Download GCSE Higher Homework Booklet

INTEGERS, RECIPROCALS, FACTORS,
MULTIPLES AND PRIME NUMBERS
GRADES : E,D
Homework 1H
BIDMAS
Follow the correct order of operations to calculate the following:
1.
5 + 2 x 3 = ___
2.
10 ÷ 2 + 7 = ___
3.
7 + 9 ÷ 3 = ___
4.
2 x 3 + 7 x 2 = ___
5.
8 ÷ 4 – 2 x 1 = ___
6.
5 x 10 + 9 ÷ 1 = ___
7.
2 + 4 x 4 + 1 = ___
8.
(2 + 4) x 8 = ___
9.
(3 – 1) x (9 – 4) = ___
10.
30 – (7 + 6) = ___
11.
20 – (4 + 10) = ___
12.
(5 + 9) ÷ (2 x 1) = ___
BRACKETS
Put brackets into the questions to make them correct.
1.
2 + 2 x 3 = 12
2.
4 – 1 x 7 = 21
3.
2 + 1 x 1 + 2 = 9
4.
9 ÷ 3 x 2 + 1 = 9
5.
50 ÷ 7 + 3 = 10
6.
6 + 2 x 4 + 3 = 51
1234
Use the digits 1, 2, 3, and 4 to make correct calculations. Use brackets where appropriate.
1 = ________________________________
2 = _________________________________
3 = ________________________________
4 = _________________________________
5 = ________________________________
6 = _________________________________
7 = ________________________________
8 = _________________________________
9 = ________________________________
10 = _________________________________
EXAM QUESTION
INTEGERS, RECIPROCALS, FACTORS,
MULTIPLES AND PRIME NUMBERS
GRADES : D,C
Homework 2H
PRIME NUMBERS
Answer TRUE or FALSE:
1.
2 is a prime number
2.
9 is a prime number
3.
15 is a prime number
4.
7 is a prime number
5.
19 is a prime number
6.
23 is a prime number
7.
21 is a prime number
8.
8 is a prime number
9.
27 is a prime number
10.
3 is the smallest prime number
11.
There are four prime numbers between 1 and 10
12.
99 is a prime number
13.
There are three primes between 20 and 30
PRIME FACTORS
Write each number as a product of its’ prime factors:
1.
21
2.
12
3.
36
4.
50
5.
150
6.
54
7.
49
8.
84
RECIPROCALS
Write down the reciprocal of each number
1.
3
2.
2
3.
5
4.
1
4
5.
1
2
6.
10
7.
1
8
8.
1
9
9.
5
10.
2
3
11.
3
4
12.
6
EXAM QUESTIONS
1.
2.
3.
INTEGERS, RECIPROCALS, FACTORS,
MULTIPLES AND PRIME NUMBERS
GRADES : D, C
Homework 3H
Multiples
Write down the first six multiples of each number:
1.
4
2.
3
3.
7
4.
9
5.
15
6.
12
7.
8
8.
11
Highest Common Factor
Find the Lowest Common Factor (HCF) for each pair of numbers.
1.
36 and 10
2.
50 and 30
3.
45 and 27
4.
100 and 36
5.
88 and 56
6.
36 and 32
Lowest Common Multiple
Find the Highest Common Multiple (LCM) for each pair of numbers.
1.
6 and 9
2.
5 and 15
3.
12 and 8
4.
2 and 11
5.
12 and 8
6.
5 and 9
EXAM QUESTIONS
1.
2.
3.
4.
ROUNDING AND APPROXIMATIONS
Homework 4H
GRADES : E, D
ESTIMATING
Copy the lists below and match up the questions to the estimated answers. The first one has been done for you.
QUESTIONS
ESTIMATED ANSWERS
3.92 x 5.05
3
6.9 x 2.9
100
30.1 ÷ 9.91
11.4
√32
15
(8.8 + 11.11) x 4.9
40
50 ÷ 7.21
7
√103
8
4.05 x (6.9 + 2.9)
20
67 ÷ 8.12
12.2
√150
5.5
EXAM QUESTIONS
1.
2.
3.
ROUNDING AND APPROXIMATIONS
GRADES : D,C
Homework 5H
SIGNIFICANT FIGURES
1. Write each number correct to one significant figure.
a) 27
b) 832
c) 8.12
d) 93
e) 77
f) 13.5
g) 95
2. Use a calculator to work out the answers and write them down correct to 1 significant figure.
a) 50 x 23
b) 5.25 x 7
c) 910 x 12
d) 9.5 x 7.3
e) 93 x 77
3. Write each number correct to two significant figures.
a) 275
b) 0.03451
c) 8.12
d) 0.956
e) 7.04
f) 7.05
g) 959
4. Write each number correct to three significant figures.
a) 27589
b) 0.03451
c) 8.1254
d) 0.95621
e) 0.0704124
f) 7.05555
g) 959595
ESTIMATING CALCULATIONS
By approximating each number, estimate the answers to these calculations. You must show how you reached your
estimate.
4.9  15.21
1.9
1.
EXAM QUESTIONS
1.
2.
3.
2.
19.89  5.2
1.05  9.03
3.
4.05  4.9  5.09
ROUNDING AND APPROXIMATIONS
GRADES : C, B
Homework 6H
ROUNDING IN CALCULATIONS
Give your final answer to each question correct to two decimal places.
Remember not to round during the intermediate steps of the calculation.
1.
6.2  3.09
3.2  8.91
2.
4.9
1.2  3.8
3.
9
8.14

