of the school population travel by some other means? A.



4.



8 3 16 3



B. 24



C. 28



D. 54



In a basketball game, Bill scored 3 times as many points as Jim. The sum of the scores of Bill and Jim was 56 points. How many points did Bill score? A. 14



B. 28



C. 42



D. 48



9.



Refer to the figure below.



a + 3b 2a + b



3a + b 3a + 2b



A. 8a + 5b



B. 9a + 7b



C. 7a + 5b



D. 6a + 6b



For items 10-12, refer to the figure below.



A θ



10



6 C 10.



What is the value of sinθ? A.



11.



8 10



10 8



8 6



B.



6 10



C.



6 8



D.



8 6



B.



10 6



C.



8 6



D.



6 8



B. II



C. III



D. IV



B. 20°



C. 40°



D. 60°



B. 20.4



C. 21.5



D. 22.8



Six consecutive integers are given. The sum of the first three is 27. What is the sum of the last three? A. 36



17.



D.



If Nelly gets 3 in his first quiz and 6 in his second quiz, and doubles his quiz every time they have a quiz, what will be his average score after their fifth quiz? A. 18.6



16.



6 8



The angles of a triangle are in the ratio 2:3:4. What is the measure of the smallest angle? A. 10°



15.



C.



6 10



State the quadrant in which P(θ) would be, given that cosθ > 0 and sinθ < 0. A. I



14.



B.



What is the value of secθ? A.



13.



8 10



What is the value of tanθ? A.



12.



B



8



B. 33



C. 32



D. 30



If Jun saves Php 10 on the first week and adds Php 4 each week, how much will he save on the last week of the third month? A. Php 58



B. Php 54



C. Php 50



D. Php 40



18.



Benjo is five years older than Mona. Four years ago he was twice as old as Mona. How old is Benjo now? A. 14 years old



19.



D. 12 years old



x



0



1



2



3



4



y



1



3



5



7



9



B. y = 2x



C. y = 2x + 1



D. y = 2x - 1



C. x > 2



Dx -2



21.



C. 9 years old



Given the table below, what is the equation of the given relation?



A. y = x 20.



B. 15 years old



B. x < -2



Which of the following statement is false? A. 2 is the only even prime number B. 5 is divisible by 25 C. 3 and 7 are both factors of 84 D. 81 is a perfect square



22.



What is the remainder when 2x3 – 5x + 10 is divided by x - 2? A. 16



23.



C. 72 cm



D. 162 cm



B. (22)2 + 22 + 2



C. (2•2•2)2



D. [(2 + 2)2]2



B. 3 2



C. 0



D. 3 2



C. m-n



D. -2(m-n)



Simplify: 31(m-n) – 32(m-n) + (m-n). A. 1



27.



B. 36 cm



Simplify the expression 3 18  3 32  3 8  3 2 . A. 2 2



26.



D. 26



Which of the following numbers is the largest? A. (2 + 2 + 2)2



25.



C. 8



The area of a square tile is 81 cm2. What is its perimeter? A. 18 cm



24.



B. 36



B. 0



Which of the following is not true? A. (2x + 3)(2x – 3) = 4x2 – 9 B. (2x + 3)(4x2 – 6x + 9) = 8x3 + 27 C. (2x + 3)(2x + 5) = 4x2 + 16x + 15 D. (2x – 3)2 = 4x2 + 12x + 9



For items 28-30, refer to the figure below.



q



m ll n, q is a transversal line C A



m



B



n



28.



What is the measure of A ? A. 145°



29.



B. 35°



C. 70°



D. 45°



C. 70°



D. 45°



What is the measure of C ? A. 145°



30.



35°



B. 35°



What is the relationship between B and C ? A. Alternate-Interior Angles B. Corresponding Angles C. Alternate-Exterior Angles D. Vertical Angles