PRACTICE TEST 2With answer key, solution and UPCAT review tips MATHEMATICS 1 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. Do let us know the deadline of your assignment. We ll try our best to submit the solution on time through your e-mail address. MATHEMATICS (30 ITEMS) 1 1 3 v 1. When 3 5 is simplified and written as decimal, what is the 10th digit after the 2 21 5 75 decimal point? (A) 5 (B) 6 (C) 7 (D) 9 2. For what value of k is the sum of the roots of the equation x 2 4 6k x k 2 ! 0 equal to twice their product? (A) k = 2 only (B) k= 2, 3 (C) k = 1, 2 (D) k = 3 only 3. Tatlong buklet ang maaaring i-print gamit ang tatlong printer sa loob ng tatlong minuto. Gaano karaming mga buklet ang maaaring i-print gamit ang anim na printer sa loob ng anim na minuto? (A) 10 (B) 12 (C) 14 (D) 16 4. Ang isang basketball team ay may layunin na maipanalo ang 90% ng kanilang mga laro. Ang kanilang rekord ay 10 panalo at 2 talo. Kung manalo sila sa natitirang bahagi ng kanilang mga laro, gaano karaming mga laro ang kinakailangan upang maabot ang kanilang layunin? (A) 2 laro (B) 8 laro (C) 10 laro (D) 3 laro 2 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. Do let us know the deadline of your assignment. We ll try our best to submit the solution on time through your e-mail address. 9 is moved 5. The circle defined by the equation . x 4 . where a and b represent distinct digits of the number. How far does the center of the circle move? (A) 2 (B) 9 (C) 10 (D) 15 6. What is a-b? (A) 3 (B) 5 (C) 6 (D) 8 8. what is the value of x? (A) 1 7 (B) 12 7 (C) 7 12 (D) 7. The number 23a74b is divisible by 9 and 8. If x 1 ! 3 1 4 1 . What is the equation of the line which passes through the point .y 3 horizontally until its center is on the line x ! 6 . ¡ ¢ 2 2 ¢ 1 7 (d) 1956 . " ang sabi ni Mang Berto noong 1971. 3. Do let us know the deadline of your assignment. What is the simplified improper fraction for 4 .2 and is parallel to the line whose equation is 3 y ! 2 x 5 . Ako ay n taong gulang sa taong n . We ll try our best to submit the solution on time through your e-mail address. (A) 2 x 3 y ! 0 (B) 2 x 3 y ! 12 (C) 2 x 3 y ! 12 (D) 2 x 3 y ! 0 2 9. 8 48 ? (A) 44 9 (B) 148 33 (C) 160 33 (D) 606 125 3 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Anong taon siya ipinanganak? (A) 1892 (B) 1812 (c) 1927 10.com. We ll try our best to submit the solution on time through your e-mail address. What is the remainder when the sum is divided by 4? (A) 1 (B) 2 (C) 3 (D) no remainder 15. width is 6 meters. A circular table is pushed into a corner of a rectangular room so that it touches both walls. What is three times the sum of x and y given that ¯ (A) 81 (B) 90 (C) 102 ® 30 2 x ! 30 2 y ° x y 15 ! 15 (D) 120 4 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. . (A) 32 (B) 162 (C) 81 (D) 126 13. Twelve consecutive integers are added together.817 (D) 189.744 (C) 167.. What is the radius of the table? (A) 20 inches (B) 12 inches (C) 15 inches (D) 17 inches 12.659 (B) 156..463 14. Find the total surface area in square meters of a rectangular solid whose length is 7 meters. and depth is 3 meters. A point on the edge on the edge of the table between the two points of contact is 2 inches from one wall and 9 inches from the other wall. Evaluate the following sum: 12 15 18 . 1002 (A) 139. Do let us know the deadline of your assignment. What is the slope of the line (A) 3 2 x y ! 1? 