2.17 0.515
4.
9.054  0.973
6.3  0.00462
5.
7.563
3.9  9.017
6.
5  3.2 2  2.1 9.2 1.1
HIGHEST AND LOWEST
1. The length of a pencil is given as 9cm to the nearest cm.
What is the minimum length that the pencil could be?
2. The height of a door is 210cm to the nearest 10cm.
What is the maximum height that the door could be?
3. The width of a piece of paper is given as 18.4cm correct to one decimal place.
a) What is the minimum width that the paper could be?
b) What is the maximum width that the paper could be?
EXAM QUESTIONS
1.
2.
3.
ROUNDING AND APPROXIMATIONS
UPPER AND LOWER BOUNDS
EXAM QUESTIONS
1.
2.
3.
4.
5.
Homework 7H
GRADES : A
WHOLE NUMBER AND DECIMAL
CALCULATIONS
Homework 8H
MULTIPLICATION AND DIVISION (WHOLE NUMBERS)
MULTIPLYING DECIMALS
DIVIDING WITH DECIMALS
EXAM QUESTION
1.
2.
GRADES : D,C
FRACTIONS
GRADES : D,C
Homework 9H
ADDING AND SUBTRACTING FRACTIONS
1. Fill in the boxes by adding the fractions.
1
3
1
2
2
3
+
2
5
3
8
2
7
2. Work out each question without a calculator. Show your working and write your answer in its’ simplest form.
a)
1 3

4 5
b)
3 1

5 3
c)
1 1

9 10
d)
3 1

4 6
c)
7 7

9 10
d)
13 9

15 20
3. Work out each question with a calculator.
a)
3 3

4 15
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
7.
b)
7 2

10 3
FRACTIONS
GRADES : D,C
Homework 10H
MULTIPLYING FRACTIONS
Fill in the boxes by multiplying the fractions.
1
2
3
5
1
2
2
3
x
3
8
2
7
MIXED NUMBERS
1.
1
3
1 2
2
5
2.
2 1
3 1
5 2
3.
3 3

