2020 MATRIC - North West

2020 MATRIC

MATHEMATICS PAPER 1 COLLECTABLE MARKS

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Collectable Marks/ NW2020

ALGEBRAIC EXPRESSIONS, EQUATIONS AND INEQUALITIES

ATP: GARDE 10

ATP: GRADE 11

Rational and irrational numbers Linear equations Quadratic equations

Literal equations (changing subject of the formula) Linear inequalities (interpret solutions graphically) System of linear equations

Word problems Exponential laws and simplify using (rational exponents) Exponential equations

Theory of numbers

Solve quadratic equations by Factorisation Taking square roots Completing the square Using quadratic formula

Quadratic inequalities (interpret solutions graphically) Equations in two unknowns One equation linear and the other quadratic Nature of roots Word problems (modelling) Simplify expressions using laws of exponents Add, subtract, multiply and divide surds Solve equations using laws of exponents Solve simple equations involving surds

VOCABULARY Expression

Equations

Quadratic formula Discriminant Perfect square Standard form

It is made up of constants, variables and number operations It only be SIMPLIFIED (write it in simple form) by grouping, adding, subtracting like terms or factorising. Expressions with equal sign. Main question is SOLVE When solving equations, you need to find the unknown values

b b2 4ac x

2a b2 4ac where y ax2 bx c A number that is the square of an integer

Linear: ax by c

Quadratic: ax2 bx c 0

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QUESTION 1

1.1 Solve for x :

1.1.1 x x 1 6

(3)

1.1.2 3x2 4x 8 (correct to TWO decimal places.)

(4)

1.1.3

(4)

4x2 1 5x

1.1.4

(4)

2x 3 x 0

1.2 Solve for x and y simultaneously:

(6)

y 2x 3 0 and x2 y x y2

[21]

QUESTION2 NW SEP 2015

2.1 Solve for x:

2.1.1

(4)

2.1.2

(Leave your answer correct to TWO decimal places.)

(4)

2.1.3

(5)

2.2 Solve for x and y simultaneously: (7)

2.3

(2)

For which values of m will

be a factor of

?

[22]

QUESTION 3 NW SEP 2016 3.1

Solve for x :

3.1.1 7x 2x 1 0

(2)

3.1.2 2x2 x 4 (Leave your answer correct to TWO decimal places.)

(4)

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3.1.3 x 4 x 5 0

(3)

3.1.4

2

1

(4)

3x5 5x5 2 0

3.2 Solve for x and y simultaneously:

2x 1; 1 y

y 1

and

3x yx y 0

(6)

3.3

Given:

f (x) 3 x2

and

g(x) 3x2. Explain why f (x) g(x) will have

only ONE root. Motivate your answer.

(3)

[22]

QUESTION 4 NW SEP 2017 4.1

Solve for x :

4.1.1

(3)

x2 5x 6

4.1.2 2x2 8x 3 0 (correct to TWO decimal places.)

(4)

4.1.3

(2)

x2 64 0

4.1.4

(4)

4x 8.2x 0

4.2 Solve for x and y simultaneously:

(7)

2xy 4 and x2 52 y2

(West Coast ED ? Sep 2014)

4.3 Given: 2mx2 3x 8, where m 0. Determinethe value of m if the roots of the

given equation are non-real.

(4)

4.4 If i 1, show WITHOUT THE USE OF A CALCULATOR, that

1 i 24 4096.

(4)

[28]

QUESTION 5 NW SEP 2018

5.1 Solve for x :

5.1.1 2x 5x 3 0

(2)

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5.1.2 x2 4 5x (Leave your answer correct to TWO decimal places.) (4)

5.1.3

x 6 2 15

(5)

x6

5.1.4 x2 2 x 3 0

(2)

5.2 Solve for x and y simultaneously:

(6)

x 2 y 3 and 3x2 4xy 9 y2 16 0

5.3 Determine the sum of the digits of: 22022.52018

(4)

[23] QUESTION 6 NW SEP 2019

6.1 Solve for x :

6.1.1

(3)

3x2 18x 0

6.1.2 7x2 4x 5 (Leave your answer correct to TWO decimal places.) (4)

6.1.3 x 5 x 2 0

(2)

6.1.4 26 52x 5x 6 2

(6)

6.2 Solve for x and y simultaneously:

(6)

x 4 y 5 and 3x2 5xy 2 y2 25

6.3

(4)

Solve for x if: x 12 12 12 12 ...

[25]

PATTERNS, SEQUENCE AND SERIES

ATP: GRADE 10 Linear patterns

ATP: GARDE 11 Linear patterns

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ATP: GRADE 12 Number patterns dealt with in grade 10 and 11

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Determine general term using Tn dn q

Determine general term using Tn dn q Exponential patterns Number patterns leading to those where there is a constant difference between consecutive terms, and the general term is therefore quadratic. Tn an2 bn c a b c First term of quadratic sequence 3a b First term from the row of first difference

2a Second difference

Patterns, including arithmetic sequences and series

Sigma notation

Derivation and application for the sum of

arithmetic series

S n a a d a 2 d ...a n 1 d

Sn

n 2

2 a n

1 d

Number patterns, including geometric sequences and series

Derivation and application of the formula for the sum of geometric series

Sn a ar ar 2 .. ar n1

a rn 1

Sn r 1 Sigma notation

Infinite geometric series

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VOCABULARY DEFINITION/ CLARIFICATION

First term or Leading term Common difference Which term or How many terms Arithmetic sequence Common ratio

Arithmetic series

Geometric sequence Geometric series

Infinite series

Quadratic sequence Sigma notation

Find Tn given Sn

a or T1

d Tn Tn1 Test T2 T1 T3 T2

n or nth term

Each term is the result of adding the same number (called the common

difference) to the previous term. Tn a n 1 d

r Tn Tn1

T2 T3 Test T1 T2

Sn

n 2

2a

n

1 d

or

Sn

n a

2

where

Tn

Each term of G. P is found by multiplying the previous term by a fixed

number (called common ratio). Tn a.r n1

a(rn 1)

Sn r 1

a 1rn or Sn 1 r

S

a 1 r

,

1 r 1

The sequence whose second difference is constant: Tn an2 bn c

n

Tn

The sum of k1

Tn Sn Sn1

QUESTION 7

7.1 The fifth term of an arithmetic sequence is zero and the thirteenth term is equal to 16. Determine:

7.1.1 The common difference

(4)

7.1.2 The first term

(2)

7.1.3 The sum of the first 21 terms

(4)

7.2

3; 1; 1 ; ...

Determine the twelfth term of the geometric sequence

3

(4)

7.3 Cells are continually dividing and thus increasing in number. A cell divides

and becomes two new cells. The process repeats itself forming a geometric

sequence. The following sketch represents this cell division.

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How many cells will there be altogether after twenty stages?

(4)

[18]

QUESTION 8

8.1 The following arithmetic sequence is given: ? 1; 6; 13; ...

Determine:

8.1.1 The 49th term

(3)

8.1.2 The sum of the first 87 terms

(3)

8.2 20; 16; ... is a geometric sequence.

(4)

Calculate the sum of the first ten terms.

8.3 The following are the consecutive terms of a geometric sequence:

3x 2; 2x 2; 4x 1 ( x is a natural number)

(6)

Calculate the value of x.

8.4 The tiles are arranged as shown below. The first arrangement has 5 tiles, the second

arrangement has 9 tiles, the third arrangement has 13 tiles and the fourth arrangement

has 17 tiles. The arrangements continue in this pattern

Derive, in terms of n, a formula for one of tiles in the nth arrangement.

(3)

[19]

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