Substitute and solve for x and y to find x = 15 cm and y = 20 cm. (60 - H) 2 - 600 = H 2 : one equation with one unknown. X + y = 60 - H : express x + y using the first equation and use the second equation to find xy = 300 and substitute in equation 5. (x + y) 2 - 2xy = H 2 : completing the square in the third equation. X + y + H = 60 : perimeter, x, y and H be the two legs and the hypotenuse of the right triangle Solve for R and r the system of first two equations then substitute in the third and solve for T to find the time. T(4R + 4r) = 1 : Find time T if 4 large and 4 small are to do one job. Let R and r the rate of work of the large and the small pumps respectivelyĤ(2R + r) = 1 : 2 large and 1 small work for 4 hours to do 1 jobĤ(R + 3r) = 1 : 1 large and 3 small work for 4 hours to do 1 job (NOTE: all the large pump have same power and all the small pumps have the same power). How long does it take 8 large and 8 small pumps to fill 50% of the swimming pool. Two large and 6 small pumps can also fill the same swimming pool in 2 hours. Find the number of boys and girls in each school.įour large and 2 small pumps can fill a swimming pool in 2 hours. The number of boys in school B is 200 higher than the number of boys in school A. The ratio of the boys in school A and the boys in school B is 1:3 and the ratio of the girls in school A and the girls in school B is 3:5. The number of pupils in school A is equal to half the number of pupils in school B. 60% of the pool is empty when pump B broke down. It takes pump A 2 hours less time that pump B to empty a swimming pool. Find the width of the river?įind the constants a and b so that all the 4 lines whose equation are given byįind the area of the right triangle shown below. We assume that each boat travels at a constant speed all along the journey. When they pass each other a second time, they are 600 meters from the other bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. They first pass each other 1400 meters from one bank. Two boats on opposite banks of a river start moving towards each other. If the splash is heard 3.5 seconds later and the speed of sound is 1087 feet/second, what is the height of the well? Find the three terms of the sequence.Ī rock is dropped into a water well and it travels approximately 16 t 2 feet in t seconds. The sum of the squares of the same terms is equal to 1092. The sum of the first three terms of a geometric sequence is equal to 42. If 276 is added to to the same integer I, another square number is obtained. If 200 is added to a positive integer I, the result is a square number. Find A and B.įind all points of intersections of the 2 circles defined by the equations When P(x) is divided by x + 3, the remainder is equal -314. When divided by x - 1, the polynomial P(x) = x 5 + 2x 3 +Ax + B, where A and B are constants, the remainder is equal to 2. When the polynomial P(x) = x 3 + 3x 2 -2Ax + 3, where A is a constant, is divided by x 2 + 1 we get a remainder equal to -5x. Find k.Ī parabola has two x intercepts at (-2, 0) and (3, 0) and passes through the point (5, 10). The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. If the equation of the parabola is given by y = -x 2 + 4x + C, find C so that the area of the triangle ABC is equal to 32 square units. Point B is also the maximum point of the parabola (vertex) and point C is the x intercept of the parabola. The right triangle ABC shown below is inscribed inside a parabola. How many choices of questions does the student have? In part B, a student must answer 6 of 8 questions and in part C, a student must answer all questions. In part A, a student must answer 2 of 3 questions. Find a.įind the equation of the tangent at ( 0, 2) to the circle with equationĪn examination consists of three parts. How many hours will it take 4 large and 4 small pumps to fill the swimming pool.(We assume that all large pumps are similar and all small pumps are also similar.)įind all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm.Ī circle of center (-3, -2) passes through the points (0, -6) and (a, 0). One large and 3 small pumps can also fill the same swimming pool in 4 hours. Two large and 1 small pumps can fill a swimming pool in 4 hours. More grade 12 math practice test are included in this website. Grade 12 math problems with detailed solutions are presented. Grade 12 Math Problems with Solutions and Answers
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