Download Examples of questions

Maths Common Entrance revision Year 8
Topic/Objective
To multiply/divide any number including
decimals by 10, 100, 1000
Examples of questions
A) 5.8 x 1000 =
B) 3.9 x 100 =
C) 517.6 ÷ 1000 =
D) 536 ÷ 10000 =
Fill in the missing blanks:
A) ______ x 1000 = 7350
B) 283 ÷ _____ = 0.0283
Harder questions:
A) _____ x 300 = 69000
B) 4600 ÷ 20 = _______
To multiply/divide/add/subtract using
decimal numbers
A) 5.36 + 0.2 =
B) 3.76 + 14 =
C) 7.98 - 2.19 =
D) 13.26 - 7.03 =
Find the area of the following rectangle:
8.4cm
6.3cm
Find the length of the missing side of the
rectangle if it’s area is 42.63cm2
xcm
7cm
If 268 x 32 = 8576.
What is A) 26.8 x 3.2?
B) 2.68 x 3.2?
C) 0.268 x 32?
D) 0.268 x 0.32?
To order decimal numbers according to
size order
Order the following decimals from smallest to
largest:
4.606, 4.6, 4.06, 4.66, 4.066
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Maths Common Entrance revision Year 8
Topic/Objective
To round numbers to the nearest whole,
ten, hundred or thousand
To round numbers to a given number of
decimals places
To round numbers to a given number of
significant figures
Examples of questions
Round the following numbers to the nearest 10:
A) 764
B) 253
C) 2874
D) 1836
E) 26.43
Round the above numbers to the nearest 1000:
(harder)
Round the following numbers to the stated
decimal place
A) 2.6843 to 2dp
B) 5.927 to 2dp
C) 5.962 to 1dp
D) 8.0999 to 3dp
Round the following numbers to the stated
number of significant figures:
A) 7.456 to 2sf
B) 0.0604 to 2 sf
C) 0.070036 to 4sf
D) 6347 to 1sf
E) 3982 to 2sf
F) 5341 to 3sf
Estimate the value of this calculation:
3.94 x 6.03
Rewrite the following calculation, rounding each
number to 1 significant figure:
Now work out the value of this.
Using a calculator, find the exact value of the
above calculation. Write down all of the digits
shown on your calculator.
Round this number to A) 3decimal places
B) 3 significant figures
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Maths Common Entrance revision Year 8
Topic/Objective
Examples of questions
To round numbers to a given number of
significant figures (Continued)
Repeat the above for the following:
To use all four operations with negative
numbers
A) -3-5
B) 2+ -6
C) 3- - 9
D) -4-6-+4- -11
What is the difference between -11˚C and 64˚C?
What is the difference between -137 and -149?
A) -3 x 5
B) -2 x -9
C) 5 x -7
D) -3 x -4
A) What is (-5)2
B) There are two answers to the following:
(x) 2 = 36. What could they be?
Fill in the missing blanks:
To be able to find equivalent fractions
or cancel down a fraction into its
simplest terms
24 = [ ]
36 6
4 = []
5
40
66 = [ ]
77 7
Cancel down the following fractions:
21
34
36 35 40
13
60 70 90 63 56 52
Write 64 centimetres as a fraction of 4 metres.
Give your answer in its simplest form.
To use equivalent fractions to size order Order these fractions from smallest to largest:
7
5
2
1
fractions
12
6
1
3
6
15
5
8
3
5
3
4
4
6
7
10
4
10
11
20
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Maths Common Entrance revision Year 8
Topic/Objective
To add/subtract fractions
Examples of questions
3
7
+
11
21
4
5
+
3
15
5
6
+
3
4
5
8
-
4
7
3 4/5
To find a fraction of an amount
To multiply and divide using fractions
+
2 1/9
2/5 of 45
3/7 of 406
3/8 of 768
5/6 of 426
Calculate ⅜ of 2 metres, giving your answer in
centimetres.
⅓ of a class of 24 children are girls. How many
children in the class are boys?
¾ of the girls and ½ of the boys learn a musical
instrument.
