Functions
What is the graph of the function f(x)=3x-2?
Straight line
Simplify: x3x2x-4
x
Solve: x2=49
x1=7, x2=-7
In a right-angled triangle an angle and the hypotenuse is given. Which trigonometric ratio would you use to calculate the length of the leg opposite the angle?
sine
Where does the function f(x)=2x-4 intersect the x-axis and the y-axis?
x=2, y=-4
Simplify: (x2)4y3xy2
x9y5
Solve: x2+100=0
No solution
In a right angled triangle the hypotenuse is 12, one of the sides is 5, what is the length of the other leg?
a=10,9
In a right-angled triangle one leg is 6 cm, the angle adjacent to it is 38°. Calculate the length of the hypotenuse.
c=7.61
How does the function f(x)=(x-2)2-1 move?
Two to the right, one down.
(2/3)x2y-2
Solve: x2-6x+9=0
x=3
Calculate the area of the isosceles triangle if its base is 5 cm, and its legs are 7 cm.
T=16.34 cm2
In a right-angled triangle the length of the legs are 4 cm and 7 cm. Calculate the angles of the triangle.
The angle opposite the 4 m-long leg:29.7°.
The angle opposite the 7cm-long leg: 60.25°.
What is the minimum / maximum of the function f(x)=-(x-3)2+1
Maximum: (3, 1)
Multiply out: 3x3+6x2-3x
3x(x2+2x-3)
Solve: (2x-2)(x+3)=0
x1=1, x2=-3
The perimeter of a rectangle is 24 cm, its area is 32 cm2. How long are its sides?
a=4, b=8
The base of an isosceles triangle is 5 cm, its legs are 7 cm. Calculate the measure of its angles.
The angles on the base: 69.07°.
The third angle:41.85°.
What is the range and zeros of function f(x)=(x+2)2-1?
Range: [-1, infinity[, zero: x1=-1, x2=-3.
Solve: (x-2)/3=(x-1)/4
x=5
Solve: 4x4-37x2+9=0
x1=3, x2=-3, x3=1/2, x4=-1/2
A square is cut with two lines which are parallel to the sides, the result is 3 congruent rectangles. The perimeter of each rectangle is 24 cm. Calculate the area of the square.
T=81 cm2
In an isosceles triangle the angle included between the legs is 40°, the base is 6 cm. Calculate the other angles, the length of the legs and the area.
The angles on the base: 70°.
The length of the leg: 8.77
The area: 24.73 cm2.