4 8
3.
2 1
2 3
3 4
5.
7 3

9 4
DIVIDING WITH FRACTIONS
1.
1 1

2 4
2.
2 1

5 10
EXAM QUESTIONS
1.
2.
3.
,
4.
5.
6.
7.
,
4.
3 1

10 5
FRACTIONS
RECURRING DECIMALS
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 11H
GRADES : B
SQUARES, CUBES,
POWERS AND ROOTS
GRADES : E, D,C
Homework 12H
POWERS AND ROOTS ‘COLLECT A LETTER’
START
1000
P
8
O
32
U
E
49
64
T
A
23
92
52
73
63
24
27
121
36
100
1
125
E
D
L
N
H
I
4
2
5
10
6
3
5
3
3
2
02
216
16
343
0
25
81
I
C
R
S
T
R
1
END
7
3
10
2
5
2
3
112
1)
√25
3²
√36
2³
√100
2)
√100
4²
2²
√81
√121
3)
5²
4² + 2²
√144
√25+√36
1³ + 3³
4)
√36 - √4
4² - 2²
1³ + 2³
√100 - 3²
1³ + 1²
EXAM QUESTIONS
1.
2.
3.
4.
SQUARES, CUBES,
POWERS AND ROOTS
GRADES : C
Homework 13H
INDEX LAWS
1. Write each of these as simply as possible using indices.
a) 2x2x2x2x2
b) y x y x y x y
c) 9x9x9
d) 8x8x8x8x8x8x8
2. Write down the value of the missing index.
a)
2 2  23  2 x
b)
38  3x  212
c)
52  5 x  59
d)
2 x  23  2 7
e)
(2 2 ) 4  2 x
f)
(26 ) x  218
g)
39
 3x
2
3
h)
48
 45
x
4
c)
(54 ) 2  56
3. State whether each equation is TRUE or FALSE.
a)
7 2  7 6  78
b)
83
 82
8
EXAM QUESTIONS
1.
5.
2.
6.
3.
7.
4.
8.
SQUARES, CUBES,
POWERS AND ROOTS
Homework 14H
FRACTIONAL POWERS and NEGATIVE POWERS
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
GRADES : A, A*
SQUARES, CUBES,
POWERS AND ROOTS
IRRATIONAL NUMBERS AND SURDS
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
7.
Homework 15H
GRADES : A, A*
POWERS OF 10 AND
STANDARD INDEX FORM
STANDARD INDEX FORM
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
Homework 16H
GRADES : A, A*
PERCENTAGES
Homework 17H
PERCENTAGE INCREASE AND DECREASE
1. Increase £90 by 10%
2. Increase £110 by 50%
3. Increase £120 by 5%
4. Decrease £40 by 20%
5. Decrease £700 by 30%
6. Decrease £320 by 5%
7. Increase £620 by 25%
8. Decrease £180 by 60%
EXAM QUESTIONS
1.
2.
How much do they pay for the washing machine?
3.
GRADES : D,C
PERCENTAGES
COMPOUND PERCENTAGE
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
7.
Homework 18H
GRADES : B, A
PERCENTAGES
REVERSE PERCENTAGE
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
Homework 19H
GRADES : B
RATIO AND PROPORTION
EXAM QUESTIONS
1.
2.
3.
4.
5.
6.
Homework 20H
GRADES : D,C
RATIO AND PROPORTION
DIRECT PROPORTION
EXAM QUESTIONS
1.
2.
3.
INVERSE PROPORTION
EXAM QUESTIONS
1.
2.
Homework 21H
GRADES : A
ALGEBRAIC MANIPULATION
Homework 22H
EXAM QUESTIONS
1.
12.
2.
13.
3.
14.
4.
15.
5.
6.
7.
8.
9.
10.
11.
GRADES : E,D,C
ALGEBRAIC MANIPULATION
EXPANDING QUADRATIC EXPRESSIONS
EXAM QUESTIONS
1.
2.
3.
FACTORISING QUADRATIC EXPRESSIONS
EXAM QUESTIONS
1.
2.
3.
4.
Homework 23H
GRADES : B
ALGEBRAIC MANIPULATION
Homework 24H
EXPANDING HARDER QUADRATIC EXPRESSIONS
EXAM QUESTIONS
1.
2.
3.
a)
b)
4.
5.
FACTORISING HARDER QUADRATIC EXPRESSIONS
EXAM QUESTIONS
1.
2.
3.
4.
GRADES : A
NON-LINEAR GRAPHS AND GRAPHICAL
SOLUTION OF EQUATIONS
EXAM QUESTION
Homework 25H
GRADES : D,C
NON-LINEAR GRAPHS AND GRAPHICAL
SOLUTION OF EQUATIONS
GRAPHICAL SOLUTION OF EQUATIONS 1
EXAM QUESTION
1.
below
Homework 26H
GRADES : A
NON-LINEAR GRAPHS AND GRAPHICAL
SOLUTION OF EQUATIONS
GRAPHICAL SOLUTION OF EQUATIONS 2
EXAM QUESTIONS
1.
2.
3.
below
Homework 27H
GRADES : A, A*
COLLECTING DATA
Homework 1H
DATA COLLECTION SHEETS AND QUESTIONNAIRES
Exam questions
1.
2.
3.
4.
GRADES : D, C
COLLECTING DATA
STRATIFIED SAMPLING
Exam questions
1.
2.
3.
Homework 2H
GRADES : A
PRESENTING DATA AND
INTERPRETING INFORMATION
Homework 3H
STEM AND LEAF DIAGRAMS
Exam questions
1.
2.
3.
(a) How many people were asked?
(b) What was the median number of driving lessons?
(c) Work out the range of the number of driving lessons.
GRADES : D
PRESENTING DATA AND
INTERPRETING INFORMATION
FREQUENCY DIAGRAMS Exam questions
1.
2.
Homework 4H
GRADES : D
PRESENTING DATA AND
INTERPRETING INFORMATION
CUMULATIVE FREQUENCY
Exam questions
1.
2.
Homework 5H
GRADES : B
PRESENTING DATA AND
INTERPRETING INFORMATION
BOX PLOTS