3 2 (B) 2 3 (C) 1 3 (D) 2 3 17.16. What 81 (B) 100 81 (C) 9 10 (D) 10 9 18. its square . The lines y ! x and y ! . The product of a positive number. and its reciprocal is is the number? (A) 81 100 100 . x 9 form a triangle in the first quadrant with the y2 axis.75 (C) 8.75 (D) 9.75 .75 (B) 7. What is the area of this triangle? (A) 6. Simplify the expression . 19. then the value of . x x x xx (A) x x x 2 (B) x xx xx (C) x 2 x xx (D) x5 20. If 4 x 4 x 1 ! 24 . Do let us know the deadline of your assignment. .com. What is the area of one face of a cube? (A) 20 cm 2 (B) 25 cm 2 (C) 41 cm 2 2 3 (D) 5 cm 2 5 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected] x x is (A) 4 2 (B) 12 2 (C) 10 5 (D) 25 5 21. We ll try our best to submit the solution on time through your e-mail address. A cube has a volume of 125 cm 3 . The vertex of a parabola y ! .22. x b 2 b h has coordinates . The diagonals of a rhombus measure 24 inches and 32 inches. What is the value of h? (A) 3 (B) 4 (C) 5 (d) 6 23.Simplify: ¸ ¹ ¹ º p ¨ xq © q p ©x ª (B) ¸ ¹ ¹ º pq (A) x 2 pq p 2 x 2 pq q 2 (C) x 2 pq (D) x pq 25. Determine the solution of the following equation. ?2 x 2 . The perimeter of a rhombus (A) cannot be determined uniquely from the given information (B) must be 80 inches (C) must be 80 2 inches (D) must be 160 inches ¨ x pq © q © x ª 24.2.5 . x 3A! 4 . Do let us know the deadline of your assignment. We ll try our best to submit the solution on time through your e-mail address. .com. 2 x 6 x 4 1 1 (B) 3 2 1 3 (A) 0 (C) 2 (D) 2 6 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. 9 miles east.26. Find the y-intercept of the perpendicular bisector of AB where A . A car traveled 3 miles south. What is the straight-line distance (in miles) between the point where the car started and where it stopped? (C) 7 3 (D)15 (A) 21 (B) 6 3 27. and then another 9 miles south. 5.8 and B . (A) 6.75 28. Do let us know the deadline of your assignment. the correct result was obtained. what is the first term? (A) 2 (B) 3 (C) 4 (D) 5 30. The sum of the first five terms of a geometric sequence is 93.75 (C) 8.75 (B) 7. We ll try our best to submit the solution on time through your e-mail address. . 2. However. A certain number was to be added to 1 1 but by mistake was divided by the 2 2 number.com. Find the number. For what value of k will the graph of y ! 3 x 2 2 x k be tangent to the x-axis? (A) 1 2 (B) 2 3 (C) 1 3 (D) 3 4 29.2 .75 (D) 8.1 2 (D) 1 or 1 4 7 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. If its common ratio is 2. (A) 2 or 1 (B) 2 or 1 (C) 1 or . . We ll try our best to submit the solution on time through your e-mail address. 8 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected] . When 3 5 is simplified and written as decimal.SOLUTION: 1 1 3 v 1. Do let us know the deadline of your assignment.com.repeating decimal 9 9 ! The 10th digit after the decimal point is 5. what is the 10th digit after the 2 21 5 75 decimal point? (A) 5 Solution: 1 1 10 1 3 v v 3 5 ! 3 5 2 21 30 21 5 75 75 2 ! 3 3 (B) 6 (C) 7 (D) 9 25 ! 2 25 v 3 3 50 5 ! 5 ! 5. 2. For what value of k is the sum of the roots of the equation x 2 . the sum of the roots is equal to and the product of the roots is c . 2 (D) k = 3 only Therefore in x 2 .4 6k x k 2 ! 0 equal to twice their product? (A) k = 2 only Solution: Recall: In the quadratic equation ax 2 bx c ! 0 . a b a (B) k= 2. 3 (C) k = 1. 4 6k x k 2 ! 0 Sum of roots = 6k 4 2 And Product of roots = k . We now solve for the value of k using the following equation 6k 4 ! 2k 2 k 2 3k 2 ! 0 . k 2 . We ll try our best to submit the solution on time through your e-mail address.k 1 ! 0 k ! 1 or k ! 2 9 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment.com. . Cross-Multiply 12 x 10 (B) 8 laro (C) 10 laro (D) 3 laro 100 10 x ! 