algebra, equations & inequalities · 2020. 6. 24. · GRADE 10-ALGEBRA, EQUATIONS AND INEQUALITIES 2 BY: AYANDA DLADLA CELL NO: 074 9947970 QUESTION 1 (NOV 12 HUD) 1.1 Given: ( )

ALGEBRA, EQUATIONS &

INEQUALITIES

MATHEMATICS GRADE 10

REVISION PACK (2020) 2ND EDITION

PAST PAPERS

BY AYANDA DLADLA/ 074 994 7970

GRADE 10-ALGEBRA, EQUATIONS AND INEQUALITIES

1 BY: AYANDA DLADLA CELL NO: 074 9947970

QUESTION 1 (NOV 06) Simplify: 1.1.1 ( )( ) (3)

1.1.2 ( )

(4)

1.1.3

(4)

1.2 ( ) (3)

1.3 It is given that where M and N are whole numbers. Determine the value of (3) 1.4 Factorise: 1.4.1 (2) 1.4.2 (3)

1.5 Write down at least THREE rational numbers between √ √ (3) [ ] QUESTION 2 (NOV 06) 2.1 Solve for in the following equations: 2.1.1 ( ) (4) 2.1.2 (Answer rounded off correctly to ONE decimal place.) (3) 2.2 Solve the following inequality. Illustrate your answer on a number line if is a real number. (4) [ ] QUESTION 1 (EXEMPLAR 12) Simplify the following expressions fully: 1.1.1 ( )( ) (3)

1.1.2

(5)

1.2 Factorise the following expressions fully: 1.2.1 (2) 1.2.2 (3) 1.3 Determine, without the use of a calculator, between which two consecutive integers

√ lies. (2)

1.4 Prove that ̇ ̇ ̇ is rational. (4) [ ]

QUESTION 2 (EXEMPLAR 12) 2.1 Determine, without the use a calculator, the value of in each of the following: 2.1.1 (3)

2.1.2

(3)

2.1.3 √

(2)

2.2 Solve for and simultaneously if: (5)

[ ]



QUESTION 1 (NOV 12 HUD) 1.1 Given: ( ) ( ) 1.1.1 Multiply out and then simplify as far possible. (3) 1.1.2 Factorise fully and then simplify as far as possible. (2) 1.1.3 Hence, without the use of a calculator, evaluate:

( ) ( ) (2)

1.3 If:

evaluate:

(2)

[ ] QUESTION 2 (NOV 12 HUD) 2.1. Factorise fully: 2.1.1 ( ) ( ) (4) 2.1.2 (2)

2.1.3

(2)

2.2. Write as a single term, fully factorised:

(4)

2.3 simplify fully:

(5)

2.4 Write as a single term, simplify fully:

( )

(7)

[ ] QUESTION 3 (NOV 12 HUD) 3.1 Solve for : 3.1.1. (4)

3.1.2

(2)

3.1.3

(2)

3.1.4

(6)

3.1.5

(4) 3.1.6 (3) 3.1.7 (4) 3.2 Given: 3.2.1 Solve for (2) 3.2.2. State your answer to (3.2.1.): 3.2.2.1. on a number line. (1) 3.2.2.2. in interval notation. (1) 3.3 Solve for and (4) [ ] QUESTION 4 (NOV 12 HUD) CALCULATORS MAY NOT BE USED INTHIS QUESTION. 4.1 Multiply out and simplify as far as possible:

(

) (2)

4.2 Simplify fully:

( )

√ (4)



4.3 If: determine the following in terms of 4.3.1. (1) 4.3.2. (1) 4.3.3. (1)

4.4 factorise fully:

(2)

4.5 Solve for

(4)

[ ] QUESTION 1(NOV 13 HUD)

1.1 If and are integers and is irrational, which of the following are rational numbers.

a)

b)

c)

d)

(2)

1.2 Rewrite ̇ ̇ as improper fraction. (3)

[ ]

QUESTION 2(NOV 13 HUD) (10marks) 2.1 Multiply the following by removing the brackets and then simplify if possible. 2.1.1 ( ) (2) 2.1.2. ( )( )( ) (2) 2.1.3. ( )( ) ( ) (4) 2.2 If ( ) and calculate the value of: (2) QUESTION 3 (NOV 13 HUD) Factorise fully: 3.1 ( ) ( ) (5)

3.2

(3)

3.3 (2) [ ]

QUESTION 4(N0V 13 HUD)

Determine without the use of a calculator:

[ ]

QUESTION 5 (NOV 13 HUD) Simplify the following fractions by making them one term, where necessary.

