NTC NUMERACY PAST QUESTION NUMBER 3

BRIGHT FRANCISDecember 7, 2022

1 6 minutes read

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Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. 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.)

Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm.

A circle of centre (-3 , -2) passes through the points (0 , -6) and (a , 0). Find a.

Find the equation of the tangent at (0 , 2) to the circle with equation (x + 2)2 + (y + 1)2 = 13

An examination consists of three parts. In part A, a student must answer 2 of 3 questions. In part B, a student must answer 6 of 8 questions and in part C, a student must answer all questions. How many choices of questions does the student have?

The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) and point C is the x intercept of the parabola. If the equation of the parabola is given by y = -x²+ 4x + C, find C so that the area of the triangle ABC is equal to 32 square units.

The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. Find k.
A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). Find the equation of this parabola.

When the polynomial P(x) = x³+ 3x² -2Ax + 3, where A is a constant, is divided by x² + 1 we get a remainder equal to -5x. Find A.

When divided by x – 1, the polynomial P(x) = x⁵+ 2x³ +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.
Find all points of intersections of the 2 circles defined by the equations
(x – 2)²+ (y – 2)² = 4

(x – 1)² + (y – 1)² = 4

If 200 is added to a positive integer I, the result is a square number. If 276 is added to the same integer I, another square number is obtained. Find I.

The sum of the first three terms of a geometric sequence is equal to 42. The sum of the squares of the same terms is equal to 1092. Find the three terms of the sequence.

A rock is dropped into a water well and it travels approximately 16t²in t seconds. 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?

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
Find the constants a and b so that all the 4 lines whose equation are given by

x + y = -1

-x + 3y = -11

ax + by = 4

2ax – by = 2

pass through the same point.

It takes pump A 2 hours less time that pump B to empty a swimming pool. Pump A is started at 8:00 a.m. and pump B is started at 10:00 a.m. At 12:00 p.m. 60% of the pool is empty when pump B broke down. How much time after 12:00 p.m. would it take pump A to empty the pool?

The number of pupils in school A is equal to half the number of pupils in school B. 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 boys in school B is 200 higher than the number of boys in school A. Find the number of boys and girls in each school.

Four large and 2 small pumps can fill a swimming pool in 2 hours. Two large and 6 small pumps can also fill the same swimming pool in 2 hours. How long does it take 8 large and 8 small pumps to fill 50% of the swimming pool. (NOTE: all the large pump have same power and all the small pumps have the same power).