Variant “Preparatory course in mathematics”

Course literature

How the course works

The course consists of 6 tutorial sessions with tutored self-studies. The first session is the two hours, the following sessions are three hours. Each hour begins with the teacher solving one or two problems on the board. Then the students solve the remaining recommended problems. Problems that are left are solved during the third hour “continuation” or as homework.

(Note that some programs have different schedule with slightly less hours. The teacher will then instruct on how the plan is to be modified.)

Observe that all recommended problems should be solved without a calculator – understanding and numeracy should go hand in hand. Ask your classmates for help!

Examination

The course ends with solutions to twelve of the recommended problems being uploaded on 27 August at 8.00-10.00. Therefore, remember to solve all the recommended problems. Write clear and detailed handwritten solutions. Get help from your assistant or friends if you have difficulty solving a problem.

It is important that you do a test upload before the examination to ensure that all aspects of the upload work.

Lesson plan

Lesson 1

Sections: 1.2 Fractional arithmetic, 1.3 Powers.

Plan Rec. problems Extra problems
Hour 1: 1.2 Fractional arithmetic 1.2:1 a,b,c
1.2:2 a,b
1.2:3 a
1.2:4 a,b
1.2:5 a,b		 1.2:1 d,e
1.2:2 c,d
1.2:3 b
1.2:4 c
1.2:5 c
1.2:6
Hour 2: 1.3 Powers 1.3:1
1.3:2
1.3:3 a,b 
1.3:4 a,b,c,d
1.3:5 a,b,c,d		 1.3:3 c,d,e
1.3.4 e 
1.3:5 e,f
1.3:6

 

Lesson 2

Sections: 2.1 Algebraic expressions, 2.2 Linear expressions.

Plan Rec. problems Extra problems
Hour 1: 2.1 Algebraic expressions 2.1:1 d,e,f,g 
2.1:2 a,c
2.1:3 b,c
2.1:4 a,b
2.1:5 a,b 
2.1:6 a,b
2.1:7 a		 2.1:2 d,e
2.1:3 e,f
2.1:4 c
2.1:5 c,d 
2.1:6 c,d
2.1:7 b
Hour 2: 2.2 Linear expressions 2.2:2 a,b
2.2:4 a,b
2.2:5 a,b
2.2:6 a,c,e		 2.2:2 d
2.2:5 c,d,e
2.2:8 a,b,c
2.2:9 a,b,c
Hour 3: Continuation

 

Lesson 3

Sections:  2.3 Quadratic expressions, 3.1 Roots, 3.2 Equations with roots.

Lektion Problems Extra problems
1: 2.3 Quadratic expressions 2.3:1 a,b
2.3:2 a,b,c
2.3:3 a,b,c
2.3:4
2.3:5 a,b
2.3:6
2.3:7		 2.3:1 d
2.3:2 e,f
2.3:3 e,f
2.3:8
2.3:9
2.3:10
2: 3.1-3.2 Roots, Equations with roots 3.1:1 b,c
3.1:2 a,b,c,d
3.1:5 a,c
3.2:1
3.2:2		 3.1:1 d
3.1:5 b,d
3.2:4
3.2:5
3: Continuation

 

Lesson 4

Sections: 3.3 Logarithms, 3.4 Logarithmic equations, 4.1 Angles and circles.

Plan Rec. problems Extra problems
Hour 1: 3.3-3.4 Logarithms, Logarithmic equations 3.3:1 a,b,c
3.3:2 a,b,c,d,e,f
3.3:4 a,b
3.3:5 a,b,c,d
3.4:1 b
3.4:2 b		 3.3:1 d
3.3:2 g,h
3.3:4 c
3.3:5 e,f
3.4:1 c
3.4:3
Hour 2: 4.1 Angles and circles 4.1:1 a,b,c
4.1:2 a,b
4.1:3 a,b
4.1:4 a,b
4.1:5 a
4.1:6 a,b		 4.1:1 d
4.1:2 c,d
4.1:3 c
4.1:4 c
4.1:5 b
4.1:6 c
4.1:7-10
Hour 3: Continuation

 

Lesson 5

Sections: 4.2 Trigonometric functions, 4.3 Trigonometric relations.

Plan Rec. problems Extra problems
Hour 1: 4.2 Trigonometric functions 4.2:1 a,b,c
4.2:2 a,b,c
4.2:3 a,b,c
4.2:4 a,b,c
4.2:5 a,b
4.2:6		 4.2:1 f
4.2:2 f
4.2:3 d,e,f
4.2:4 d,e,f
4.2:5 c,d
Hour 2: 4.3  Trigonometric relations 4.3:1 a
4.3:2 a
4.3:3 a,c,e
4.3:5		 4.3:1 c
4.3:2 b
4.3:4 a,c,e
4.3:6
4.3:7
Hour 3: Continuation

 

Lesson 6

Sections: 4.4 Trigonometric equations.

Plan Rec. problems Extra problems
Hour 1-2: 4.4 Trigonometric equations 4.4:1 a,b
4.4:2 a,b,d
4.4:3 a
4.4:4		 4.4:2 f
4.4:5 a,c
4.4:7 a,c
4.4:8 a,c
Hour 3: Continuation