In this worksheet, you will find 40 questions that include many of the level 3 topics that you have learned this year.
Work through the questions carefully.
Calculators may not be used unless the question says that you may use one.
Good luck!
This is a level 3 revision exercise to help prepare for Year 9/end of Key Stage 3 tests.
In this worksheet, you will find 40 questions that include many of the level 3 topics that you have learned this year.
Work through the questions carefully.
Calculators may not be used unless the question says that you may use one.
Good luck!
Work out:
8403  8.403 × 3
Work out:
78.39 × 8.7 ÷ 0.3
Is 

closer to 

or to 

? 
By which of the given numbers is the following number divisible?
1 663 893
Select all the number types which could describe the number:
√25
The number 37 999 is rounded to 38 000.
To how many significant figures could it have been rounded?
Select all the possible answers.
On your calculator, work out:
¼ × 3.7 × 2.5 + ½ (5.2^{2} + 3.4^{2})
Write the answer to 1 decimal place.
Subtract these numbers, written in standard form.
3.1 × 10^{2 } 3.1 × 10^{2}
Write your answer as a decimal.
Work out:
8    4  +  5 
15  18  21 
(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)
Work out:
8  ÷  4  ×  5 
15  18  21 
(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)
Change this fraction to a decimal:
3 
7 
Give your answer correct to 4 decimal places.
Work out:
(  6  )^{3} 
8 
(Write your answer in its lowest terms in the form a/b.)
Simplify:
5^{3} × 5^{4}
Round each of these numbers to 1 sig. fig. to work out an approximate answer to:
29.1^{2} × 31.9 
√857.8 
You may use a calculator for this question.
At this year's annual fete, Jack sold 476 hotdogs, which is a 12% increase compared to last year.
How many hotdogs did he sell in total in the two years, i.e this year and last year?
A book costs £24.56 but the price is increased by 12.5%.
This new price is then decreased by 12.5%.
Is the final price... ?
Find the first 5 terms in the sequence given by the formula:
T_{n} = 100  2n^{2}
where n is the position of the term in the sequence.
Also find the 20^{th} term and the 100^{th} term.
value  
T_{1}  
T_{2}  
T_{3}  
T_{4}  
T_{5}  
T_{20}  
T_{100} 
Simplify:
a(3a + 1)  2a(a  3)
Select the correct HCF (Highest Common Factor) of these two algebraic expressions:
7p^{5}q^{4}r and 21pq^{6}r^{6}
Simplify:
15x^{4}y^{3} 
35y^{4} 
Answers
1.  3x^{4}  2.  5x^{4}  3.  3x^{3}  
7y  7y^{4}  7y^{2} 
Multiply out and simplify:
(4n  1)^{2}
Simplify:
(2p^{3}q^{4})^{7}
Solve for a:
3(5  2a) = 2  5(4  a)
(Just write the value of a as a number.)
Solve simultaneously:
6x + 5y = 32
3x + y = 10
answers  
x  
y 
You may use a calculator for this question.
Solve the following equation:
2a  +  3a  =  57 
3  5 
(Just write the value of a.)
State the gradient of a line which is perpendicular to the line with equation:
y = 4  7x
(If it is not a whole number, write it as a fraction in the form a/b.)
Use the graph shown below to solve the quadratic equation:
2x^{2}  x  5 = 0
Select all the values of x that satisfy the quadratic equation.
The speed of light is approximately 300 000 000 m/s.
The average distance from the sun to the earth is 150 000 000 km.
Find the time taken for light to travel from the sun to the earth to the nearest minute.
(Just write the number.)
Convert the following area into one measured in cm^{2}.
12.6 m^{2}
(Just write the number.)
You may use a calculator for this question.
Find the area in cm^{2 }of a circle of circumference 16 cm.
(Just write the number to 1 decimal place.)
You may use a calculator for this question.
Calculate the diameter, d cm, of a circle which has an area of 201 cm^{2}.
Give your answer to 3 sig. figs.
(Just write the number.)
You may use a calculator for this question.
The formula for the volume of a sphere, V, in terms of its radius, r, is:
V = 4/3πr^{3}
A sphere has a volume of 1000 cm^{3}.
Calculate its radius in cm and its surface area in cm^{2}.
Give your answers to 3 sig. figs.
(Just write the number.)
answers  
radius  
surface area 
You may use a calculator for this question.
A regular polygon has an interior angle of 168¾º.
How many sides does it have?
You may NOT use a calculator for this question.
Look at these rightangled triangles, which are not drawn to scale.
Which side is longer, a or c?
You may use a calculator for this question.
Using trigonometry, calculate the side length x to 3 sig. figs.
You may use a calculator for this question.
Using trigonometry, find the height of this isosceles triangle in metres to 3 sig. figs.
(Just write the number.)
These two fair spinners are spun and the two scores are added together.
Use a samplespace diagram to answer the question.
What is the probability of getting a total score of 5?
(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)
There are 7 red balls and 5 yellow balls in Bag 1.
There are 6 red balls and 4 yellow balls in Bag 2.
I take one ball from Bag 1 and then one ball from Bag 2.
What is the probability that I select a ball of each colour?
A tree diagram has been started for you below.
(Give your answer as a reduced fraction in the form a/b.)
You may use a calculator for this question.
This table shows the masses of children in a Year 9 class at school.
Estimate the total mass in kg of all the children in the class.
Mass (m kg)  Frequency 

