Unit 11
Maju Minda
Maju Minda
Ulang kaji semua kemahiran dalam bab Koordinat, Nisbah dan Kadaran.
Jawab setiap soalan. Jika salah, baca petunjuk dan cuba lagi.
全章复习 = ulang kaji bab
这一课把坐标、比和比例的技能全部复习一次：读坐标、描点、轴上的点、写比、先换单位、单一法，以及用条形模型解比的问题。每一题答错时，先打开抽屉看方法，再试一次。
例子：看到“1 克比 1 公斤”，要想到先换单位。
注意：每一题都先想清楚它考的是哪一个技能。
chapter revision = ulang kaji bab
This lesson revises every skill in coordinates, ratio and proportion: reading coordinates, plotting, points on the axes, writing ratios, changing units first, the unitary method, and solving ratio problems with bar models. If you get a question wrong, open the drawer to see the method and try again.
Example: when you see '1 g to 1 kg', remember to change the units first.
Watch out: for each question, first decide which skill it is testing.
Satah Cartes
Titik persilangan paksi-x dan paksi-y dinamakan …
两轴的交点 = titik persilangan paksi
横轴和纵轴在左下角相交，这一点是所有坐标开始数的地方，用字母 O 表示。想一想它的马来文名称。
例子：数坐标 (3, 2) 时，手指从这一点出发。
注意：坐标是两个数字，轴是一条线，这些都不是这个点的名称。
where the axes meet = titik persilangan paksi
The x-axis and the y-axis meet at the bottom-left corner; this is where every coordinate is counted from, and it is marked with the letter O. Think of its Malay name.
Example: when counting (3, 2), your finger starts at this point.
Watch out: a coordinate is a pair of numbers and an axis is a line; neither is the name of this point.
Baca koordinat
Apakah koordinat titik K?
读坐标 = baca koordinat
从原点往右数到点的正下方，写第一个数字；再往上数到点，写第二个数字。图上有一个点的两个数字一样但次序相反，小心不要选错。
例子：往右 5、往上 1 → (5, 1)。
注意：先横后竖。
reading a coordinate = baca koordinat
Count right from the origin until you are below the point for the first number, then count up to it for the second. One point on the grid has the same numbers in the opposite order, so do not pick the wrong one.
Example: 5 right and 1 up → (5, 1).
Watch out: across first, then up.
Titik pada paksi
Titik M terletak pada …
轴上的点 = titik pada paksi
先读出这个点的坐标，看哪一个数字是 0：第一个数字是 0，点不往右走；第二个数字是 0，点不往上走。再想想它落在哪一条轴上。
例子：(6, 0) 在横轴上。
注意：原点是两条轴的交点，坐标是 (0, 0)。
a point on an axis = titik pada paksi
Read the point's coordinate and see which number is 0: a first number of 0 means no movement right; a second number of 0 means no movement up. Then decide which axis it lies on.
Example: (6, 0) lies on the x-axis.
Watch out: the origin is where the two axes meet, at (0, 0).
Bentuk
Titik P (1, 1), Q (5, 1), R (5, 5) dan S (1, 5) disambungkan mengikut tertib. Bentuk apakah terbentuk?
连点成形 = sambung titik
先把四个点画在方格上，按次序连起来。再算每条边的长度：横边看第一个数字相差多少，竖边看第二个数字相差多少。四条边一样长、四个直角，是什么图形？
例子：(0, 0)、(3, 0)、(3, 1)、(0, 1) 连起来，长 3、宽 1，是长方形。
注意：要把四条边都算出来再判断。
joining points = sambung titik
Plot the four points on a grid and join them in order. Work out each side: for a horizontal side find the difference of the first numbers, for a vertical side the difference of the second numbers. Four equal sides and four right angles make which shape?
Example: (0, 0), (3, 0), (3, 1) and (0, 1) joined give a 3 by 1 rectangle.
Watch out: work out all four sides before deciding.
Nisbah
Apakah nisbah 1 g kepada 1 kg?
不同单位的比 = nisbah unit berbeza
两个量的单位不一样，要先把公斤换成克，两边都用克，再写比，最后不写单位。
例子：1 毫米比 1 米 → 1 毫米 : 1 000 毫米 → 1 : 1 000。
注意：1 公斤不是 100 克。
a ratio with different units = nisbah unit berbeza
The two quantities use different units, so change the kilogram into grams so both sides are in grams, then write the ratio without units.
Example: 1 mm to 1 m → 1 mm : 1 000 mm → 1 : 1 000.
Watch out: 1 kg is not 100 g.
