2nd-degree equations
Problems (2nd-degree)
Systems of equations
Problems (systems)
Functions
100
Solve the following equation as an incomplete second-degree equation without using the formula.
4x2 - 100 = 0
+5 and -5
100
Find the natural number that is 90 units less than its square.
The number is 10
100
Is x=2 and y=3 the solution to the following system of linear equations? Why?
3x - y = 3
6x - 2y = 5
No, it isn't, because it's not true for the second equation
100
Calculate two numbers so that their sum is 63 and the difference between twice the first and second is 30.
31 and 32
100
Give the coordinates of points A and B.
A(0,3)
B(-3,-2)
200
Solve the following equation as an incomplete second-degree equation without using the formula.
3x2 = 6x
0 and 2
200
If a number increased by three units is multiplied by the same number decreased by three units, 216 is obtained. What number is it?
15 or -15
200
Solve the following system of linear equation. Recommendation: use the elimination method.
x + y = 4
x - y = 2
x=3 and y=1
200
Calculate the dimensions of a rectangular plot knowing that the longest side is 100 meters longer than the shortest side and that the perimeter is 1,800 meters.
the dimensions are 500 meters long and 400 meters wide
200
The graph below represents a bus trip for a group of students. It reflects the time (hours) and the distance (km) that separates them from the study center.
How long were they at the destination?
Did they make any stops on the outward journey?
And on the return trip?
They were 2 hours at the destination place.
No, they didn't.
Yes, they did.
300
Solve the following complete second-degree equation using the formula.
2x2 - 3x - 2 = 0
2 and -1/2
300
In my pocket I carry a certain number of bills and coins. If I have two less coins than bills and the product of both amounts is 15, how many coins and bills do I have?
5 bills and 3 coins
300
Solve the following system of linear equation. Recommendation: use the substitution method.
x - 2y = 7
2x - 3y = 13
x=5 and y=-1
300
In a bar they charge us 2.5 euros for two coffees and a soft drink and for a coffee and three soft drinks we pay 3.5 euros. How much does a coffee cost? And a soft drink?
coffee costs 80 euro cents and soft drink costs 90 euro cents
300
Complete the table of values corresponding to the function y = x2 - 4x.
x= -1 0 1 2
Y= _ _ -3 _
x= -1 0 1 2
Y= 5 0 -3 -4
400
How many solutions has the following second-degree equation? Why?
2x2 + 4x + 2 = 0
Only one solution or a double solution because the square root of zero is zero and you get the same result by adding or subtracting zero.
400
Calculate the dimensions of a rectangle knowing that its base measures 3 meters more than its height and that its surface is 54 m2.
The base of the rectangle is 9 m and the height is 6 m
400
Solve the following system of linear equation.
2x - y = 3
4x - 2y = 7
There is no solution for that system of linear equations
400
A worker earns 40 euros on a day shift and 75 euros on a night shift. In one month he has done 22 shifts in total and has earned 1,300 euros. How many day shifts have you done? And at night?
10 day shifts and 12 night shifts
400
Represent the following function, indicate what type of function it is and indicate its slope:
y = -3x
It's a proportional function.
Its slope is m=-3.
500
How many solutions has the following second-degree equation? Why?
2x2 + 4x + 3 = 0
None because there is no square root of negative number.
500
The perimeter of a rectangle is 42 meters and its area is 108 m2. What are its dimensions?
The dimensions of the rectangle are 9 m and 12 m
500
Find all possible solutions to the following system of linear equation.
x - 4y = 7
-2x + 8y = -14
It's not possible because there are infinite solutions to that system of linear equations
500
What quantities of two kinds of oil, one at 3.9 euros/litre and the other at 1.4 euros/litre, must be mixed to obtain 50 liters of mixture at 2.5 euros/litre?
22 liters of the most expensive oil and 28 liters of the cheapest
500
Represent the following function, indicate what type of function it is, indicate its slope and the point where it cuts the OY axis:
y = 3 - x
It's a linear function.
Its slope is m=-1.
It cuts the axis OY at the point (0,3).