Exam questions
1.
2.
Homework 6H
GRADES : B
PRESENTING DATA AND
INTERPRETING INFORMATION
HISTOGRAMS
Exam questions
1.
2.
3.
Homework 7H
GRADES : A
PRESENTING DATA AND
INTERPRETING INFORMATION
Homework 8H
TIME SERIES Exam questions
1.
Copy the graph and plot all the other moving averages.
2.
GRADES : B
MEASURES OF AVERAGE AND SPREAD
AVERAGES FROM TABLES
Exam questions
1.
2.
3.
Homework 9H
GRADES : C
SCATTER DIAGRAMS AND
CORRELATION
SCATTER DIAGRAMS AND CORRELATION
Exam questions
1.
2.
3.
Homework 10H
GRADES : C
PROBABILITY
RELATIVE FREQUENCY - Exam questions
1.
2.
Homework 11H
GRADES : B
PROBABILITY
TREE DIAGRAMS - Exam questions
1.
2.
Homework 12H
GRADES : C, B
PROBABILITY
Homework 13H
COMBINED PROBABILITIES (AND RULE / OR RULE)
Exam questions
1.
2.
3.
4.
GRADES : B
PROBABILITY
DEPENDENT EVENTS
Exam questions
1.
2.
3.
4.
Homework 14H
GRADES : A
Compound area + perimeter
(mathswatch clip 73)
1) Find the area and perimeter of each shape.
Homework 1H
GRADE : D
Circumference of circles
(mathswatch clip 72)
Homework 2H
GRADE : D
Area of circles
(mathswatch clip 71)
Volume of cuboids +
Homework 3H
GRADE : D,C
prisms(mathswatch clip 34 + 122)
Homework 4H
GRADE : D - C
1) Find the volume of the following cuboids
7cm
3cm
5cm
7cm
12cm
4cm
2)
3)
4)
5) A cuboid has a volume of 80cm3 a width of 5cm and a depth of 2 cm find it’s
height?
Surface area
Homework 5H
GRADE : C -B
(mathswatch clip 121)
1) Find the surface area of the following cuboids
7cm
3cm
7cm
12cm
4cm
5cm
2)
3)
4) A cuboid has a surface area of 36cm2 a width of 5cm and a depth of 2 cm find
it’s height?
Volume of Spheres and
Cones
Homework 6H
GRADE : A-A*
(mathswatch clip 177)
1)
4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram.
The hemisphere has a radius of 4 cm.
4 cm
5 cm
10 cm
10 cm
Not to scale
Calculate the volume of the paperweight.
Volume of Spheres and
Cones
Homework 6H
GRADE : A-A*
(mathswatch clip 177)
1)
4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram.
The hemisphere has a radius of 4 cm.
4 cm
5 cm
10 cm
10 cm
Not to scale
Calculate the volume of the paperweight.
Length / Area of arcs,
sectors
Homework 7H
GRADE : A-A*
1) The diagram shows a sector of a circle of radius 9 centimetres.
Not drawn accurately
9 cm
80º
Find the perimeter of the sector.
Give your answer in terms of .
2)
A giant paper clip is placed alongside a centimetre ruler.
The curved ends are semicircles.
Not drawn accurately
0
1
2
3
4
5
6
7
cm
Calculate the length of wire used to make the clip.
3)
A circle fits inside a semicircle of diameter 10 cm as shown.
10 cm
Calculate the shaded area.
8
9
10
Polygons
Homework 8H
(mathswatch clip 70)
1) find angle x if the following shape is a rhombus
x
32o
2)
x
3)
GRADE : C
Sequences
Homework 9H
GRADE : C
1) Write the first five terms of the following sequences whose nth terms are
n2+3
n+3
2n2
3n
n3
8n -2
n2-5
2) Find the nth term of the following;
3, 8, 13, 18, 23, ….
20, 13, 6, -1, ….
2, 8, 18, 32, 50, …..
½ , 1, 4 ½ , 8, 12 ½ , ……
A sequence of numbers is shown.
5
(a)
9
13
17
21
(a)
Find an expression for the nth term of the sequence.
(b)
Explain why 83 will not be a term in this sequence.
Part of a number grid is shown below.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
The shaded cross is called C11 because it has the number 11 at the centre.
This is Cn
n–7
n
Fill in the empty boxes.
(b)
Kevin notices the following number sequence in the grid.
1, 9, 17, 25, 33,...
Write down the nth term of this sequence.
Straight lines
Homework 10H
( mathswatch clip 114 + 143 )
6)
Find the midpoints of the following co-ordinates
i)
(0,4) (3, 13)
ii)
(0,7) (2, -1)
iii) (10,5) (22, 18)
GRADE : C
Solving Equations
(Mathswatch clip 105)
8)
9)
10)
11)
12)
1)
4y + 3 = 2y + 10
2)
2x + 17 = 5x – 4
3)
2x + 7 = 16 – 4x
4)
20x -15 = 18x -7
5)
5(x + 3) = 2 (x + 6)
6)
4 (2y + 1) = 2 (12 - y)
7)
7 - 3x = 2 ( x + 1)
x3
5
2
2x  4
7
3
40  x
 4 x
3
2x  1 x  3 5