5.1

(3)

5.2

(4)

5.3

(6)

[ ]

QUESTION 6 (N0V 13 HUD) 6.1 Solve for

6.1.1

(1)

6.1.2 (2) 6.1.3 (3)



6.1.4 (4)

6.1.5

( )

(2)

6.1.6

(4)

6.1.7 √

(4)

6.2 Given:

6.2.1 Solve for (2) 6.2.2 State your answer for 6.2.1 on a number line. (1) 6.2.3 State your answer for 6.2.1 in interval notation. (1)

6.3 Solve for and : 6.4 Solve for : (5)

[ ] QUESTION 7 (NOV 13 HUD) (8marks) 7.1 Simplify the following fully: 7.1.1 ( ) (2)

7.1.2

(

) (2) 7.2 If rewrite the following in terms of 7.2.1 (2) 7.2.2 (2) QUESTION 1 (NOV 15) 1.1 factorise the following expressions fully: 1.1.1 (2) 1.1.2 (3) 1.2 Simplify the following expressions fully:

1.2.1

(5)

1.2.1

(4)

1.3 Consider the following numbers: √ √

√ Which ONE of these numbers is: 1.3.1 Irrational (1) 1.3.2 Non-real (1)

[ ] QUESTION 2 (NOV 15) 2.1 Solve for 2.1.1 (4)

2.1.2

(2)

2.2 The following inequality is given: ( )

2.2.1 Solve for in the in the inequality. (3) 2.2.2 Represent your answer to QUESTION 2.2.1 on a number line. (1) 2.3 Mary gave one third of her money to Nazeem and fifth of her money to Elwethu. Elwethu received less than Nazeem. How much money did Mary have originally? (1)

[ ] QUESTION 1 (NOV 17)

1.1 Given: √ 1.1.1 Determine the value of if , and . (2) Leave your answer in simplest surd form 1.1.2 State whether is rational or irrational. (1)



1.1.3 Between which TWO consecutive integers does lie? (1) 1.2 Factorise the following expressions fully:

1.2.1 ( ) (3)

1.2.2

(2)

1.3 Simplify the following completely: 1.3.1 ( )( ) (2)

1.3.2

( ) (3)

1.3.3

(3)

[ ]

QUESTION 2 (NOV 17)

2.1 Given where 2.1.1 Solve the inequality. (2) 2.1.2 Hence, represent your answer to QUESTION 2.1.1 on a number line (1) 2.2 Solve simultaneously for and : and (4)

2.3 Solve for

2.3.1 ( )

(3)

2.3.2 √ (2) 2.4 Tabelo is currently four times as old as his daughter, Linda. Six years from now, Tabelo will be three times as old as Linda. Calculate Linda’s age currently. (4)

[ ] QUESTION 1 (MAY 07 WB) Find the following products:

1.1 (

) (2)

1.2 ( )( ) (2) 1.3 ( ) ( )( ) (4) [ ] QUESTION 2 (MAY 07 WB)

Factorise each of the following: 2.1 (2) 2.2 (3) 2.3 (4) 2.4 (4) 2.5 ( ) (3)

[ ]



QUESTION 3 (MAY 07 WB)

Simplify the following:

3.1

(2)

3.2

(5)

3.3

(6)

3.4

(5)

[ ]

QUESTION 4 (MAY O7 WB)

Find the value of m if ( )( )( ) [ ]

QUESTION 5 (MAY 07 WB)

Solve for in each of the following:

5.1

(4)

5.2

( ) (6)

5.3 (3)

5.4

(4)

5.5 (3)

[ ]

QUESTION 6 (MAY07 WB)

Solve for and in the following simultaneous equation:

[ ]

QUESTION 1 (MARCH 18)

1.1 Determine the product of the following expressions:

1.1.1 ( )( ) (2)

1.1.2 ( √

) (

√

) (2)

1.2 Simplify the following expressions fully:

1.2.1

(4)

1.2.2

(3)



[ ]


2.1 Without using a calculator, simplify the following expression fully:

(3)

2.2 Solve for in the following equations:

2.2.1

(2)

2.2.2 (3)

2.3 Given: and 2.3.1 Show that if and (2) 2.3.1 Show that if and (1) 2.3.3 Hence or otherwise, find the value of (4)

[ ]


3.1 Solve for

3.1.1 (2)

3.1.2 √

(2)

3.1.3 ( )( ) 3.1.3.1 (1) 3.1.3.2 (1) 3.2 Solve for . Write your answer in interval notation. (2) [ ]

QUESTION 1 (JUNE 12 HUD)

1.1 Between which TWO consecutive natural numbers does √

lie?