108 9 x x !8 10 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Ang kanilang rekord ay 10 panalo at 2 talo. gaano karaming mga laro ang kinakailangan upang maabot ang layunin? (A) 2 laro Solution: 10 x 9 ! . Ang isang basketball team ay may layunin na maipanalo ang 90% ng kanilang mga laro. Tatlong buklet ang maaaring i-print gamit ang tatlong printer sa loob ng tatlong minuto. We ll try our best to submit the solution on time through your e-mail address.com. . Do let us know the deadline of your assignment.3. Gaano karaming mga buklet ang maaaring i-print gamit ang anim na printer sa loob ng anim na minuto? (A) 10 (B) 12 (C) 14 (D) 16 Solution: Number of printers Time in minutes 3y3 6y6 ! 3 x Number of booklets x ! 12 4. Kung manalo sila sa natitirang bahagi ng kanilang mga laro. 5. The circle defined by the equation . x 4 2 . y 3 2 ! 9 is moved horizontally until its center is on the line x ! 6 . How far does the center of the circle move? (A) 2 Solution: The center of the circle . x 4 2 . y 3 2 ! 9 is . 4. The distance between the point .3 . 3 and the line x ! 6 is 6 . 4. Multiply both sides by 12 x . 4 ! 10. We ll try our best to submit the solution on time through your e-mail address. we have x 3 4 12 ! 4 x 3 x 7 x ! 12 12 x! 7 11 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. (B) 9 (C) 10 (D) 15 6. Do let us know the deadline of your assignment. what is the value of x? (A) 1 7 (B) 12 7 (C) 7 12 (D) 1 7 Solution: x 1 ! 3 1 4 1 1 1 1 ! . If x 1 ! 3 1 4 1 . .com. where a and b represent distinct digits of the number. so is the entire number. The last 3 digits of 23a74b are 74b. We ll try our best to submit the solution on time through your e-mail address. Simplifying 2+3+a+7+4+4 the result is a+20. A number is divisible by 9 if the sum of the digits is divisible by 9 23a744 is divisible by 9 if 2+3+a+7+4+4 is divisible by 9. 74b is divisible by 8 when b=4. 12 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. The number 23a74b is divisible by 9 and 8. Do let us know the deadline of your assignment. The value of a-b is 3.7. . therefore a=7. What is a-b? (A) 3 (B) 5 (C) 6 (D) 8 Solution: If the last 3 digits are divisible by 8.com. 8. What is the equation of the line which passes through the point . 2 and is parallel to the line whose equation is 3 y ! 2 x 5 . 3. A) 2 x 3 y ! 0 (B) 2 x 3 y ! 12 (C) 2 x 3 y ! 12 (D) 2 x 3 y ! 0 (To get the slope of 3 y ! 2 x 5 express it in the form y ! mx b the result is y! 2 5 2 5 x . All lines parallel to y ! x has a slope of 2 . 3 3 3 3 3 Point: . 3.2 slope : 3 2 We use the point-slope form of the equation of the line y y1 ! m. x x1 y2 ! 2 . We ll try our best to submit the solution on time through your e-mail address. .x 3 . multiply both sides by 3 3 3y 6 ! 2x 6 2 x 3 y ! 12 13 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. Do let us know the deadline of your assignment. 2 9. We ll try our best to submit the solution on time through your e-mail address. " ang sabi ni Mang Berto noong 1971. Anong taon siya ipinanganak? (A) 1892 Solution: (B) 1812 (c) 1927 (d) 1956 n 39 40 41 42 43 44 45 difference between the square of n and n(this is the year of square of n birth).com. . Do let us know the deadline of your assignment. 1521 1600 1681 1764 1849 1936 2025 1482 1560 1640 1722 1806 1892 1980 The most realistic answer 14 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Ako ay n taong gulang sa taong n . .8484 - Therefore. We ll try our best to submit the solution on time through your e-mail address. 100 x x ! 