40 ≤ m < 45  2 
45 ≤ m < 50  5 
50 ≤ m < 55  9 
55 ≤ m < 60  3 
60 ≤ m < 65  1 
You may use a calculator for this question.
This chart shows the heights of children in a Year 9 class at school.
Estimate the mean height of all the children in cm to 1 decimal place.
(Just write the number.)
Work out:
8403  8.403 × 3
Work out:
78.39 × 8.7 ÷ 0.3
Is 

closer to 

or to 

? 
By which of the given numbers is the following number divisible?
1 663 893
Select all the number types which could describe the number:
√25
The number 37 999 is rounded to 38 000.
To how many significant figures could it have been rounded?
Select all the possible answers.
On your calculator, work out:
¼ × 3.7 × 2.5 + ½ (5.2^{2} + 3.4^{2})
Write the answer to 1 decimal place.
Subtract these numbers, written in standard form.
3.1 × 10^{2 } 3.1 × 10^{2}
Write your answer as a decimal.
Work out:
8    4  +  5 
15  18  21 
(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)
Work out:
8  ÷  4  ×  5 
15  18  21 
(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)
Change this fraction to a decimal:
3 
7 
Give your answer correct to 4 decimal places.
Work out:
(  6  )^{3} 
8 
(Write your answer in its lowest terms in the form a/b.)
Simplify:
5^{3} × 5^{4}
Round each of these numbers to 1 sig. fig. to work out an approximate answer to:
29.1^{2} × 31.9 
√857.8 
You may use a calculator for this question.
At this year's annual fete, Jack sold 476 hotdogs, which is a 12% increase compared to last year.
How many hotdogs did he sell in total in the two years, i.e this year and last year?
A book costs £24.56 but the price is increased by 12.5%.
This new price is then decreased by 12.5%.
Is the final price... ?
Find the first 5 terms in the sequence given by the formula:
T_{n} = 100  2n^{2}
where n is the position of the term in the sequence.
Also find the 20^{th} term and the 100^{th} term.
value  
T_{1}  
T_{2}  
T_{3}  
T_{4}  
T_{5}  
T_{20}  
T_{100} 
Simplify:
a(3a + 1)  2a(a  3)
Select the correct HCF (Highest Common Factor) of these two algebraic expressions:
7p^{5}q^{4}r and 21pq^{6}r^{6}
Simplify:
15x^{4}y^{3} 
35y^{4} 
Answers
1.  3x^{4}  2.  5x^{4}  3.  3x^{3}  
7y  7y^{4}  7y^{2} 
Multiply out and simplify:
(4n  1)^{2}
Simplify:
(2p^{3}q^{4})^{7}
Solve for a:
3(5  2a) = 2  5(4  a)
(Just write the value of a as a number.)
Solve simultaneously:
6x + 5y = 32
3x + y = 10
answers  
x  
y 
You may use a calculator for this question.
Solve the following equation:
2a  +  3a  =  57 
3  5 
(Just write the value of a.)
State the gradient of a line which is perpendicular to the line with equation:
y = 4  7x
(If it is not a whole number, write it as a fraction in the form a/b.)
Use the graph shown below to solve the quadratic equation:
2x^{2}  x  5 = 0
Select all the values of x that satisfy the quadratic equation.
The speed of light is approximately 300 000 000 m/s.
The average distance from the sun to the earth is 150 000 000 km.
Find the time taken for light to travel from the sun to the earth to the nearest minute.
(Just write the number.)
Convert the following area into one measured in cm^{2}.
12.6 m^{2}
(Just write the number.)
You may use a calculator for this question.
Find the area in cm^{2 }of a circle of circumference 16 cm.
(Just write the number to 1 decimal place.)
You may use a calculator for this question.
Calculate the diameter, d cm, of a circle which has an area of 201 cm^{2}.
Give your answer to 3 sig. figs.
(Just write the number.)
You may use a calculator for this question.
The formula for the volume of a sphere, V, in terms of its radius, r, is:
V = 4/3πr^{3}
A sphere has a volume of 1000 cm^{3}.
Calculate its radius in cm and its surface area in cm^{2}.
Give your answers to 3 sig. figs.
(Just write the number.)
answers  
radius  
surface area 
You may use a calculator for this question.
A regular polygon has an interior angle of 168¾º.
How many sides does it have?
You may NOT use a calculator for this question.
Look at these rightangled triangles, which are not drawn to scale.
Which side is longer, a or c?
You may use a calculator for this question.
Using trigonometry, calculate the side length x to 3 sig. figs.
You may use a calculator for this question.
Using trigonometry, find the height of this isosceles triangle in metres to 3 sig. figs.
(Just write the number.)
These two fair spinners are spun and the two scores are added together.
Use a samplespace diagram to answer the question.
What is the probability of getting a total score of 5?
(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)
1  2  3  4  

1  2  3  4  5 
2  3  4  5  6 
3  4  5  6  7 
4  5  6  7  8 
The probability of getting a total of 5, P(5) = 4/16 = 1/4.
There are 7 red balls and 5 yellow balls in Bag 1.
There are 6 red balls and 4 yellow balls in Bag 2.
I take one ball from Bag 1 and then one ball from Bag 2.
What is the probability that I select a ball of each colour?
A tree diagram has been started for you below.
(Give your answer as a reduced fraction in the form a/b.)
You may use a calculator for this question.
This table shows the masses of children in a Year 9 class at school.
Estimate the total mass in kg of all the children in the class.
Mass (m kg)  Frequency 

40 ≤ m < 45  2 
45 ≤ m < 50  5 
50 ≤ m < 55  9 
55 ≤ m < 60  3 
60 ≤ m < 65  1 
You may use a calculator for this question.
This chart shows the heights of children in a Year 9 class at school.
Estimate the mean height of all the children in cm to 1 decimal place.
(Just write the number.)
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