latihtubi pmr 2010

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Review Exercise for PMR 2010: 1. By completing the factor trees, write down the prime factors of the given numbers. 1. (c) (b) (d) 2. Answer the question below by filling the correct number in the box given. (a) (b) 1 −3 −2 −1 2 0 1 4 3 (+7 ) + = +7 −1 0 1 2 3 4 5 (+ 5) + −1 = +5 24 × 6 × × × × × 24 = × × × 54 = × 54 × × × × × 24 = × 75 × × × 5 18 3 × 6 × × × × 18 =

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Page 1: Latihtubi PMR 2010

Review Exercise for PMR 2010:

1. By completing the factor trees, write down the prime factors of the given numbers.

1. (c)

(b) (d)

2. Answer the question below by filling the correct number in the box given.

(a)

(b)

(c)

1

−3 −2 −1 2 0 1 4 3

(+ 7)+ =

+7

−2 −1 0 1 2 3 4

+ −2=

−1 0 1 2 3 4 5

(+ 5)

+ −1=

+5

24

× 6

× × ×

× ×24 = ×

× ×54 = ×

54

×

× × ×

×24 = ×

75

× × ×

5

18

3 × 6

× ×

× ×18 =

Page 2: Latihtubi PMR 2010

Review Exercise for PMR 2010:

(d)

3. Find the value of the following.(a) (18 − 7) × (3 + 9) =

(b) 4(35 ÷ 5 + 2) − 14 =

(c) 80 + (9 × 6 − 10) ÷ 11 =

(d) 109 − (23 × 3 + 74 ÷ 2) =

4. Calculate each of the following:(a) 4.13 – (–4.838) ÷ (–2.05) =

(b) (–21.3) + 3.66 × 7.55 – (–0.84) =

(c) 1.1 × (–6.34) + (–18.75) ÷ 2.5 =

(d) 8.109 – (–28.707) ÷ 10.5 + (–14.06) =

2

−6 −5 −4 −1−3 −2 1 0

+ =

Page 3: Latihtubi PMR 2010

Review Exercise for PMR 2010:

5. Calculate each of the following.

(a) =

(b) =

(c) =

(d) =

6. Find the value of the following:(a) 0.052

(b) (21 – )3

7. Determine the value of the following:(a) (–0.02)3

(b) (13 – )2

8. Find each of the following:

(a)

(b) ( – 33)2

3

Page 4: Latihtubi PMR 2010

Review Exercise for PMR 2010:

Algebraic Expression:

1. Simplify each of the following.(a) m + 3m (e) 5n – 7n

(b) –2p – 11p (f) –9t + 13t

(c) 32p – 19p (g) 3r –

(d) + (h) – –

2. Simplify each of the following:(a) (4py + 4) – (–3py – 2)

(b) (–13tq – 9kbc) – (3kbc + 15tq)

(c) (7auv + 4bpq2) – (auv – 8bpq2)

(d) (4t2q2 – 10abc) – (–4abc + 10t2q2)

3. Expand each of the following:(a) p(4qr + 1)

(b) 2r(5rs – 3p)

(c) –4m(6mn + n2 – 3)

(d) bc(10b – 4c)

4. Factorise each of the following:

(a) 3q2 + 4pq

(b) 8mn – n

(c) 6 + 12a

(d) 3ac – 2ab

(e) x2 – 4

(f) 36 – y2

(g) 9h2 – k2

(h) 169m2 – 100n2

4

Page 5: Latihtubi PMR 2010

Linear Equations:

1. Simplify each of the following:(a) x + 3 = 7 (b) k + 5 = 11 x + 3 – = 7 – k + 5 – = 11 –

x = k =

(c) u – 8 = 5 (d) z – 5 = –12 u – 8 + = 5 + z – 5 + = –12 + u = z =

2. Simplify each of the following(a) 2p = 12 (b) 5q = –20

= =

p = q =

(b) = 1 (d) = –2

× = 1 × × = –2 ×

w = z =

3. Solve the following linear equations.(a) 3 + 2h = 3 (b) 5k + 1 = 11

(b) 10m – 2 = 8 (d) –6 + 3n = –18

(c) – 10 = –2 (f) + 8 = –3

(d) + 5 = 9 (h) – 1 = 4

Page 6: Latihtubi PMR 2010

Geometrical Constuctions

1) By using a protractor, measure the angle x.

(a) (b)

(c) (d)

2) Construct a triangle JKL with sides JK = 6 cm, KL = 5cm and JL = 4 cm.