484. the result is 100 x ! 484.8484 99 x ! 480 x! 480 99 x! 160 33 15 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment.com.848 . 8 48 ? (A) 44 9 (B) 148 33 (C) 160 33 (D) 606 125 Solution: Let x ! 4. What is the simplified improper fraction for 4 . Since two digits are repeating multiply both sides by 102. 4.8484 .10. 11. A circular table is pushed into a corner of a rectangular room so that it touches both walls. The equation of the circle with radius r and center . What is the radius of the table? (A) 20 inches Solution: (B) 12 inches (C) 15 inches (D) 17 inches Denote the walls as the x and y axes. A point on the edge on the edge of the table between the two points of contact is 2 inches from one wall and 9 inches from the other wall. r is .r. x r 2 . .9) is a point on the circle. we have.y r 2 ! r 2 The point (2. we substitute this to the equation of the circle and solve for r. 2 r 2 . 9 r 2 ! r2 4 4 r r 2 81 18r r 2 ! r 2 r 2 22 r 85 ! 0 . . . r 17 . 16 .com.r 5 ! 0 r ! 5. r ! 17 because r ! 5 is not feasible it has to be r ! 17 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. We ll try our best to submit the solution on time through your e-mail address. Do let us know the deadline of your assignment. w= width. h = height Using the formula the Surface area of a rectangular solid in our problem is 2 . and depth is 3 meters. (A) 32 (B) 162 (C) 81 (D) 126 Solution: h w l Surface Area = 2 lh 2 lw 2 wh where l=length. Find the total surface area in square meters of a rectangular solid whose length is 7 meters. width is 6 meters.12. 7 v 3 2 . 7 v 6 2 . . We ll try our best to submit the solution on time through your e-mail address.6 v 3 ! 162 17 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. Do let us know the deadline of your assignment. 744 (C) 167. Evaluate the following sum: 12 15 18 .659 Solution: (B) 156. you need to know three things.. a n ! 1002 ..817 (D) 189.13. 1002 (A) 139. In our problem the common difference is d ! 3 . the last term ?a n Aand the number of terms ?nAand use the formula . The sum of the members of a finite arithmetic progression is called an arithmetic series To find the sum of a finite arithmetic series. 1002 . a1 ! 12 . to get the value of n use the formula for the n th term of arithmetic sequence which is a n ! a1 .463 An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same. The first term ?a1 A. ¨ a an ¸ Sn ! n© 1 ¹ ª 2 º In 12 15 18 . n 1 d a n ! a1 . n 1 d 1002 ! 12 . n 1 3 990 ! 3 . 817 18 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. ¨ a an ¸ Sn ! n© 1 ¹ ª 2 º ¨ 12 1002 ¸ ! 331 © ¹ 2 º ª ! 167 .n 1 330 ! n 1 n ! 331 Therefore.com. Do let us know the deadline of your assignment. We ll try our best to submit the solution on time through your e-mail address. . The integers are x x 1 x2 x3 x4 x5 x6 x7 x8 x9 x 10 x 11 Remainder when the sum of 12 consecutive integers is divided by 4 (B) 2 (C) 3 (D) no remainder Sum = 12 x 66 = 4 . What is the remainder when the sum is divided by 4? (A) 1 Solution: Let x be the first integer. Twelve consecutive integers are added together.14. 3x 16 2 15. What is three times the sum of x and y given that ¯ (A) 81 Solution: 2 x 2 y ! 60 30 2 x ! 30 2 y x y ! 30 ¯ ¯ ° x y ! 30 ° x y 15 ! 15 ° x y 15 ! 15 (B) 90 (C) 102 Therefore three times the sum of x and y is 3 . x y ! 3. £ 30 2 x ! 30 2 y (D) 120 ¤ ¤ . Do let us know the deadline of your assignment.30 ! 90 .com. We ll try our best to submit the solution on time through your e-mail address. 19 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. We ll try our best to submit the solution on time through your e-mail address. 