Show all relevant working out. Calculators may not be used. (2)

1.2 Multiply out and simplify as far as possible:

1.2.1 ( ) (1)

1.2.2 (

)

(2)

1.3 factorise fully: 1.3.1 (3) 1.3.2 (2)

1.3.3

(2)

1.4 Simplify, leaving your answer as single term:

1.4.1

(2)

1.4.1

( )( )

( ) (4)

[ ]




2.1 Solve for

2.1.1 (

) (2)

2.1.2

(4)

2.1.3 ( ) ( ) (4) 2.1.4 (3) 2.1.5 (3)

2.1.6

(3) 2.1.7 (3)

2.2 Given:

2.2.1 Solve the given inequality, for . (2) 2.2.2 State the answer to (2.2.1.): 2.2.2.1. on a number line. (2) 2.2.2.1 in interval notation. (2)

2.3 solve for and :

(4)

[ ]


CALCULATORS MAY NOT BE USED IN THIS QUESTION 3.1 Simplify fully:

3.1.1 (

)

√

( ) (4)

3.1.2

(3)

3.2 Factorise fully:

(2)

3.3 Solve for

3.3.2 √ (3) 3.3.3 (4)

[ ]


1.1 Write ̇ as an improper fraction, showing all working out;

Calculators may not be used. (3)

1.2 Show between which two consecutive whole numbers √

lies; show all working out and do notuse a calculator. (2)



1.3 Given; √

write down a value of which will result in being:

1.3.1 Non-real (1)

1.3.2 Undefined (1)

[ ]


2. Multiply out and simplify as far as possible: 2.1 ( ) (2)

2.2 (

) (

) (2)

2.3 ( )( ) ( ) (3) 2.4 ( )( ) (3)

[ ]


3. Simplify fully, leaving your answer as a single a single term:

3.1

(2)

3.2

(6)

3.3

(4)

The area of a rectangle is given by The breadth of the rectangle is given by the expression

Calculate the length in terms of where (3)

[ ]


Factorise fully:

4.1 ( ) (3) 4.2 (2) 4.3 ( ) ( ) ( ) (3) 4.4 (3)

4.5

(3)

4.6 (3)

4.7

(2)

[ ]


5.1 Simplify, leaving your answer with no negative exponents:



(4)

5.3 If evaluate:

5.3.1 (1)

5.3.2 (

)

(3)


6. Solve for

6.1 (1) 6.2 (3)

6.3

(4)

6.4 √

without a calculator (3) 6.5 (3) 6.6 (3)

6.7

(3) 6.8 (3)

[ ] QUESTION 7(JUNE 15 HUD)

7.1.1 Solve for (2)

7.1.2 Express your solution to 6.2.1:

7.1.2.1 on a number line (1)

7.1.2.2 in interval notation (1)

7.2 Solve for and

(4)

[ ]


1.1 Determine the product of the following and simplify fully: ( )( ) (2)

1.2 Factorise the following expression fully:

(3)



1.3 Simplify the following expression fully:

(5)

[ ]


2.1 The total surface area of a closed right cylinder is given by Write down the height of the cylinder, in terms of and (2)

2.2 Solve for and if: and (4)

2.3 Solve the following inequality: Hence, illustrate your answer on a number line if x is a real number. (4) 2.4 Solve for ( )( ) (4) 2.5 The length of a rectangle is longer than its breadth. If the area of the rectangle is ,

calculate the length of the rectangle. (4)

[ ]


If and calculate the value of

[ ]


4.1 Without using a calculator, simplify the following expressions fully:

4.1.1 ( ) (

)

(4)

4.1.2

(4)

4.2 Solve for in of the following equations: 4.2.1 (1)

4.2.2 (3)

[ ]


If determine the value of [ ]


The area of a square is .

6.1 Is the length of the side of the square a rational number or an irrational number? Explain your answer. (2)

6.2 Without calculating the length of the side of the square, show that its value lies between and



[ ]


A calculator may not be used in this question.