How many children learn a musical instrument?
2/3 x 4/5
3/4 x 7/5
2/9 x 5/3
4/3 ÷ 3/8
2/3 ÷ 6/7
2/9 ÷ 1/3
Find the area of the following rectangles:
3/7cm
4/9cm
2 ⅓ cm
5⅜ cm
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Maths Common Entrance revision Year 8
Topic/Objective
To multiply and divide using fractions
(continued)
To find a percentage of an amount
To express one number as a percentage
of another
To find percentage increase and
decrease
Examples of questions
It takes ⅔ of an hour to drive the red bus round
its route.
The red bus is driven round its route for six
hours each day.
How many times does the red bus complete its
route each day?
Sheba the cat drinks ⅔ of a pint of milk each
day.
For how long will 6 pints of milk last Sheba?
A) 30% of £710
B) 25% of £640
C) 38% of £540
D) 33⅓% of £963
E) 5% of £340
F) 66⅔% of 1462
Work out 15% of £12
Calculate 90% of £15
Mrs Collins sold a rare book on a website for £60
She then paid a fee of 12% of the selling price.
How much was the fee?
During 2010, Callumʼs height increased by 12%.
At the start of the year, he was 1.50 metres tall.
Calculate his height at the end of the year.
Write 45 as a percentage of 150
Write 48 as a percentage of 60.
A T shirt marked at £18 was sold for £14.40.
What percentage discount was given on the
marked price?
During 2010, Callumʼs mass increased from 55
kilograms to 59.4 kilograms.
Calculate the percentage increase in his mass.
Mrs Collins sold a book for £60 to Mr Hudson.
He later sold the book for cash for £87
Calculate his profit as a percentage of the price
he paid for the book.
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Maths Common Entrance revision Year 8
Topic/Objective
To find percentage increase and
decrease (Continued)
To know fraction/decimal/percentage
equivalents
(Pupils should memorise these:
½=0.5=50%
¼ = 0.25 = 25%
1/10 = 0.1 = 10%
1/5 = 0.2 = 20%
1/100 = 0.01 = 1%
Examples of questions
Miss Venn sells calculators in the school Maths
shop. Each calculator costs her £3.72
During 2008, she sold these calculators for
£5.50 each.
(i) How much profit did she make on each
calculator?
(ii) Calculate this profit as a percentage of the
price she pays.
Give your answer correct to 1 decimal place.
Write these numbers in order, smallest first:
Write these numbers in order, largest first:
⅓ = 0.3333... = 33 1/3 %
⅔ = 0.6666... = 66 2/3 %)
To understand the order of operations
(BIDMAS)
Write 3/20 as a percentage
Write 8% as a decimal
Write 6/25 as a percentage
Write 0.16 as a fraction in its simplest form.
Calculate:
i)
4+5x6
ii)
To know what a prime number, square
number and cube number is
iii)
14 + 6 x 4 – 2
iv)
27 – 18 ÷ 32
From the list of numbers below, identify a square
number, a cube number and a prime number:
13, 8, 12, 49, 120, 27
Why is 126 not a prime number?
What is the first prime number?
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Maths Common Entrance revision Year 8
Topic/Objective
To know what a prime number, square
number and cube number is (Continued)
To write a number as the product of its
primes
Examples of questions
16 and 9 are both square numbers. If you add
them together, the result is also a square
number. Can you find two other square numbers
that do the same?
Write 60 as the product of its primes
What is the largest odd number that divides into
60?
Write 132 as the product of its prime factors,
using index notation if necessary.