3 2 .Multiply both sides by 6 2x 3y ! 6 3 y ! 2 x 6 y! m !2 2 x2 3 3 20 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. m is the slope and b is the y-intercept of the line. .com. Express x y !1 3 2 x y ! 1 in the form y ! mx b .16. Do let us know the deadline of your assignment. What is the slope of the line (A) 3 2 x y ! 1? 3 2 (B) 2 3 (C) 1 3 (D) 2 3 Solution: In y ! mx b . 17. The product of a positive number. its square . and its reciprocal is is the number? (A) 81 100 100 . What 81 (B) 100 81 (C) 9 10 (D) 10 9 Solution: Let x be a positive number. ¨ . x . .com. We ll try our best to submit the solution on time through your e-mail address. Do let us know the deadline of your assignment.x 2 1 ¸ ! 100 © ¹ ª xº 81 100 81 x2 ! x! 10 9 21 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. The lines y ! x and y ! .18. 75 (D) 9. x ! 2x ! x 9 3x ! 9 x ! 3.75 4.75 (C) 8.75 Solution: We sketch the graph of the two lines the result is: (B) 7. What is the area of this triangle? (A) 6. y ! 3 .5 units 3 units We solve for the point of intersection of the lines y ! x and y ! substitution method we have.x 9 form a triangle in the first quadrant with the y2 axis. x 9 2 . . Therefore. the height of the triangle is 3 units.x 9 by 2 The distance from the point of intersection to the base of the triangle formed is 3 units. 22 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. We ll try our best to submit the solution on time through your e-mail address.com. Do let us know the deadline of your assignment. 75 square units. 2 . The area of the triangle is half the product of the height and base ! 3 v 4.The difference between the y-intercepts of the lines y ! x and y ! to the height of the triangle which is equal to 4.5 ! 6.5 units. Simplify the expression (A) .x 9 is equal 2 19. . com. Do let us know the deadline of your assignment. We ll try our best to submit the solution on time through your e-mail address.x x x xx x x x 2 (B) x xx xx (C) x 2 x xx (D) x5 23 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. . Solution: . . x x x xx Use the Law of exponent for power . it becomes .a ! a m n mn . . Do let us know the deadline of your assignment.x x 2 xx Use again the Law of Exponent for power It becomes Use the Law of Exponent for product xx x 2 yx x a m y a n ! a mn It becomes x x2 24 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. We ll try our best to submit the solution on time through your e-mail address. If 4 x 4 x 1 ! 24 .20. then the value of . Multiply both sides by 4 we have.2 x x is (A) 4 2 (B) 12 2 (C) 10 5 (D) 25 5 Solution: 4 x 4 x 1 ! 24 4x 4 ! 24 . 4 x 4 4 x 4 x ! 96 3 4 x ! 96 x 2x 5 . . . ! 32 4 . . ! 2 2 2x ! 5 x!5 2 Therefore. 2 x x 5¸ ¨ ! ©2 y ¹ 2º ª 5 2 ! . 5 2 1 2 ! 52 y 5 ! 25 5 1 2 25 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment.com. . We ll try our best to submit the solution on time through your e-mail address. s!5 The area of one face of a cube which is a square is s 2 ! 25 22. A cube has a volume of 125 cm 3 .21. What is the area of one face of a cube? (A) 20 cm 2 Solution: The volume of the cube is equal to s 3 ! 125 (B) 25 cm 2 (C) 41 cm 2 2 3 (D) 5 cm 2 s3 . The vertex of a parabola y ! . x b 2 b h has coordinates . What is the value of h? (A) 3 (B) 4 (C) 5 (d) 6 Recall: The vertex of the parabola y ! a .2.5 . x h 2 k is . com. k . b ! 2 and b h ! 5 2h!5 h!3 26 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment. .h. We ll try our best to submit the solution on time through your e-mail address. Do let us know the deadline of your assignment.com. The perimeter of a rhombus is 20 in v 4 ! 