UNILAG Mathematics 2019/2020 Model 3 Past Questions

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'If A is true, then B is false' is logically equivalent to which of the following I: if A is false, then B is true II: If B is false, then A is true, III: If B is true, then A is false.

The larger of two numbers exceeds twice the smaller number by 8. The sum of twice the larger and 3 times the smaller number is 65. If x is the smaller number, which equation determines the correct value of x?

A company earned a profit of N 8.0 million each year for 3 consecutive years. For each of the next 2 years the company earned a profit of N9,0million. What is the company's average yearly profit in million Naira for this 5-year period?

The probability of obtaining a number less than 5 in a single loss of a fair die is

Four of the faces of a fair die are coloured black and the remaining two faces are coloured white. One throwing the die two consecutive time, the probability that both throws will show a black face is

If the coordinates of three points x,y and Z are given as (6,3), (1,2) and (7,2) respectively. Find the coordinates of the midpoint of the line XY.

A person 2 metres tall casts a shadow 3 meters long. At the same time, a telephone pole casts a shadow 12 meters long. How tall is the pole?

The average of all grades on a certain test was 90. If the average of the eight male's grades was 87, and the average of the females grades was 92, how many females took the test?

The ratio of the side lengths for a triangle is exactly 12:14:15. In a second triangle similar to the first the shortest side is 8cm long. What is the length of the longest side of the second triangle?

The geocenter of two positive numbers is defined as the positive square root of their product. If the geocenter of 5 and x is 9, what is the value of x?

A bag contains 5 red balls and 3 green balls. Two balls are picked one after the other, without replacement. The probability that both are the same colour is

Four cars, A, B, C and D, finished a race with the following respective times for completing the course. 1 hour, 11/12 hours, 01/12 and 06/ 6 hours. Which car finished the race first?

The volume of a balloon which is being blown increases at the rate of (60 -3t²)cm³s^-1, where t is the time in seconds. If the initial volume of the balloon is zero, its volume after 3 seconds is

The probability that a sum of 10 will appear in two tosses of a fair die is

A die is rolled 100 times with the following outcomes.

Number	1	2	3	4	5	6
Frequency	15	20	18	14	17	16

The experimental probability of obtaining a 2 is

This table shows the scores of students in a class test on mathematics.

Score	2	3	4	5	6	7	8
No of Students	1	4	6	3	3	2	1

The probability that a student randomly from the class scored 5marks is

If a + b = 10 and both a and b are positive integers what is the largest possible value for a?

The original price P of a certain item is first discounted by 20 percent, and then 5 percent of the discount price is added for sales tax. If the final price, including the sales tax is N71.40 the original price of P is

Which of the following is the equation of a line that makes a 45° angle with the x-axis and has a y intercept of 2