Hence write 132 x 6 as a product of its prime
factors, using indices
Find the HCF of 48 and 36
Find the LCM of 48 and 36
Two numbers e and f are written as a product of
their prime factors below:
e = 22 x 34 x 5 x 73
f = 24 x 5 4 x 7
To collect like terms in an expression
Find the HCF of e and f
Simplify the following expressions:
a)
b)
c)
d)
e)
To simplify algebraic expressions,
including using laws of index notation
2x + 3y + 5x + 4y
8p – 3q + 10p – 6q
5x + 7y – 3y + 8x – 4y
8x2 + 9x + 3x2 + 2x
3m – 9 + 2y + 16 – 15m – 3y
Simplify:
2a x -3b
2a2 x 3a3
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Maths Common Entrance revision Year 8
Topic/Objective
To multiply out brackets and simplify
Examples of questions
Multiply out the bracket 3(4e - 5)
Simplify 10 - 3(4e- 5)
NB: REMEMBER NEGATIVE RULES!!!
To factorise an expression
To solve linear equations
Multiply out the bracket and simplify
7p - 2(3p - 4)
Multiply out the bracket and simplify
8x- 5(3 - x)
Factorise fully:
12p + 18r
8g + 20
24 - 8y
Solve the following equations:
2b - 7 =15
¼ a = 12
3(2c + 1) =0
2 - d = 10 + 3d
3f - 2 = f +11
To form an algebraic expression and
solve a related equation.
3(2y + 5) = 3
Mr and Mrs Ode have three daughters, Ann, Cath
and Di.
Let a represent Annʼs age in years.
Cath is twice as old as Ann.
(i) Write down Cathʼs age, in terms of a.
Di is 2 years younger than Ann.
(ii) Write down his age, in terms of a.
The total of the ages of the three girls is 22
years.
(iii) Form an equation, in terms of a, and solve it
to find the value of a.
(iv) What will the total of the girlsʼ ages be
exactly 3 years from now?
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Maths Common Entrance revision Year 8
Topic/Objective
To substitute into an expression
To use ratio and proportion to answer
problems
Examples of questions
Given that x=3, y=-1 and z=4, find the value of:
i)
3x + 2z
ii)
x2 - y2
iii)
xyz
iv)
y+z
y
If c=5, d= -3 and e= -1, find the value of:
i)
3c + d
ii)
d–c
iii)
(2d)2
iv)
d+e
d-e
A formula used in physics is v = u + at
Find v when u = 10, a = -2 and t = 8.
To make custard for 4 people, Claire uses
300 millilitres of milk
2 eggs
tablespoon of vanilla essence
80 grams of caster sugar
(i) How much milk does Claire need to make
custard for 10 people?
(ii) Claire has plenty of milk, eggs and vanilla
essence, but only 280 grams of caster sugar. If
she uses all the caster sugar, for how many
people can she make custard?
Ianʼs packet of sweets contains only toffees and
fruit centres in the ratio 3 : 5
There are 24 toffees in the packet.
(i) How many sweets are there altogether in the
packet?
Ian eats 4 fruit centres from his packet of
sweets.
(ii) What is the ratio of toffees to fruit centres
remaining in the packet?
Give your answer in its simplest form.
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Maths Common Entrance revision Year 8
Topic/Objective
To use ratio and proportion to answer
problems (continued)
Examples of questions
A large packet of sweets contains 50% more
sweets than a standard packet.
What is the ratio of the number of sweets in a
large packet to the number of sweets in a
standard packet?
Give your answer in its simplest form.
To know the sum of angles in a triangle
is 180⁰
What is the size of each angle in an equilateral
triangle?
To know the properties of a right
angled, isosceles and equilateral triangle.
To know what vertically opposite angle
are and that they are equal.
To know what corresponding angles are
and that they are equal.
To know what alternate angles are and
that they are equal
To know that interior angles
(supplementary angles) add up to 180°
To know the sum of angles on a straight
line is 180⁰ and around a point is 360⁰
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Maths Common Entrance revision Year 8
Topic/Objective
Examples of questions
To use all of the above angle facts to
calculate missing angles
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Maths Common Entrance revision Year 8
Topic/Objective
To find the probability of an event
occurring (and not occurring)
To complete a possibility space and find
related probabilities
Examples of questions
When a fair six-sided die is rolled, what is the
probability of
(a) scoring 4?
(b) scoring a square number?
(c) not scoring 6?
Tim rolls his die 60 times.
How many times would you expect him to score
4?