6
3
2
y2 y6

 16
3
4
Homework 11H
GRADE :D-B
Homework 12H
Reflections and rotations
(Mathswatch clip 74 + 75)
GRADE :D-C
Circle theorems
(Mathswatch clip 150)
Homework 13H
GRADE :B
Trial and improvement
(Mathswatch clip 110)
Homework 14H
GRADE :C
Translation
(Mathswatch clip 77)
Homework 15H
GRADE :C
Enlargement
(Mathswatch clip 76)
Homework 16H
GRADE :C
Transformations
Homework 17H
GRADE :C-B
(Mathswatch clip 74,75,76,77)
y
6
5
4
A
3
2
1
–5
–4
–3
–2
–1 O
1
2
3
4
5 x
–1
–2
–3
–4
(i)
Describe fully the single transformation that takes the shaded triangle to
triangle A.
(ii) On the grid above translate the shaded triangle by 2 squares to the right and
4 squares down.
y
6
The rectangle is
rotated 90’
clockwise about
the point ( 1, 0)
and then
translated by
  4
vector  
5 
4
2
–6
–4
–2
0
2
4
6 x
–2
–4
–6
Draw the Final position of the rectangle after these transformations.
The diagram shows four shapes, A, B, C and D.
6
5
B
4
3
2
A
C
1
–4
–3
–2
–1 O
1
2
3
4
5
6
7
8
–1
–2
–3
D
–4
(a)
Describe fully the single transformation that takes shape A onto shape B.
(b)
Describe fully the single transformation that takes shape B onto shape C.
(c)
Describe fully the single transformation that takes shape C onto shape D.
(b)
Triangle P is an enlargement of the shaded triangle. Find the scale factor and
centre of enlargement.
y
6
5
4
3
2
1
P
–5
–4
–3
–2
–1 O
1
2
–1
–2
–3
–4
(i)
What is the scale factor of the enlargement?
3
4
5 x
Similar Shapes
Homework 18H
GRADE :C-B
(Mathswatch clip 123)
Two similar bottles are shown below.
The smaller bottle is 20 cm tall and holds 480 ml of water.
The larger bottle is 30 cm tall.
Not to scale
30 cm
20 cm
How much water does the larger bottle hold?
Dimensions of Formulae
Homework 19H
(Mathswatch clip 124)
2) a, b, and c represent lengths combine a, b, c, to find five formulae that could represent
i)
volume
ii)
area
GRADE :C-B
Compound Measures
(Mathswatch clip 126)
Homework 20H
GRADE :C-B
Bounds
Homework 21H
GRADE : B
(Mathswatch clip 125)
6) Sameera runs 100m (to the nearest 10m) in 12 seconds (correct to the nearest
second).
Last time she ran the race her maximum possible speed was 8.2 metres per second
– can she be sure that she has run faster his time?
Give a reason for this answer
Real life graphs
(Mathswatch clip 117)
Homework 22H
GRADE : C
Real life graphs
Homework 23H
GRADE : C
(Mathswatch clip 117)
Mr Smith leaves the home at 10 am to go to the shopping mall.
He walks to the station where he catches a train.
He gets off the train at the mall.
The travel graph shows his journey.
15
10
Distance
from home
(km)
5
0
10 am
11 am
12 am
1pm
2 pm
Time
After shopping Mr Smith goes home by taxi.
The taxi leaves the mall at 1 pm and arrives at his home at 1.45 pm.
(a)
Complete the travel graph.
(2)
(b)
Calculate the average speed of the taxi.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .......................................................km per hour
(2)
Substitution
(Mathswatch clip 65)
Homework 24H
GRADE : C
Forming Equations
Homework 25H
GRADE : C
(Mathswatch clip 106)
GRADE : C
Changing the subject of a
formulae
(Mathswatch clip 107)
Homework 26H