9th grade revision

Set theory

100

A={1;2;3;6}, B={2;3;5;7} , A∩ B=?

A∩ B={2;3;}

200

There are 8 friends in a group. 6 of them goes running regularly, 5 does yoga regularly. How many people do both?

3

300

U={2;3;4;5;6;7}, A={2;3;6}, A'=?

A'={4;5;7}

400

AUB={1;2;3;4;5}, A∩ B={1;2}, B-A={3}, A=?

A={1;2;4;5}

500

There are 23 mistakes in a text. Anna found 10, Betty found 9 and Cece found 13. 3 were found by all of them. Anna found 5 of the same mistakes as Betty and 4 of the same as Cece. Betty found 4 mistakes that were also found by Cece. How many mistakes were found only by Cece?

8

Algebra

100

a²xa⁸xa^-3=?

a⁷

200

(a⁵xb³)/(a²xb^-4)

a³xb⁷

300

(2x-3)²=

4x²-12x+9

400

Factorise: 21x⁵y - 7x²y³+14x³y³=

7x²y(3x³-y+7xy²)

500

Simplify the fraction: (x²-6x+9)/(x²-9)

(x-3)/(x+3)

Functions

100

Where does the graph of funcion f(x)=3x-2 intersect the y-axis and what is its slope?

y=-2, m=3

200

Where does the function f(x)=(1/3)x-3 intersect the x axis?

x=9

300

f(x)=5x-12, calculate f(1) and f(-3)

f(1)=-7

f(-3)=-27

400

Funcion f(x)=2x-1 is defined over the interval [-1; 3] , what is the range?

R=[-3;5]

500

Function f(x)=-(1/2)x+2 is defined over the interval [-4;6]. What is the range?

R=[-1;4]

Equations

100

Solve for x: 3x-2=3-5x

x=5/8

200

2(x-3)+4(x-1)=12

x=11/3

300

-3(x-1)-2(x+1)=5x

x=1/10

400

x(x-3)+2(3x-1)=x(x+2)-1

x=1

500

(x-3)²-4(x+2)=x(x+1)+9

x=-8/11