3) Construct :a) Perpendicular bisector of line AB.

b) Perpendicular to the line PQ that passes through point T.

c) Perpendicular line from P to AB.

d) Parallel line to AB at a distance of 1.5cm.

A B

P QT

A B

P

A B

Page 7: Latihtubi PMR 2010

e) Angle ABC = 600.

f) Angle PQR = 1200.

4)

Beginning with the two straight lines LE and ET given in the diagram, a) construct the quadrilateral LETH such that ELH = 60° and LH = LE,

i) HP, the bisector of the angle LHT such that P lies on the straight line LE,ii) LG, the perpendicular from L to the straight line TH produced such that THG is a

straight line.b) Measure the angle GLH.

A B

P Q

Page 8: Latihtubi PMR 2010

Loci in two dimension1.

The diagram shows a regular hexagon ABCDEF with sides of length 4 cm. G is the midpoint of CF.

c) A point X moves inside the hexagon ABCDEF such that its perpendicular distances from AB and AF are equal. Describe the locus of X.

d) On the diagram, construct i) the locus of the point Y that moves inside the hexagon ABCDEF such that its

perpendicular distance from the line AC is 3 cm.ii) the locus point Z that moves inside the hexagon ABCDEF such that its distance

from the point G is 3 cm.e) State the number of points of intersection of the locus of X and the locus of Y.f) Mark with the symbol all the points that satisfy the conditions of the locus of Y

and the locus of Z.

Page 9: Latihtubi PMR 2010

2.

In the diagram, the x-axis and the y-axis are drawn on square grids with sides of length 1 cm. Three points X, Y and Z move inside the quadrilateral GHKP.

(a) Construct the locus of the(i) point X such that JX = 2 cm.(ii) point Y such that it is equidistant from the lines HG and HK.(iii) point Z such that its perpendicular distance from the x-axis is 1 cm.

(b) State the coordinates of all the points that satisfy the conditions of the locus Y and locus Z.

(c) Mark with the symbol , all the points that satisfy the conditions of locus X and locus Z.

Page 10: Latihtubi PMR 2010

Transformations:

1) In the diagram, the line HL is the axis of a reflection.

i. Draw the image of the triangle ABC under the reflection.ii. State the coordinates of the images of point B and point C under the

reflection.

2.

The diagram shows two parallelograms M and N. M is the image of N under a transformation.

i. Describe in full the transformation.ii. Point (–1, k) is the image of point (f, 9) under the same

transformation. Determine the values of f and k.

Page 11: Latihtubi PMR 2010

3.

In the diagram, quadrilateral F is the image of quadrilateral W under a clockwise rotation about the centre P.(b) State the angle of rotation.(c) Point M' is the image of the point M under the same rotation. Find the coordinates

of M'.

Page 12: Latihtubi PMR 2010

Solid Geometry

1.

The diagram shows a solid consisting of a cuboid and a right pyramid. If the height of vertex M of the right pyramid from the base PQRS is 12 cm, calculate the surface area of the solid.

2. The diagram shows a solid consisting of a right cylinder and a hemisphere. By taking

π = , calculate the surface area of the solid.

3.

The diagram shows a solid consisting of a hemisphere and a right cone. The diameters of the hemisphere and the base of the cone are 10 cm whereas the slant height of the cone is 13 cm.

(a) Calculate the height of the cone.

(b) By taking π = , calculate the volume of the solid.

4.

The diagram shows a solid consisting of a cuboid and a semi cylinder of height 7 cm. By

taking π = , calculate the curved surface area of the solid and the volume of the solid.

Page 13: Latihtubi PMR 2010

Statistics:

1. A school has 75 classrooms. The number of students in each classroom is shown in the frequency table below.

Number of students

35 36 37 38 39 40

Frequency 10 5 12 k 14 16

(a) Find the value of k.(b) Calculate the percentage of the total number of classrooms in the school that

has more than 37 students in each classroom.2.

The pictogram above shows the number of cars leaving a car park during a period of time.

(a) State the total number of cars leaving the car park.(b) If the rate of parking is fixed at RM1.80 per car per entry, calculate the total

collection received.

3.

The composite bar chart shows the number of workers in three factories X, Y and Z.

(a) Find the difference between the total number of male workers and the total number of female workers in the three factories.

(b) It is given that the average ages of the male and the female workers are 34 years and 28 years respectively. Calculate the average age of all the workers in the three factories.

Toyota

Proton Wira

Ford

Honda

represents 5 cars

Page 14: Latihtubi PMR 2010

4.

