DIRECTED NUMBERS

Calculate the value of

1.

-9 6 (-3) 3 =

2.

(-3 6) 9 (-4) =

3.

-64 [ 8 (-4)] 16 =

4.

[ 7 (-5) + 8 ] (-16) =

5.

-28 (-7) 2 (-3) 6 =

6.

-12 16 5 =

7.

24 4 (5-8) =

8.

-25 (-10 + 5) - (-29) =

9.

21 3 (-16) =

10.

-24 8 -14 =

INTEGER, FRACTION AND DECIMAL.

1. ( )432.114 =

2. Calculate the value of 56

52

32

and express the answer as a fraction in its

lowest terms. .

3. Calculate the value of ( ) 4.012.71071 and express the answer correct to the

two decimal places.

4. Evaluate 856.512

5. Calculate the value of

+

21

549.0 and express the answer as a decimal.

6. Calculate the value of ( ) )5(8.461

+

7. Calculate the value of ( )542.020

8. Calculate the value of

54

435.1 and express the answer as a decimal.

.

SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

1.

a) =

b)

2.

a)

b)

3

a)

b)

4.

a)

b)

5.

a)

b)

6.

a)

b)

7.

a)

b)

8.

a)

b)

9.

a)

b)

10.

a)

b)

ALGEBRAIC EXPRESSIONS

1. Expand each of the following expressions

(a) ( )212 x =

(b) ( )223 x = (c) ( )234 +k =

(d) ( )243 +x =

(e) ( )214 x =

(f) ( )223 m =

(g) ( )225 +r =

(h) ( )22 kx =

(i) ( )23 qp =

(j) ( )24 nm + =

(k) ( )25qp =

(l) ( )22 yx =

(m) ( )223 ts + =

(n) ( )22yx =

2 Simplify each of the following expressions:

(a) ( )x 432 = (b) ( )qpqp 5232 =

(c) ( )1235 + yy =

(d) ( )nmnm 2325 + =

(e) ( ) ( )qpqp 3223 + =

(f) ( ) ( )kxkx 5342 =

(g) ( ) ( )gfgf + 4233 =

(h) ( ) ( )mkmk 52324 ++ =

(i) ( )yxyx 3524 + =

(j) ( ) srsr 54323 + =

(k) ( ) yxyx 232 + =

(l) ( ) nmnm 5723 + =

(m) ( )622

64+

kk =

(n) 533

96+

xx

=

LOCI

1. The diagram in the answer space shows a square KMLN drawn on a grid of equal squares with side of 1 unit.

X, Y and Z are three moving points in the diagram. (a) X moves such that it is equidistance from the straight lines KN and LM.

By using the letters in the diagram, state the locus of X. (b) On the diagram, draw,

(i) the locus of point Y, such that its distance from point M is always 7 units.

(ii) The locus of point Z, such that it is equidistant from the straight line KL and LM

(c) Hence, mark all the possible positions of the intersection of the loci of the locus of Y and the locus of Z with symbol .

Answer:

(a) ..................................................................................

(b) and (c)

K L

N M

O

P R

Q

2. The diagram in the answer space shows two congruent squares ABEF and BCDE of sides 4 units. X, Y and Z are three moving points inside the diagram. (a) Using the letters in the diagram, describe the locus of point X which moves

such that it is equidistant from points A and point C. (b) On the diagram, construct

(i) the locus of the point Y such that it is constantly 4 units from point E. (ii) the locus of the point Z which moves such that it is equidistant from

line AB and line AF.

(c) Hence, mark with the symbol the intersection of the locus of Y and the locus of Z.

Answer:

(a) (b) and (c)

F E D

A B C

3. The diagram in the answer space provided shows a square ABCD. P, Q, R and S are the midpoints of AB, BC, CD and AD respectively.

X, Y and Z are the three points that move in the diagram. (a) X is the point which moves such that it is equidistant from the straight lines

AB and AD. By using the letters in the diagram, state the locus of X. (b) On the diagram, draw (i) the locus of point Y, such that OY = OP. (ii) the locus of point Z such that it is constantly 2 cm from the line SQ. (c) State the number of intersection of the locus of Y and the locus of Z.

Answer:

(a) .

(b) and (c)

S

D

Q O

R C

A B P

4. The diagram in the answer space is drawn on a square grid of sides 1 unit. W, X and Y are three moving points on the diagram. (a) W is a moving point such that it is always equidistant 2 units from the line

KN. Describe in full the locus of W. (b) On the diagram, draw

(i) the locus of X such that AX = AD (ii) the locus of Y such that BY = YD.

(c) Hence, mark with symbol all the intersection of the locus X and the locus of Y.

Answer:

(a) .

