spm mathematics

1. MATHEMATICAL FORMULAE
RUMUS MATEMATIK
The following formulae may be helpful in answering the questions. The
symbols given are the ones commonly used.
Rumus-rumus berikut mungkin boleh membantu anda menjawab soalan.
Simbol-simbol yang diberi merupakan simbol yang biasa digunakan.
RELATIONS
PERKAITAN
1 𝑎 𝑚 × 𝑎 𝑛 = 𝑎 𝑚+𝑛
2 𝑎 𝑚 ÷ 𝑎 𝑛 = 𝑎 𝑚−𝑛
3 ( 𝑎 𝑚) 𝑛 = 𝑎 𝑚𝑛
4 𝐴−1 =
1
𝑎𝑑−𝑏𝑐
(
𝑑 −𝑏
−𝑐 𝑎
)
5 𝑃( 𝐴) =
𝑛(𝐴)
𝑛(𝑆)
6 𝑃( 𝐴′) = 1 − 𝑃(𝐴)
7 Distance / Jarak = √( 𝑥1− 𝑥2)2 − ( 𝑦1 − 𝑦2)2
8 Midpoint / Titik tengah
( x, y ) = (
𝑥1+𝑥2
2
,
𝑦1+𝑦2
2
)
9 Average speed =
distance travelled
time taken
Purata laju =
𝑗𝑎𝑟𝑎𝑘 𝑦𝑎𝑛𝑔 𝑑𝑖𝑙𝑎𝑙𝑢𝑖
𝑚𝑎𝑠𝑎 𝑦𝑎𝑛𝑔 𝑑𝑖𝑎𝑚𝑏𝑖𝑙
10 Mean =
sum of data
number of data
Min =
ℎ𝑎𝑠𝑖𝑙 𝑡𝑎𝑚𝑏𝑎ℎ 𝑛𝑖𝑙𝑎𝑖 𝑑𝑎𝑡𝑎
𝑏𝑖𝑙𝑎𝑛𝑔𝑎𝑛 𝑑𝑎𝑡𝑎
11 Mean =
sum of ( class mark ×frequency)
sum of frequencies
Min =
ℎ𝑎𝑠𝑖𝑙 𝑡𝑎𝑚𝑏𝑎ℎ ( 𝑘𝑒𝑙𝑎𝑠 𝑡𝑒𝑛𝑔𝑎ℎ ×𝑓𝑟𝑒𝑘𝑢𝑒𝑛𝑠𝑖)
ℎ𝑎𝑠𝑖𝑙 𝑡𝑎𝑚𝑏𝑎ℎ 𝑠𝑒𝑚𝑢𝑎 𝑓𝑟𝑒𝑘𝑢𝑒𝑛𝑠𝑖
12 Pythagoras Theorem 𝑐2 = 𝑎2 + 𝑏2
13 m =
𝑦2−𝑦1
𝑥2−𝑥1
14 m = −
𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝑥−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
SHAPES AND SPACES
BENTUK DAN RUANG
1 Area of trapezium =
1
2
× sum of parallel sides × height
Luas trapezium=
1
2
× ℎ𝑎𝑠𝑖𝑙 𝑡𝑎𝑚𝑏𝑎ℎ 𝑑𝑢𝑎 𝑠𝑖𝑠𝑖 𝑠𝑒𝑙𝑎𝑟𝑖 × 𝑡𝑖𝑛𝑔𝑔𝑖
2 Circumference of circle = πd = 2πr
Lilitan bulatan = πd = 2πj
3 Area of circle = π𝑟2
Luas bulatan = π𝑗2
4 Curved surface area of sphere = 2πrh
Luas permukaan melengkung sfera = 2πjt
5 Surface area of sphere = 4π𝑟2
Luas permukaan sfera = 4π𝑗2
6 Volume of right prism = cross sectional area × length
Isi padu prisma tegak = luaskeratan rentas × panjang

2. 7 Volume of cylinder = π𝑟2h
Isi padu kuboid = π𝑗2t
8 Volume of cone =
1
3
π𝑟2ℎ
Isi padu kon =
1
3
π𝑗2 𝑡
9 Volume of sphere =
4
3
π𝑟3
Isi padu sfera =
4
3
π𝑗3
10 Volume of right pyramid =
1
2
× base area × height
Isi padu pyramid tegak =
1
2
× 𝑙𝑢𝑎𝑠 𝑡𝑎𝑝𝑎𝑘 × 𝑡𝑖𝑛𝑔𝑔𝑖
11 Sum of interior angles of a polygon = ( 𝑛 − 2) × 180o
Hasil tambah sudut pedalaman poligon = ( 𝑛 − 2) × 180 𝑜
12
Arc length
Circumference of circle
=
Angle subtended st centre
360o
𝑃𝑎𝑛𝑗𝑎𝑛𝑔 𝑙𝑒𝑛𝑔𝑘𝑜𝑘
𝐿𝑖𝑙𝑖𝑡𝑎𝑛 𝑏𝑢𝑙𝑎𝑡𝑎𝑛
=
𝑆𝑢𝑑𝑢𝑡 𝑝𝑢𝑠𝑎𝑡
360 𝑜
13
Area of sector
Area of circle
=
Angle subtended at centre
3600
𝐿𝑢𝑎𝑠 𝑠𝑒𝑘𝑡𝑜𝑟
𝐿𝑢𝑎𝑠 𝑏𝑢𝑙𝑎𝑡𝑎𝑛
=
𝑆𝑢𝑑𝑢𝑡 𝑝𝑢𝑠𝑎𝑡
360 𝑜
14 Scale factor / Faktor skala,k =
𝑃𝐴′
𝑃𝐴
15 Area of image = 𝑘2 × area of object
Luas imej = 𝑘2 × 𝑙𝑢𝑎𝑠 𝑜𝑏𝑗𝑒𝑘