80 in 27 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. We ll try our best to submit the solution on time through your e-mail address. The diagonals of a rhombus measure 24 inches and 32 inches. Using Phytagorean Triple 3-4-5. . Multiply 3-4-5 by 4 it becomes 12-16-20 The hypotenuse is 20. The perimeter of a rhombus (A) cannot be determined uniquely from the given information (B) must be 80 inches (C) must be 80 2 inches (D) must be 160 inches We just divide 32 by 2 16 12 We just divide 24 by 2 Diagonals of a rhombus are perpendicular and bisect each other. Therefore one side of a rhombus measures 20 inches. ¨ x pq © q © x ª 24.Simplify: ¸ ¹ ¹ º p ¨ xq © q p ©x ª (B) ¸ ¹ ¹ º pq (A) x 2 pq p 2 x 2 pq q 2 (c) x 2 pq (D) x pq Solution: ¨ x pq © q © x ª ¨ xq © q p ©x ª ¸ ¹ ¹ º p xp xp ¸ ¹ ¹ º pq ! . x . . We ll try our best to submit the solution on time through your e-mail address.com.x x x p p p pq p2 ! p 2 pq ! x pq 28 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment. 25. ?2 x 2 . Determine the solution of the following equation. x 3A! 4 . 2 x 6 x 4 1 1 2 (B) 3 1 (C) 2 (A) 0 3 (D) 2 Solution: ?2 x 2 . x 3A! 4 . 2 x 6 x 4 1 1 distribute -2 distribute 4 ?2 x 2 2 x 3A! 4 8 x 6 x 4 cancel 1 ! 2 x x! 1 2 29 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. We ll try our best to submit the solution on time through your e-mail address. . Do let us know the deadline of your assignment.com. The car started at the origin and stopped at the point . and then another 9 miles south. A car traveled 3 miles south.26. we can use the coordinate plane. What is the straight-line distance (in miles) between the point where the car started and where it stopped? (C) 7 3 (D)15 (A) 21 (B) 6 3 Solution: 3 miles 9 miles 12 miles below the x-axis 9 miles To solve this problem. 9 miles east. 9. We get the distance between .12 . 0 and .0. 12 using the distance formula: d! ! .9. x2 x1 2 . y 2 y1 2 . 9 2 . com. . We ll try our best to submit the solution on time through your e-mail address. 12 2 ! 225 ! 15 30 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Do let us know the deadline of your assignment. 27.2) (A) 6.75 A(5.8) B(-2.8) and B(-2.75 (C) 8.75 (D) 8.2) First we get the slope of AB using the formula m! y 2 y1 x 2 x1 m! 82 5 .75 Solution: (B) 7. Find the y-intercept of the perpendicular bisector of AB where A(5. 2 6 7 m! The slope of the line perpendicular to AB is the negative reciprocal of 6 7 which is 7 . 6 31 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected]. . We ll try our best to submit the solution on time through your e-mail address. Do let us know the deadline of your assignment. Next we get the midpoint of AB using the formula . y m ! ¨ x1 x 2 . y1 y 2 ¸ ¹ © ª 2 2 º ¨ 2 5 2 8¸ !© .x m . ¹ 2 º ª 2 ! 3 .5 2 . . Next we get the equation of the line with slope of 7 6 and passing through the point 3 2 . 5 using the point-slope form of the equation of the line. y y1 ! m. already in the form y ! mx b. where b is the y6 4 intercept y-intercept = 27/4 or 6. . We ll try our best to submit the solution on time through your e-mail address. Do let us know the deadline of your assignment. 6ª 2º transpose -5 to the right 7¨ 3¸ distribute 7 6 y ! © x ¹ 5.com.x x1 7¨ 3¸ y 5 ! ©x ¹. 6ª 2º 7 21 y ! x 5 6 12 7 7 y ! x 5 6 4 7 27 y ! x .75 32 If you have questions or homework in Math (from elementary to college level) send to us at
