Download Welcome to mathematics at Plantsbrook

Year 10 to Year 11 Holiday work
In this booklet you will find a selection of past paper questions based on the topics we have
covered this year (except Transformations). The topics we have covered are:
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Data Handling
Statisitics
Angles
Number skills
Fractions and Percentages
Expressions
Algebraic Methods
Equations
Inequalities
Length, Area, Volume
Transformations
Linear Graphs
Probability
Constructions
Ratio
Real-life graphs
Sequences
Pythagoras
Trigonometry
Quadratic Equations
Use the topic analysis you have from half-term tests and the past paper to influence your
decision on which topics to focus your work on. You are expected to chose at least 5 topics
and answer each question on that topic. If you don’t know how to answer one of the
questions, go and look it up.
Grades: D,C
Fractions
MIXED NUMBERS
1
3
2 1
2 1
1.
2.
3.
1 2
3 1
2 3
2
5
5 2
3 4
DIVIDING WITH FRACTIONS
1 1
2 1
3 3
3 1
7 3
1.
2.
3.
4.
5.
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
2 4
5 10
4 8
10 5
9 4
EXAM QUESTIONS
3
1. Linda uses 5 of a tin of paint to paint a fence panel. What is the least number of tins she needs to
paint 8 fence panels?
1
3
2. On Monday Joe drinks 2 3 pints of milk. On Tuesday he drinks 1 4 pints of milk.
Work out the total amount of milk that Joe drinks on Monday and Tuesday.
3.
3
4. Work out 7 x 28
3
5. Work out 5 ÷ 6
RECURRING DECIMALS
1. Which of these fractions can be written as recurring decimals?
1
1
5
2
5
6
8
3
2
2. Express 9 as a recurring decimal.
3. Express 0. 4̇8̇ as a fraction in its simplest form.
4. Express 0.31̇5̇ as a fraction in its simplest form.
5.
Grade: B
6.
Percentages
COMPOUND PERCENTAGE
1.
2.
3.
Grades: B,A
4.
5.
6.
REVERSE PERCENTAGE
1.
2.
3.
4.
5.
Grades: D,C
Ratio
1.
2.
3.
4.
Grades: E,D,C
Algebraic Manipulation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
EXPANDING QUADRATIC EXPRESSIONS
1.
Grade: B
2.
3.
FACTORISING QUADRATIC EXPRESSIONS
1.
3.
Forming Equations
2.
4.
Factorise
Grades: C
1.
Substitution
1.
Grades: C
2.
Collecting Data
Grades: D,C
1.
(b) Re-write a question and response section which would be suitable
Presenting Data & Interpreting Information
STEM AND LEAF DIAGRAMS
1.
2.
Grades: D
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.
FREQUENCY DIAGRAMS
1.
Measures of Average and Spread
Grades: C
AVERAGES FROM TABLES
1.
2.
Scatter Graphs & Correlation
Grades: C
1.
(d) Use your graph to estimate the reaction time of a pupil in year 6 and a pupil in year 12
Probability
Grades: B
RELATIVE FREQUENCY
1.
TREE DIAGRAMS
1.
Grades: C, B
AND RULE/OR RULE
1.
Grades: B
2.
DEPENDENT EVENTS
1.
2.
Grades: A
Compound Area & Perimeter
1.
2.
Find the area and perimeter of each shape
Grades: D
Area & Circumference of circles
1.
2.
3.
4.
Grades: D,C
Grades: D,C
Volume of cuboids & prisms
1.
2.
3.
4.
A cuboid has a volume of 80cm3, a width of 5cm and a depth of 2cm. What is its height?
Grades: A,A*
Length/Area of arcs and sectors
1.
The diagram shows a sector of a circle of radius 9 centimetres.
Not drawn accurately
9 cm
80º
2.
Find the perimeter of the sector.
A circle fits inside a semicircle of diameter 10cm as shown.
10 cm
Calculate the shaded area.
Grades: C
Sequences
Write the first five terms of the following sequences whose nth terms are
1.
n2+3
n+3
2.
3.
3n
2n2
n3
n2-5
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
9
13
2.
3.
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.
Solving Equations
1.
8n -2
a)
4y + 3 = 2y + 10
b)
2x + 17 = 5x – 4
c)
2x + 7 = 16 – 4x
d)
20x -15 = 18x -7
a)
5(x + 3) = 2 (x + 6)
b)
4 (2y + 1) = 2 (12 - y)
c)
7 - 3x = 2 ( x + 1)
x3
5
a)
2
2x  4
7
b)
3
40  x
 4 x
c)
3
Grades: D-B
Trial and Improvement
Grades: C
1.
2.
Compound Measures
1.
2.
3.
4.
Grades: C-B