5. The line graph shows the total export of durians from the years 1989 to 1993 of a state.

(a) Find the total export of durians for the five years.(b) Determine the percentage decrease in the total (c) export of durians between 1990 and 1991.(d) Given that the total export of durians for 1993 is (e) 4% less than the total export for 1994. Calculate (f) the total export of durians for 1994.

6.

Colour Green Red Yellow Blue White

Number of children 24 x 6 18 22

Angle Of sector

The table shows the colour of shirts worn by a group of 80 children.i. Find the value of x.

ii. Calculate the angle of each sectoriii. Construct a pie chart to represent the information given in the table.

Page 15: Latihtubi PMR 2010

Polygon

(1) Copy and complete the table below.

Regular polygon

Number of triangles Sum of the interior angles

Equilateral triangle

Square

Pentagon

Hexagon

Heptagon

Octagon

2) Copy and complete the table below.

Regular polygon

Number of sides

Exterior angle

Interior angle

Equilateral triangle

Square

Pentagon

Hexagon

Heptagon

Octagon

3) By using formula, find the sum of the interior angles for the regular polygon that has

a) 7 sidesb) 9 sidesc) 10 sidesd) 14 sides

Page 16: Latihtubi PMR 2010

4) Copy and complete the following table.

Interior angle

108° 162° 140°

Exterior angle

90° 15°

Number of sides

5) Find the value of p + q in each of the following polygons.

(a) (b) (c)

Page 17: Latihtubi PMR 2010

Indices

1) Simplify x7y2 ÷ (x4y–1)3.

2) Calculate the value of 3 × 30 × .

3) It is given that 53 ÷ = 57. Find the value of w.

4) Simplify (fk – 3)6 ÷ (f –1k2)2.

5) Calculate the value of 27 × .

6) Simplify (2p7q2)3 × (p–2q5)2.

Algebraic Formulae

7) It is given that v = (x + 6y)hk.

a) Expressi) x in terms of h, k, y and v.

ii) y in terms of h, k, x and v.

b) Findi) the value of x when h = 3, k = 4, y = 2 and v = 150.

ii) the value of y when h = 2, k = 5, x = 26 and v = 235.

Linear Inequalities

6) Determine the solution for each of the following linear inequalities.

(a) 2x − 1 > 9

(b) 6x + 2 ≤ −10

(c) 7 − 4x ≥ 3

(d) −3 − x < −5

Tranfomations : Similarity

Page 18: Latihtubi PMR 2010

1) The following pairs of triangles are similar. Find the values of x and y.

(a)

(b)

2)

In the diagram, ABE and ACF are straight lines. If AE = 8 cm and AF = 10 cm, find the length of

(a) AC(b) BC

3) Scale drawing:

The figure in the diagram is drawn on square grids. By using the scale of 1 : 2, draw the figure on the given square grids.

Graph of functions

Page 19: Latihtubi PMR 2010

1) Copy and complete the table below for y = 13 − 6x.

2) Copy and complete the table below for y = 10-2x.

3) By using the scales and the table of values given, draw the graph of the following functions.

a) y = x 3 − 8, −2 ≤ x ≤ 3

i) 1 : 1 on the x-axisii) 1 : 5 on the y-axis

b) y = 2 − x − x2 , −3 ≤ x ≤ 3

i) 1 : 1 on the x-axisii) 1 : 4 on the y-axis

c) y = x2 − 5x + 4, −1 ≤ x ≤ 6

i) 1 : 1 on the x-axisii) 1 : 2 on the y-axis

d) y = 3x3 − 27x, −3 ≤ x ≤ 3

i) 1 : 1 on the x-axisii) 1 : 5 on the y-axis

Rates, Ratios and proportions (Average Speed)

x -6 -3 3 7

y

x -5 -2 4 6

y

x − 2 − 1 0 1 2 3y − 16 − 9 − 8 − 7 0 19

x − 3 − 2 − 1 0 1 2 3y − 4 0 2 2 0 − 4 − 10

x − 1 0 1 2 3 4 5 6y  10 4 0  − 2  − 2   0 4 10

x − 3 − 2 − 1 0 1 2 3y 0 30 24 0 − 24 − 30 0

Page 20: Latihtubi PMR 2010

1. Complete the table below:

2. Gurhan walks at an average speed of 6 km/h for 15 minutes to his friend’s house and then

cycles at an average speed of 15 km/h for 1 hours. Calculate

a. the total distance travelled,b. the average speed for the whole journey.

Initial speed Final speed Time taken Acceleration

(a) 10 m/s 18 m/s 16 s

(b) 22 m/s 21 s m/s2

(c) 9 m/s 10 s − m/s2

(d) 24 m/s 20 m/s − m/s2