(b) and (c)

D C

K N

A B

5. The diagram in the answer space shows a rhombus. S, X and Y are three moving points in the diagram.

(a) S is a moving point which moves such that its distance from points A and point C are the same. By using he letters in the diagram, state the locus of S.

(b) On the diagram, draw (i) the locus of point X that is constantly 2 cm from the line AC. (ii) the locus for the point Y that is constantly 4 cm from the point A.

(c) Hence, state the number of intersection points of the locus of X and the locus of Y.

Answer:

(a) ..

(b) and (c)

D

C

B

A

6. Diagram in the answer space shows a square PQRS drawn on a grid of equal squares with sides of 1 unit. M, X and Y are three moving points in the diagram. (a) M is the point which moves such that its distance from point Q and point S

are the same. By using the letters in the diagram, state the locus of M (b) On the diagram, draw (i) the locus for the point X that is constantly 5 units from the line QR (ii) the locus for the point Y that is constantly 7 units from the point R

(c) hence, mark with the symbol the intersection of the locus of X and the locus of Y

S

Q R

P

7. Diagram in the answer space shows a square JKLM drawn on a grid of equal squares with sides of 1 unit. W, X and Y are three moving points in the diagram .

(a) W is the point which moves such that its equidistant from the straight line JK and JM. By using the letters in the diagram, state the locus of W

(b) On the diagram, draw (i) the locus for the point X that is constantly 5 units from the point J. (ii) the locus for the point Y that is constantly 4 units from the straight

line KL.

(c) Hence, mark with the symbol the intersection of the locus of X and the locus of Y.

K

M L

J

8. Diagram in the space answer shows a square, ABCD .Point J, K and L move in the diagram. (a) J is a point that moves with equal vertical distance from the straight lines AD

and BC .Draw locus J. (b) In the answer space, draw

(i) locus K such that it is 4 cm from point C (ii) locus L such that it is 4 cm from point B

(b) Mark on all points of intersection of locus K and L

C D

B A

9. It is given that ABC is a right-angled triangle with the side of 3, 4 and 5 units respectively.

(a) Construct the locus of a moving point P in the diagram, which is always has a perpendicular distance from the straight line AC of 2 cm.

(b) Construct the locus of point Y such that its distance from the straight lines AB and BC is always the same.

(c) State the number of intersection points of two loci.

B C

A

10. The diagram below shows a rectangle ABCD. In the same diagram, construct the locus of

(a) point X which moves in such a way that its distance from A is always 3 cm. (b) point Y which moves in such a way that it is always equidistant from lines

AC and BD.

Hence, mark the point/points of intersection of the two loci using the symbol .

A B

D C

ALGEBRAIC FORMULAE

1. Given that 243 rqp = , express q in term of p and r.

2. Given that dnaT )1( += , express d in term of T, a and n.

3. Given that t

uts

543 2

= , express u in

term of t and s.

4. Given vuf111

+= , express f in term of u and v.

5. Given that )3(4 qpp = 5, express q in term of p.

6. Given that pr 53 2 = , express r in term of p.

LINEAR EQUATIONS

Solve each of the following equations:

1. a) 4y 5 = 5y

b) 74

23=

x

2. a) 20

45

=

m

b) 974

3=+

x

3. a) 4

32

=p

b) 43

2+=

tt

4. a) 5x 16 = x

b) 3

64 =+ kk

5. a) 3x = 5x 8 b)

52

43 yy +

=

6. a) p + 18 = 4p

b) ( ) 13135 = yy

7. a) 12

43

=r

b) ( ) xx 2631

=+

8. a) 248 = y

b) ( ) xx = 423

9. a) mm = 16

b) 25

3+= pp

10. a) 83 =+k

b) 3354 nn +=

LINEAR INEQUALITIES

1. a) Solve the inequality 3 + x 4

b) List all the integer values of v which satisfy both the inequalities 43

v 1 and 11 v < 0

2. Solve the inequality 9 4x < 6 x

3. List all the integer values of v which satisfy both the inequalities

3v 1 and 1 2v < 3

4. a) Solve the inequality 5 + x 2 . b) List all the integer values of x which satisfy both the inequalities 3x + 1 > 2 and

3x + 1 13.

5. a) Solve the inequality 3 + y > 2.

b) List all the integer values of y which satisfy both the inequalities 21 2y 9

and 2y

+ 3 > 2.

6. a) Solve the inequality 3 + y 17

b) List all the integer values of y which satisfy both the inequalities 12

y 3 and 4 y < 6

7. a) Solve the inequality 4x + 5 > 4 + 3x

b) List all the integer values of x which satisfy both the inequalities 7 5x 12 and 16