Nisbah
Apakah nisbah panjang sisi kepada perimeter bagi sebuah segi empat sama?
边长和周长的比 = nisbah sisi kepada perimeter
正方形四条边一样长，周长就是四条边加起来，也就是一条边的几倍？把一条边看成 1 份，周长就是那么多份，再按题目的次序写比。
例子：等边三角形三条边一样长，边长比周长是 1 : 3。
注意：题目先说边长，所以边长写在前面。
side to perimeter = nisbah sisi kepada perimeter
A square has four equal sides, so its perimeter is all four sides added: how many times one side is that? Treat one side as 1 part; the perimeter is that many parts. Then write the ratio in the question's order.
Example: an equilateral triangle has three equal sides, so side to perimeter is 1 : 3.
Watch out: the side is mentioned first, so it is written first.
Kadaran
5 bungkus gula-gula berjisim 1.25 kg. Berapakah jisim 2 bungkus?
小数的单一法 = kaedah unitari dengan perpuluhan
先求一包的重量：1.25 公斤除以 5，可以先换成 1 250 克再除。再乘以 2。最后可以换回公斤。
例子：4 包共 2 公斤，1 包 0.5 公斤，3 包 1.5 公斤。
注意：小数点的位置要放对。
unitary method with decimals = kaedah unitari dengan perpuluhan
Find the mass of one packet first: 1.25 kg ÷ 5; you can change it to 1 250 g before dividing. Then multiply by 2 and change back to kilograms if needed.
Example: 4 packets weigh 2 kg, so 1 packet is 0.5 kg and 3 packets are 1.5 kg.
Watch out: put the decimal point in the right place.
Kadaran
Sebuah motosikal bergerak 180 km dalam 3 jam dengan laju yang sama. Berapakah jarak dalam 5 jam?
路程的单一法 = kaedah unitari untuk jarak
速度一样，先求 1 小时走多少公里（除以小时数），再乘以要求的小时数。
例子：2 小时 120 公里，1 小时 60 公里，4 小时 240 公里。
注意：算完用除法检查一次。
unitary method for distance = kaedah unitari untuk jarak
At the same speed, find the kilometres in 1 hour (divide by the hours), then multiply by the hours asked for.
Example: 120 km in 2 hours is 60 km in 1 hour and 240 km in 4 hours.
Watch out: check once with division afterwards.
Kadaran
6 buah buku latihan berharga RM16.80. Berapakah harga 10 buah?
钱的单一法 = kaedah unitari untuk wang
先求一本的价钱（除以 6），再乘以 10。可以把令吉换成仙来算。
例子：4 个 RM10.40，1 个 RM2.60，5 个 RM13.00。
注意：求出一本的价钱还不是答案，还要乘。
unitary method for money = kaedah unitari untuk wang
Find the price of one book (divide by 6), then multiply by 10. You can work in sen.
Example: 4 cost RM10.40, so 1 costs RM2.60 and 5 cost RM13.00.
Watch out: the price of one is not the answer yet; you still have to multiply.
Model palang
Nisbah setem Ali kepada setem Bala ialah 1 : 3. Bala ada 45 keping setem. Berapakah setem Ali?
比的条形模型 = model palang nisbah
1 : 3 表示 Ali 是 1 份，Bala 是 3 份。Bala 的数目是 3 份的总和，先求 1 份，Ali 就是 1 份。
例子：比 1 : 5，大的是 35，1 份是 7。
注意：Ali 的比较少，答案应该比 45 小。
bar model for ratio = model palang nisbah
1 : 3 means Ali has 1 part and Bala has 3 parts. Bala's number is the total of 3 parts; find 1 part, and Ali has exactly 1 part.
Example: with a ratio of 1 : 5 and the larger amount 35, 1 part is 7.
Watch out: Ali has fewer, so the answer should be less than 45.
Pergerakan
Seekor tupai di (2, 1) bergerak 3 unit ke kanan dan 4 unit ke atas. Di manakah tupai itu?
从别的点移动 = bergerak dari titik lain
不是从原点出发，所以要在原来的坐标上加：往右几格加在第一个数字，往上几格加在第二个数字。
例子：从 (1, 0) 往右 2、往上 3 → (3, 3)。
注意：不要把移动的格数直接当成坐标。
moving from another point = bergerak dari titik lain
The move does not start at the origin, so add to the starting coordinate: the units right go onto the first number and the units up onto the second.
Example: from (1, 0), 2 right and 3 up → (3, 3).
Watch out: do not use the movement itself as the coordinate.
Ringkasan