Revision For Maths
Year 7 :
This booklet will help you Catherine Pass Your End
of year 7 test xo.
Negative numbers:
Negative numbers are less than zero: -1, -2, -3, -4, -5, etc. A number line can be used to order negative and
positive numbers. Zero, 0, is neither positive nor negative.
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The sum of two negative numbers is a negative number. For example, -5 + (-1) = -6
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The sum of a positive number and a negative number is the difference between two
numbers. The sign of the bigger absolute value is placed before the result. For example, -9 +
3 = -6
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The product of a negative number and a positive number is a negative number. For example,
-9 × 2 = -18
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The product of two negative numbers is a positive number. For example, -6 × -3 =18
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While dividing negative numbers, if the signs are the same, the result is positive. For
example, -56 ÷ -7 = 8
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While dividing negative numbers, if the signs are different, the result is negative. For
example, -32 ÷ 4 = -8
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When we need to subtract a positive number from a positive number, we follow the
subtraction rule given above. For example, 5 - (+6) becomes 5 + (-6) = 5 - 6 = -1
Multiplying by 10,100,1000:
When we multiply by 10, 100 and a 1000 we shift all the digits to the left. One place left for 10, two places
left for 100 and three places left for 1000. When we divide by 10, 100 and a 1000 we do the opposite and
shift all the digits to the right instead.
Ordering decimals:
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Set up a table with the decimal point in the same place for each number.
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Put in each number.
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Fill in the empty squares with zeros.
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Compare using the first column on the left.
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If the digits are equal move to the next column to the right until one number wins.
Estimating:
The general rule for estimating is to look at the digit to the right of the digit you want to estimate.
Estimating or rounding to the nearest whole number means looking at the digit to the right of the
decimal. If you see a digit greater than 5, round up, and if it's less than 5, round down.
Adding, Subtracting, Multiplying, Dividing Decimals:
You should become efficient in using the four basic operations involving decimals—addition, subtraction,
multiplication, and division. To add or subtract decimals, just line up the decimal points and then add or
subtract in the same manner you would add or subtract whole numbers.
Sequences:
Sequences can be linear, quadratic or practical and based on real-life situations. Finding general rules
helps find terms in sequences.
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Number sequences are sets of numbers that follow a pattern or a rule.
If the rule is to add or subtract a number each time, it is called an arithmetic sequence.
If the rule is to multiply or divide by a number each time, it is called a geometric sequence.
Each number in a sequence is called a term.
A sequence which increases or decreases by the same amount each time is called a linear
sequence.
The term to term rule of a sequence describes how to get from one term to the next.
How to find the nth term. To find the nth term, first calculate the common difference. Next multiply each
term number of the sequence (n = 1, 2, 3,) by the common difference. Then add or subtract a number
from the new sequence to achieve a copy of the sequence given in the question.
Perimeter and Area:
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The area is the measurement of space enclosed by a closed geometric figure. Like the perimeter
formula, there is also a set of area formula for polygons that can be represented using
algebraic expressions.
For example, if you want to know the area of a square box with side 40 cm, you will use the formula:
Area of Square = a2, where a is the side of the square.
Similarly, the area of a triangle can also be found using its Area formula (1/2 × b ×h).
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A Perimeter is the length of the boundary of a closed geometric figure. Algebraic expressions can
be used to represent the perimeter formula for the regular polygons. Say that the length of each
side of a regular polygon is l. The perimeter of shapes formula for each of the polygons can be
given using the same variable l.
Example: To find the perimeter of a rectangular box, with length as 6 cm and Breadth as 4 cm, we need to
use the formula,
Perimeter of a Rectangle = 2 (L+B) = 2 (6 cm + 4 cm) = 2 × 10 cm = 20 cm.
Volume:
Volume = a³ , where a is length of each side. Volume = l × w × h , where l is length, w is width and h is
height. Volume = 4/3 πr³ , where r is the radius. Volume = πr²h , where r is the radius and h is the height.