Spring break revision

Functions

100

What is the graph of the function f(x)=3x-2?

Straight line

200

Where does the function f(x)=2x-4 intersect the x-axis and the y-axis?

x=2, y=-4

300

How does the function f(x)=(x-2)²-1 move?

Two to the right, one down.

400

What is the minimum / maximum of the function f(x)=-(x-3)²+1

Maximum: (3, 1)

500

What is the range and zeros of function f(x)=(x+2)²-1?

Range: [-1, infinity[, zero: x1=-1, x2=-3.

Algebra

100

Simplify: x³x²x^-4

x

200

Simplify: (x²)⁴y³xy²

x⁹y⁵

300

Simplify: 6x⁴y²/9x²y⁴​​​​

(2/3)x²y^-2

400

Multiply out: 3x³+6x²-3x

3x(x²+2x-3)

500

Solve: (x-2)/3=(x-1)/4

x=5

Quadratics

100

Solve: x²=49

x1=7, x2=-7

200

Solve: x²+100=0

No solution

300

Solve: x²-6x+9=0

x=3

400

Solve: (2x-2)(x+3)=0

x1=1, x2=-3

500

Solve: 4x⁴-37x²+9=0

x1=3, x2=-3, x3=1/2, x4=-1/2

Geometry

100

What triangles is the Pythagorean theorem about?

Only right-angled triangles

200

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

300

We draw a tangent from point P to circkle k. The length of the tangent segment is 10 cm, the radius of the circle is 5 cm. How far is point P from the centre of the circle.

11.18 cm

400

The perimeter of a rectangle is 24 cm, its area is 32 cm². How long are its sides?

a=4, b=8

500

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