Complete the table below to show all the possible
outcomes.
What is the probability that
(a) the number on Hayleyʼs card is higher than
the number on Jackʼs card?
(b) both cards show a multiple of 3?
Given that Hayleyʼs card shows a square number,
what is the probability that the two numbers
have a sum of 10?
To find the mean, mode, median and
range of a set of data.
Find the mode of the following sets of data:
A) 3, 2, 7, 6, 3
B) 4, 3, 0, 5, 0
C) 5, 6, 10, 6, 9, 3, 5, 4, 2
D) 2, 9, 7, 6, 5, 4
Find the range of the following data:
A) 9, 3, 8, 7, 24
B) 7, 6, -3, 4, 2
C) 6, 3, 0, 10, 21
D) -5, -9, -20, -3
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Maths Common Entrance revision Year 8
Topic/Objective
To find the mean, mode, median and
range of a set of data (Continued)
Examples of questions
Find the median of the following sets of data:
a) 3, 2, 7, 6, 9
b) 5, 10, 3, 7, 6, 12
c) 16, -2, 9, 8, -4, 7, 20
Find the mean of the following sets of data:
a) 7, 3, 2, 6, 7
b) 6, 0, 0, 4, 5
c) -6, 2, 7, -3, 5
The eight swimmers in a 25 metres freestyle
race recorded the following times in
seconds:
16.5 21.2 17.5 15.9 17.7 18.3
17.5 17.8
To find the mean, mode, median and
range from a frequency table
(i) What was the range of the times?
(ii) What was the median time?
(iii) Work out the mean time to complete the
race.
(iv) By how much time did the winner beat the
second-placed swimmer?
Here is some information about the number of
pets owned by each of the 18 children in David’s
class. One child owns 7 pets.
i) What is the modal number of pets owned?
(ii) What is the median number of pets owned?
(iii)
(a) Calculate the total number of pets owned.
(b) Calculate the mean number of pets owned.
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Maths Common Entrance revision Year 8
Topic/Objective
Examples of questions
To display data in graphical form e.g. pie
chart
Ma Bakerʼs Coffee Shop sells four different types of
cake.
One week, Ma Baker sold 90 cakes as follows:
35 were lemon
⅓ were chocolate
10% were ginger
the rest were coffee
How many degrees will show each cake on a pie chart?
Draw a fully-labelled pie chart to show Ma Bakerʼs
cake sales.
Here is a pie chart showing the results of a survey
carried out by Tim. He kept a record of the number
of birds in his garden at 9 am each morning for a
month.
What was the modal number of birds during this
month?
To continue a given sequence
Given that this month had 30 days, on how many days
did he record 3 birds?
Find the next 4 terms of the following sequences:
a) 3, 5, 7, 9, ....
b) 2, 7, 12, 17, ...
c) 12, -5, -22, -39, ...
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Maths Common Entrance revision Year 8
Topic/Objective
To continue a given sequence
Examples of questions
In this number sequence, the next term is
obtained by adding the two previous terms.
For example, 4 + 5 = 9
1, 4, 5, 9, 14, 23, 37 . . .
(i) Write down the next two terms after 37
(ii) How many prime numbers less than 100 are
there in the sequence?
Another sequence follows the rule: halve the
number, then add 1
(i) Write down the second and third terms if the
first term is 62
Using the same rule with a different first term,
Suzie noticed that the third term in her
sequence was larger than the second term.
(ii) Write down a number she could have used as
the first term.
To find any term of a sequence given its
nth term
To find the nth term of a linear
sequence
In each questions find the stated term given the
nth term:
a) 3n – 2 (12th term)
b) 6 – 5n (8th term)
c) 4n + 3 (29th term)
Find the nth term of the following sequences:
a) 2, 9, 16, 23, ....
b) -4, -1, 2, 5, ...
c) 20, 12, 4, -4, ...
d) -13, -18, -23, -28, ....
The 11th term of a sequence is 92. Given that the
sequence increases in nines, can you write down
the nth term?
Using this nth term, what is the 19th term of the
sequence?
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