1.1 Complete the following table using Y (Yes) and N (No).

√

(1)

1.2 If is a positive write down one value for x so that

√

Will be:

1.2.1 Rational (1)

1.2.2 Non- Real (1)

1.2.3 Equal to zero (1)

1.2.4 Undefined (1)

1.3 Between which two consecutive natural numbers does √

lie. Show all your working out. (3)

1.4 Write ̇ ̇ as an improper fraction. Show all your working out. (3)

[ ]


2.1 Multiply out then simplify the following:

2.1.1 ( ) (2)

2.1.2 ( )( ) (2)

2.1.3 ( ) (2)

2.2 What is the value of , if ( ) is a factor od (2)

[ ]


Factorise the following fully:

3.1 (2)

3.2

(2)



3.3 ( ) ( ) (4)

3.4 (3)

3.5 (2)

3.6 (3)

3.7

(2)


4.1 Simplify the following, without the use a calculator:

(3)

4.2 Write the following as a single term:

(2)

4.3 Simplify fully:

(4)


Solve for in each of the following:

5.1 (2)

5.2

(5)

5.3 ( ) (4)

5.4 (3)

5.5 ( )( ) (4)

5.6

(2)

[ ]


6.1.1 Solve for (2)

6.1.2 Write your answer to 6.1.1 in interval notation (2)

6.1.3 Represent your answer to 6.1.1 on a number line (1)



6.2 Solve for and repectively

Given:

(4)

[ ]

QUESTION 1 (MAY 07 BISHOPS)

1.1 √ √ √

√

√

From the numbers above write down

(a) two rational numbers

(b) a positive irrational less than

(c) the biggest

(d) the one nearest in value to 1

(e) a number whole square is irrational ( )

1.2.1 Which integer is closest to √ ? (1)

1.2.2 Write down in exact form an irrational number between and (2)

1.3 A decimal fraction starts after that each successive digit is the remainder when four times the

previous digit is divided by

(a) Find the first of this fraction (3)

(b) Express ̇ ̇ as a rational number (4)

[ ]

QUESTION 2 (MAY 07 BISHOPS) 12 marks

2.1 Multiply out and simplify ( )( ) (2)

Factorise 2.2.1 (1)

2.2.2 ( ) ( ) (3)

2.2.3 ( ) ( ) ( ) (3)

2.2.4 (3)


3.1 Solve for if

3.1.1 ( ) ( ) (2)

3.1.2

(3)



3.1.3 ( ) ( )( ) (4)

3.2 The numerator of a fraction is smaller than the denominator by . If the numerator is now increased

by = , the value of the fraction increases by Set up an equation and hence determine what the

original fraction was. (5)

[ ]


4.1 Make the subject of

(3)

4.2 Given an object, a lens and the image of the object formed by the lens, if the object itself is at a

distance from the lens, and the focal length of the lens is then the distance away from the lens of

the image is where

Show how we can change this formula so as to be able to calculate for any values of and (4)

[ ]


5.1 Solve for if

5.1.1 ( )( ) (2)

5.1.2 (2)

5.1.3 ( )( ) (4)

5.2 Solve for if

(4)

[ ]


6.1 Solve the following inequality and illustrate your answer on a number line: ( ) ( ) (4)

6.2 If the length of the rectangle is and it breadth is and the sides of the square are given by

. It is known that the area of the rectangle is greater than the area of the square. Find the

possible values of (4)

[ ]


7.1 Simplify

7.1.1

(3)



7.1.2

(4)

7.1.3

(3)

7.2 If it is known that find the value of

(3)

[ ]

QUESTION 1 (NOV 18)

1.1 Factorise the following expressions fully:

1.1.1 (2)

1.1.2 (2)

1.1.3 (3)

1.2 Simplify the following expressions fully:

1.2.1 ( )( ) (2)

1.2.2

(3)

1.2.2

(3)

1.3 Determine the value of ( ) if and (3)

[18]

QUESTION 2 (NOV 18)

2.1 Solve for

2.1.1 (2)

2.1.2 (3)



2.1.3 (

)

(3)

2.2 Given:

2.2.1 Solve for (2)

2.2.2 Hence, write down the number of integers that satisfy the inequality. (1)

2.3 Solve simultaneously for and (4)

and

[15]

HUD JUNE 19





algebra, equations & inequalities · 2020. 6. 24. · GRADE 10-ALGEBRA, EQUATIONS AND INEQUALITIES 2 BY: AYANDA DLADLA CELL NO: 074 9947970 QUESTION 1 (NOV 12 HUD) 1.1 Given: ( )

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