Maths
STAGE 9: WORKBOOK Cambridge Lower Secondary
Summary of key points
a5 means a × a × a × a × a
The number 5 is known as a power or index. It tells you how many times a is multiplied by itself. When you multiply, add the powers.
When you divide, subtract the powers.
an × am = an + m
Example: m2 × m4 = m6
3
1 Write these expressions in power form.
2 Match the equivalent expressions.
3 Write each expression as a single power of x.
4 Use ticks (✓) and crosses (✘) to mark Priti’s homework.
5 Complete these statements. a) tt t × 48 = b) tt t 311 × = c) t t t 14 5 = d) t tt t 10 2 × =
6 Explain why p4 × q3 cannot be simplified. …………………………………………………………………………………………………
7 Toni thinks that (d4)3 simplifies to d 7 . Treya thinks that it simplifies to d12 .
Who is correct?
Explain how you know.
8 Draw a ring around the pair(s) of numbers that give the same value for xy and yx.
Think about
9 Make up 10 questions involving multiplication and division of indices that simplify to y10 .
5.4 Algebraic fractions
Summary of key points
To manipulate algebraic fractions, you apply the same rules as you use for arithmetic fractions.
Examples:
Work out: 4 3 10 x y +
First find a suitable common denominator, in this case 20. = xx 4 5 20 and = yy 3 10 6 20
Exercise 4
1 Work out:
2 Is each statement true or false?
3 Calculate:
4 Complete these statements.
9 1 3 23 9 += + n
5 Complete these calculations. a) 12 9 3 33 3 a = () = b) 10 5 5 bc 25 + = () 2b + = c) 32 2 xx xx + = () 2 + = ………………………..
6 Simplify these fractions.
7 Simplify these fractions.
4 5 2 3 x ×
8 Draw a ring around the calculations that simplify to 2x + 3.