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A grade B student can …
GCSE Foundation Revision
Grade D to C
Name: ______________
a grade D student can …
Number
Estimate answers to calculations involving division
Use the terms square, positive and negative square root, cube and cube root
Recall integer squares from 2×2 to 15×15 and the corresponding square roots
Recall the cubes of 2, 3, 4, 5 and 10
Multiply two decimals such as 2·4 × 0·7
Convert decimals to fractions and fractions to decimals
Do calculations with simple fractions involving subtraction
Increase or decrease a quantity by a given percentage
Algebra
Multiply out expressions with brackets such as 5(3x – 2)
Factorise expressions
Write the terms of a sequence or a series of diagrams given the nth term
Draw lines such as y = 2x + 3
Solve problems involving straight lines
Solve linear equations with unknowns on each side such as 3x – 4 = 5 + x
Solve linear equations with brackets such as 2(5x + 1) = 28
Substitute numbers into more complicated formulae such as
Solve problems involving graphs, such as finding where the line y = x + 5 crosses the line y = 1
Draw graphs of simple quadratic functions such as y = 2x2 and y = x2 + 2
Shape and Space
Find the area of a triangle, parallelogram, kite and trapezium
Find the area and perimeter of compound shapes
Calculate the circumference of a circle to an appropriate degree of accuracy
Calculate the area of a circle to an appropriate degree of accuracy
Reflect shapes in lines such as x = 2 or y = –1
Rotate shapes about the origin
Describe fully reflections and rotations about the origin
Identify reflection symmetry in 3-D solids
Translate a shape using a description such as 4 units right and 3 units down
Enlarge a shape by a positive scale factor from a given centre
Calculate simple average speeds from distance–time graphs
Draw a quadrilateral such as a kite or a parallelogram with given measurements
Construct and recognise the nets of 3-D solids such as pyramids and triangular prisms
Draw plans and elevations of 3-D solids
Data Handling
Calculate the mean for a frequency distribution
Construct a stem-and-leaf diagram (ordered)
Construct a frequency diagram
Interpret a time series graph
Draw a scatter graph by plotting points on a graph
Interpret the scatter graph
Classify and know the difference between various types of data
Design and use data collection sheets and questionnaires
Use a variety of different sampling methods
Use a two-way table to find a probability
Understand mutually exclusive events
Use the fact that the probabilities of mutually exclusive events add up to 1
a grade C student can …
Number
Find the least common multiple (LCM) and highest common factor (HCF) of two simple numbers
Write a number as a product of prime factors
Solve numerical problems using a calculator efficiently and appropriately
Find minimum and maximum values
Divide a number by a decimal such as 1 ÷ 0·2
Work out a percentage increase or decrease
Express one quantity as a percentage of another
Do calculations with mixed numbers and simple fractions involving division
Solve complex ratio problems, such as sharing out money between two groups
Solve ratio and proportion problems using the unitary method
Algebra
Multiply out expressions with brackets such as y(3y – 8)
Expand and simplify two expressions of the form (x + n)
Use index notation and index laws for positive and negative powers
Write the nth term of a sequence or a series of diagrams
Solve more complex linear equations such as 3x – 12 = 2(x – 5)
Form and solve equations such as x3 + x = 12 using trial and improvement methods
Rearrange linear formulae such as s = 4q - 7
Find the gradients of straight-line graphs
Solve inequalities such as 3x < 9 and 4x – 3 < 10 and 4x < 2x + 7
Represent sets of solutions on the number line
Shape and Space
Solve problems involving circles such as finding the area and perimeter of a semicircle
Calculate volumes of triangular prisms, parallelogram-based prisms and cylinders
Solve problems involving surface areas of prisms
Convert between measures of area and volume
Classify a quadrilateral by geometric properties
Use angle and symmetry properties of polygons and angles in parallel lines
Calculate exterior and interior angles of a regular polygon
Find the midpoint of a line segment
Use and understand coordinates in three dimensions
Reflect shapes in the lines y = x and y = –x
Rotate shapes about any point
Describe fully reflections and rotations about any point
Find the centre of a rotation and describe it fully
Combine reflections and rotations
Translate a shape by a vector such as
Transform shapes by a combination of translation, reflection and rotation
Understand and use compound measures such as speed and density
Construct a perpendicular bisector of a line, from a point to a line, from a point on a line
Construct angles of 60° and 90° and the bisector of an angle
Identify congruent shapes
Use Pythagoras’ theorem
Construct loci
Data Handling
Find the mean, median class and modal class for grouped data
Use measures of average and range to compare distributions
Draw a line of best fit on the scatter graph by inspection
Identify possible sources of bias in the design and use of data collection sheets & questionnaires
Understand relative frequency as an estimate of probability
Use relative frequency to compare outcomes of experiments
Number D
1. Estimate the value of:
38 197
83
(4)
2. For only this question use a calculator work the answer to:
2∙24 16∙8
(6∙8 – 1∙9)
Write down all the numbers on your calculator display
(2)
3. Given that 67 112 = 7504, write down the answers for:
a) 6∙7 1∙12
(1)
b) 7504 ÷ 670
(1)
4. A computer is reduced by 15% in a sale. The original price is £560. Calculate the sale price.
(3)
5. Fred can’t decide which microwave to buy. The ‘Burnyourmouth’ model is £60 + 17∙5% VAT but the ‘PingPingPing’ model is £70 including VAT. Which is the better deal?
