CLASSI
LINES AND ANELLI
Learning Omtram The learner verlies the properties of vanvous puurk na angles
formed when a trunswrnal cus two lines
Reema purchased a flat in a high asing buldoga 13 Thur. From the
halouny of her flat she could see the full view of the any She sun that in front
of her building a mnd crowser a ralway line at an unple or as shown in the
figure. Sering at the court or parallel lines liked her mund and whe
started to find the different angles made by the two Help Reems to find theme
angles market in the figure
a
Answers
Answer:
these work before moving on:
(a) 3a + 12b – 5a + 7b – 2a = – 4a + 19b
(b) x² + 5x – 5 + 4x² – 3x + 5 = 5x² + 2x (these two terms can not be added as one is x and the other is x²)
(c) 2p + 3pq – 5pq² + 6p – pq = 8p + 2pq – 5pq²
Practice Questions
Work out the answer to each question then click on the button marked to see if you are correct.
Simplify these expressions by collecting like terms:
(a) 3p + 6q – 5p + 3q
(b) x3 – 4x2 + 7x – 3 + 7x2 – 9x + 1
(c) ab2 + 3ab - 3a + 2ab2 - 5ba + 4a
Laws of Indices
Rules to learn
positive powers an means multiply together n lots of a
e.g. a5 = a × a × a × a × a
multiplying powers If the bases are the same then you add the powers: am × an = a(m + n)
e.g. x5 × x3 = x8
dividing powers If the bases are the same then you subtract the powers: am ÷ an = a(m – n)
e.g. y2 ÷ y6 = y– 4
This also works for powers in fractions: e.g. p7 = p3 p4
powers of powers The powers are multiplied: (am)n = a(mn)
e.g. (z2)5 = z10
special powers a1 = a and a0 = 1
e.g. b4 ÷ b3 = b1 = b
e.g. d 3 × d – 3 = d 0 = 1
multiplying terms To multiply terms, multiply the coefficients to get the new coefficient then multiply each letter in turn:
e.g. 3x2 × 5x3 = 15x5
e.g. 4xy 2 × x3 × 3x