Download Post-Learning Assessment Year 9 Module 2

Post-Learning
Assessment
Year 9 Module 2: Algebraic manipulations
Name: ………………………………………………………………….
Class: ……………………………………………………………………
Teacher: ……………………………………………………………….
You need:
 A Pen
 A Pencil
 A Ruler
 A calculator
What are we learning this half term?
Unit 5: Sequences

In this unit you will meet a variety of number pattern. You will consolidate work from Year 7 and Year 8 on
finding the nth term and also explore some other types of sequences such as square numbers and triangular
numbers
Unit 6: Changing the subject of the formula

In this unit you will develop your algebraic skills by representing worded facts as algebraic formulae and by
using earlier knowledge of solving equations to change the subject of familiar formulae
Unit 7: Expanding and factorising

In this unit you will consolidate earlier work on brackets and meet some new techniques. You will expand and
factorise single bracket expressions and learn to multiply two or more brackets together.
Pre-Learning Assessment Mark:
60
Teacher Comment:
Post-Learning Assessment Mark:
60
Teacher Comment:
Unit 5
1) Explain how you would find the next two terms in this sequence:
2, 5, 8, 11, 14, …
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………… (1)
2) Write down the next two terms in each sequence below:
a) 2, 4, 6, 8, 10, _____ , ______
(1)
b) 7, 4, 1, -2, ______, _______
(1)
c) 2, 6, 18, 54, ______, _______
(1)
d) 1, 2, 4, 8, 16, _______, _______
(1)
3) Find the rule for the 𝑛𝑡ℎ term for each sequence below:
a) 1, 4, 7, 10, 13, ………………………………...
(2)
b) 7, 11, 15, 19,
(2)
…………………………………
4) The rule for the 𝑛𝑡ℎ term of a sequence is 4𝑛 + 3. Write down the first 3 terms in the sequence.
…………………………………………………………………………………………………………………………………………………… (2)
5) Carmen makes patterns from matchsticks:
a) Draw the next pattern in the sequence.
(1)
b) How many matchsticks will the 5th pattern need? ……………………………………………
(1)
c) Find the rule for the 𝑛𝑡ℎ term of the number of matches in each pattern.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
(2)
d) How many matchsticks will the 20th pattern need?
………………………………………………………………………………………………………..………………………
…………………………………………………………………………………………………………………………………
(2)
e) Show that there is not a pattern in the sequence made of 42 matchsticks.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
(2)
Unit 6
6) You can use this rule to work out the number minutes it takes to cook a turkey:
Multiply the turkey’s weight, in kg, by 55 and then add 20.
a) Ginny has a turkey that weighs 4 kg. How long will she need to cook it for?
.....................................................................................................................................
(1)
b) Thomas has a turkey that weighs 𝑛 𝑘𝑔. Write an expression to show how long he will need to
cook it for.
……………………………………………………………………………………………………………………………………………
(2)
7) Tom drives a taxi. He charges £1.60 per mile, using the formula to work out the total cost:
C = 1.6 x M
a)
Tom drives one passenger for 3.5 miles. How much will he charge for this journey?
…………………………………………………………………………………………………………………………………………………
(1)
b) Another passenger was charged £6.40. How far was her journey?
…………………………………………………………………………………………………………………………………………………
(2)
c) Rearrange the formula to make M the subject.
…………………………………………………………………………………………………………………………………………………
(1)
d) Jacob’s taxi company charges a flat fee of £4 plus £2.10 per mile. Write a formula for the total
cost (c) of a journey in terms of the number of miles (m) travelled.
…………………………………………………………………………………………………………………………………………………… (2)
8) Make c the subject of each formulae below:
a) 𝑑 = 𝑐 + 7 …………………………………………………………………………………..
(1)
b) 3𝑐 – 4 = 𝑡 ……………………………………………………………………………………..
(2)
c) 3𝑐𝑑 = 𝑒
(2)
……………………………………………………………………………………..
9) The formula for finding the surface area of a cube is:
𝐴 = 6𝑥 2
Rearrange this to make 𝑥 the subject of the formula.
……………………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………….. (2)
10) 2𝑦 – 5𝑥 = 9 is the equation of a straight line.
a) Rearrange this to be in the form 𝑦 = 𝑚𝑥 + 𝑐
………………………………………………………………………………………………………………………………………………
(2)
b) What is the gradient of the straight line?
………………………………………………………………………………………………………………………………………………
(1)
Unit 7
11)
a) Find an expression for the area of the shape below:
𝑡
2
3
………………………………………….
(1)
b) Expand 5(𝑤 + 3)
……………………………………………………………………..
(2)
c) Expand 2𝑑(𝑑 – 5)
…………………………………………………………………….
(2)
d) Expand and simplify 3(𝑓 + 2) + 2(𝑓 – 6)………………………………………………………………………
………………………………………………………………………………………………………………………………..
(2)
e) Expand and simplify (ℎ – 4)(ℎ + 1) …………………………………………………………
……………………………………………………………………………………………………………………………………
(2)
12)
a) Factorise 4g + 8 by filling in the gaps:
4𝑔 + 8 = 4 ( … + … )
(2)
b) Factorise 5𝑦2 – 𝑦
……………………………………………………………………………..
(2)
c) Factorise 8𝑏 + 24𝑏3
………………………………………………………………………….
(2)
13) Find an expression for the area of each of these shapes:
a)
𝑡
s
(1)
b)
𝑣 + 2
8
(2)
c)
ℎ
(2)
4ℎ
d) The rectangle in part b) has area 36 cm2. Use this to find the value of 𝑣.
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
(2)
Finishing Task
This is a 3x3 magic square.
6
7
2
1
5
9
8
3
4
Each row, each column and each diagonal all add up to 15. This is known as the magic number.
Task 1
Using the digits 1-9 ONCE each, create a 3x3 anti-magic square: each row, column and diagonal
must add up to a different total.
Task 2
Using the digits 1-16 ONCE each, create a 4x4 magic square with the magic number of 34.
Some digits have been placed to help you.
3
10
7
1