Revision Topics
Multiplying/Dividing by negative numbers
HCF and LCM
Powers and Roots
Prime Factors
Alternate and Corresponding angles
Interior and Exterior Angles of Polygons
The Circle
Circumference of a Circle
Area of a Circle
Solving Equations
Equations involving negative numbers
Equations with unknowns on both sides
Stem and Leaf Diagrams
Expand and Simplify
Solving Equations by Trial and
Improvement
Plans and Elevations
Loci
Bearings
* To multiply by negative numbers
* To divide by negative numbers
* To find the highest common factor of two integers
* To find the lowest common multiple of two integers.
* To apply Integers between 1 and 10 to various powers.
* To apply the second and third roots to various integers
* To write a number as a product of its prime factors
* To find the HCF and LCM of two numbers by finding their prime factors.
* To identify alternate and corresponding angles
* To calculate missing angles using alternate and corresponding angles.
* To calculate interior and exterior angles in regular polygons
* To understand the definition of a circle.
* To recognise and name the various parts of a circle
*To learn the formula to calculate a circles circumference
* To use the formula to calculate the circumference
*To learn the formula to calculate a circles area
* To use the formula to calculate the area
* To construct and solve linear integer equations
* To construct and solve linear integer equations with negatives
* To construct and solve linear integer equations with unknowns on both
sides
* To create stem-and-leaf diagrams given a set of data.
* to calculate statistics for sets of discrete and continuous data
* Simplify expressions by collecting like terms
* Expand and simplify single brackets
* Expand and solve linear equations
* to find an approximate solution to a non-linear equation through trial and
improvement
* To draw the plan and elevations of a 3D shape
* To draw a 3D shape given its plan and elevations
* To find simple loci to produce shapes and paths
* Use bearings to specify a direction from one position to another
Chapter 1 Number and Algebra 1
1.Calculate:
a +2 x –4 b –5 × +3 c +7 × –4
d –7 × –4 e –1 × –3 f 4 × –9 × –2
2.Calculate:
a –9 ÷ +3 b +10 ÷ –5 c +4 ÷ –1
d –6 ÷ –3 e –10 ÷ –2 f (–30 ÷ +10) ÷ –3
3.Calculate the following expressions, showing your working.
a 2 × 6 ÷ 3 b 3 × 8 ÷ –4 c (–10 ÷ 5) × –2
d 4 ÷ (–3 + 1) e –7 × (–9 – 1) f (15 – 6) ÷ –3
4.a Copy and complete the lists of factors for the numbers below.
12: 1, 2, …
28:
30:
24:
b Use your lists from part a to find the highest common factor of:
i 12 and 28 ii 28 and 30 iii 30 and 24 iv 24 and 12
Find the lowest common multiple of:
5.a 3 and 5 b 6 and 8 c 24 and 12 d 9 and 12
6.a Copy and complete the prime-factor tree for the number 72.
Check your answer by multiplying together all the prime factors. (The answer should be 72.)
72
2
36
7Calculate:
a 4 (–3)2 b –9 ÷ (–1)2 c (–5 – 1)2 ÷ –3
a Find the highest common factor (HCF) and lowest common multiple (LCM) of 72 and 180.
b Write down two positive numbers with an HCF of 2 and an LCM of 30.
8.Calculate:
a 100 b 10 000 c 31000 d 38
e (–1)2 f (–1)3 g (–2)5 h (–1)57
Chapter 2 Shape, Space and Measures 1
Chapter 5 Algebra 2
1.Write each of the following expressions, without the multiplication signs, in as simple a form as possible.
a6 x
x b m x11 c 3r x
dt÷3
e 7a x b f 15p ÷ 5 g f x3g x2h h 15m ÷ 20
i 30r ÷ r j 49y ÷ 7y k 3s ÷ 2s
2.Add together like terms to write each of the following expressions as simply as possible:
a x + 3x b x + y + 5y c 8p – q – p
d 7ab + ab + b e 10j – 20j + 2j f 5t + 4u + t + u
g 2s + 4t – 2s – 3t h –k + 2l – 2k – l i 5x2 + 2x + 4 – x2
j 10ab + 5b + 5a – 10ab
3.Expand each of the following expressions.
a 2(x + y) b 5(2r + t) c b(10a + 3) d x(7 – y)
e –3(v + 4) f –2(j – 2k) g 10 – (d + 2e) h –5(5 + 5x + z)
i 5(l – 2m) – 2(m – 2l) j 3(3x + y) – (3y + 3)
mxmxm can be written as m3 using index notation.
4.Use index notation to write each of the following expressions as simply as possible.
ax×xbc×c×c×ccp+p×p
d v × v × v × v × 10 e f + f + 3f + f × 3f f n5 ÷ n
g 2r × r ÷ r 2 h 15w6 ÷ w4
5.Expand each of the expressions below. Use index notation to simplify your answers as far as possible.
a m(m + 5) b x(5 + 5x) c u(3u – v)
d y(1 – 10y) e 3a(b + a) f 5p(2 – p) g t 2(5t + 3) h 3r 2(3r – 4)
6.Expand each of the expressions below and simplify the expression as far as possible.
a x + 7(y + 5x)
b 10y(5 + 2y) + 5y2
c 15f 3– 2f 2(2f + 7)
d 5u(1 + 3v) + 10v(2u + 2)
Chapter 6 Shape, Space and Measures 2
Chapter 10 Algebra 3
1.Find the value of x in each of the following equations. Show your working.
a 5x = 10 b x + 3 = 7 c 3x + 11 = 14 d 2x + 5 = 19
e 4x – 1 = 11 f 20x – 5 = 75 g 9 + 4x = 25 h 23 = 3x – 1
2.Find the value of x in each of the following equations. Some of the solutions are negative. Give your
answers as whole numbers or decimals.
a 2x + 3 = 12 b –5x = 25 c 4x + 1 = –3 d 3 + 2x = 2
e 10 – x = 7.5 f 20 = 26 + 2x g 6 – 2x = 2 h –15 + x = –20
3.Find the value of x in each of the following equations.
a 3x = 10 + x b 7x = 2x + 25 c 3x + 2 = 9 + 2x
d 6x – 5 = 1 + 3x e 3(x + 3) = 16 + 2x f 5x + 4 = 2 g 3(3x – 2) = 2
(3 + 2x)
(4x + 3)
4.Find the value of each of the following expressions when (i) x = 2, (ii) x = –1.
a 4x – 1 b 20 – 2x c x2 + 7
5.For all values of x between –2 and +2, the value of the expression x2 is less than 4.
For what ranges of values of x are the values of the following expressions less than 4?
a (x + 1)2 b (x – 1)2 c 1
x
6.Merline is a window cleaner. She uses the following formula to work out how much to
charge her customers:
C = 5 + 0.5g + f
In the formula, C is the charge in pounds, g is the number of ground-floor windows that
the house has, and f is the number of first-floor windows.
a How much does Merline charge for cleaning the windows of:
i a house with four ground-floor windows and four first-floor windows?
ii a house with three ground-floor windows and three first-floor windows?
iii a bungalow with seven ground-floor windows?
b Merline charges £11.50 for a house with four first-floor windows. How many
ground-floor windows does the house have?
Chapter 11 Handling data 2
Chapter 13 Algebra 5
Chapter 15 Shape, Space and Measures 4