[email protected] Answer:6. then the parabola y ! ax 2 bx c intersects the parabola at t o points I ± I b 2 4 ac ! 0.28.axis ° y ! 3 x 2 2 x k is tangent to the x-axis when 2 2 4. then the parabola y ! ax 2 bx c does not intersect the x . then the parabola y ! ax 2 bx c is tangent to the x . For what value of k will the graph of y ! 3 x 2 2 x k be tangent to the x-axis? (A) 1 2 (B) 2 3 (C) 1 3 (D) 3 4 Solution: The number of points of intersection of the parabola y ! ax 2 bx c and the x-axis is ® b 2 4 ac " 0.axis ¯ ± I b 2 4 ac 0. 3 . com. . Do let us know the deadline of your assignment. The sum of the first five terms of a geometric sequence is 93.k ! 0 k! 1 3 29. what is the first term? (A) 2 (B) 3 (C) 4 (D) 5 Solution: Let x be the first term of the geometric sequence x 2 x 4 x 8 x 16 x ! 93 31x ! 93 x!3 33 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. If its common ratio is 2. We ll try our best to submit the solution on time through your e-mail address. 30. (A) 2 or 1 (B) 2 or 1 (C) 1 or . the correct result was obtained. However.1 2 (D) 1 or 1 4 Solution: 1 2 ! x 1 . multiply both sides by 2 x . the result is 2 x 1 ! 2x 2 x 2x 2 x 1 ! 0 . Find the number. A certain number was to be added to 1 1 but by mistake was divided by the 2 2 number. 2 x 1 . Do let us know the deadline of your assignment.com. We ll try our best to submit the solution on time through your e-mail address.x 1 ! 0 x ! 1 or x ! 1 2 ANSWER KEY IN UPCAT PRACTICE TEST 2 1 2 3 4 5 6 7 8 9 10 A C B B C B A B A C 11 12 13 14 15 16 17 18 19 20 D B C B B B D A A D 21 22 23 24 25 26 27 28 29 30 B A B D C D A C B C UPCAT review tips next page 34 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. . GENERAL SCIENCE 1. Nature of Solution II.Structure of Atom 5. Properties of Elements 7. Investigating Matters BIOLOGY 1. Forms and transformation of energy 5. Genetics -Mendellian patterns of heredity 7. Effect of earth's motion. Rational Numbers 3. Linear Equations/ Inequalities/Equalities 5. Algebraic Expressions 3. shape and inclination on time and seasonal changes 2. Triangles/ Rectangles/ Circles V. Polynomials 6.com. ARITHMETIC 1.UPCAT review tips MATHEMATICS I. We ll try our best to submit the solution on time through your e-mail address. carbon and its Compounds 6. Decimal/Money/Percent 4. Chemical and cellular basis of life 3. Ecosystem 6. Diversity of life CHEMISTRY 1. WORD PROBLEMS 1. conserving and protecting man's environment 4. Changes of Matter 3. Exponents/ Scientific Notation/ Radicals 8. Force and motion 3. Organ Systems 4. . Statistics IV. Whole Numbers 2. Geometry 1. Plane Coordinates/ Lines 2. Do let us know the deadline of your assignment. Properties of Colloids 2. ALGEBRA 35 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Measurement 5. Integers 2. Sequences and Series III. Restless Molecules -Behavior of Gases 4. Reproduction 2. Ratio and Proportion SCIENCE AND TECHNOLOGY I. Quadratic Equations 4. Graphs/ Angles 3. Rational Expression 7. Life Energy 5. Improving. Do let us know the deadline of your assignment.com.PHYSICS 1. Object's Motion with rfespect to a reference point 5. Vocabulary 5. Analogy 36 If you have questions or homework in Math (from elementary to college level) send to us at reviewermath@yahoo. Adding vector quantities (graphically) 3. . Logical Organization 4. Reading Comprehension Skills 3. Acceleration of a Falling Body 4. Solving average velocity VERBAL ABILITY ENGLISH AND FILIPINO 1. Communication Skills. Differentiating distance from displacement 6. Conversion of one unit of measure to another 2.Grammar and Correct Usage Verbal relationship 2. We ll try our best to submit the solution on time through your e-mail address.