(4)
6. Sheila got 183 out of 300 in a test. Bob got 24 out of 40 on a different test. Who got the higher percentage?
(3)
7. Bert runs of a mile every day. What is the number of miles Bert runs in a week to the nearest mile?
(3)
8. Calculate
(3)
9. Calculate simplifying your answer.
(4)
10. Grandma Margaret's Butterfly Cakes (for 12 people)
2 eggs
100g of sugar
120g of flour
150g of margarine
What ingredients are needed for 18 people?
eggs
g of sugar
g of flour
g of margarine
------- ------ -------- ------
(4)
11. Albert and Ethel share £240 in the ratio 3 : 5 . How much does Ethel receive?
(3)
12. Buzz travels 150 kilometres in 1hour 30 minutes. Calculate Buzz’s speed in km/h.
(3)
13. Write these numbers in order of size.Start with the smallest number.
65%0.72
................................................................
(2)
Number C
1.
a) Write 60 as a product of prime factors
(3)
b) Write 45 as a product of prime factors
(3)
c) Find the HCF of 45 and 60
(2)
d) Find the LCM of 45 and 60
(2)
2. If x = 5, write down the value of 2x²
(2)
3. Work out 4 - 1
(4)
4. Hannah measures the length of her train. She says it is about 21cm to the nearest cm. What is the greatest and least value of the length of the train?
(2)
5. Calculate the % increase from 45cm² to 54cm².
(3)
6. Calculate the compound interest on £2500 for 3 years at 5% p.a. Use a calculator
(4)
7. A coach carries 54 passengers. How many coaches are needed to transport 528 supporters to the Man United match?
(3)
Algebra D
1. Write down the first three terms of the sequence described by the nth term n² - 3.
(3)
2. P = F(B -1) . Calculate the value of P when B = -5 and F = 20.
12
(2)
3. a) Write down an expression for the total cost in pence of x chocolate bars at 80p and y ice creams at 75p each.
(2)
b) Write down a formula for the total cost, C, in pence.
(1)
4. Sam buys t Spiderman toys at 60p and 3 at £1.20. The total cost is £6.
a) Construct an equation.
(3)
b) Solve the equation to find the value of t.
(2)
5.
x + 5
x
a) Write down an expression for the perimeter,P, of the rectangle in terms of x.
(2)
b) If the P = 30cm, find the longest side of the rectangle.
(3)
6. Find the value of the largest angle.
2x+60º
x
x+20º
120º
Diagram not drawn to scale
(4)
7. Simplify:
a) 5a + 2b – 3a + b
(2)
b) p² + p² + p²
(2)
8.Expand 3(x – 4)
(2)
9. Factorise completely:
a) 5a – 20
(2)
b) p² - 5p
(2)
10. Solve:
a) 2x – 4 = 14
(2)
b) + 3 = 18
(2)
c) 4(3x + 2) = 44
(3)
d) 5x + 3 = 13 + 3x
(3)
11.
a) Complete the table of values for y = x² + 3.
x
-2
-1
0
1
2
y
7
4
(3)
b) Draw the graph of y = x² + 3
y
x
(2)
12. Draw the graph of y = 2x – 4.
y
x
(2)
13. Hannah likes to feed the ducks at her local park. She leaves the house at 11.00a.m. The distance time graph shows her journey:
(min)
a) On the way to the park, Hannah stops to have a snack. At what time did this occur?
(1)
b) How long did Hannah stay at the park?
(1)
c) What was Hannah’s average speed on the way home?
(3)
Algebra C
1. Simplify the following:
a) p³ p²
b) 2t² 5t4
c) b7
b³
d) 24k6
3k²
e) (y3)2
(10)
2.
a) Simplify 3(x + 4) + 2(x +3)
(4)
b) Simplify 5(y + 3) – 4(y – 6)
(4)
3. Make x the subject of the y = 3x -6
(2)
x + 5
4.
Diagram not drawn to scale
x
x
x - 2
The perimeter of the trapezium is 13cm. Calculate the longest side.
(4)
5. Find the value of the smallest angle.
2x+60º
x
x+20º
120º
Diagram not drawn to scale
(3)
6. Solve 4x – 5 7.
(2)
Show your answer on the number line below:
(2)
Shape D
1. Rotate triangle EFG 90º clockwise about the origin. Label
y
the new triangle E’F’G’.
x
G
E
F
(3)
2. Reflect triangle PQR in the line y = -1. Label the image P’Q’R’.
y
x
R
Q
P
(3)
3. Describe the transformation of shape A to shape B.
y
A
B
x
(3)
4. Enlarge the triangle by a factor of 2 from centre P.
y
P
x
(3)
5. Find the missing angle in each diagram giving reasons for your answers:
a)
x = Reasons:
(3)
b)
x = Reasons:
(2)
c)
s = Reasons:
(3)
6. Calculate the interior angle of a regular hexagon
(3)
7. Draw a plane of symmetry on the solid:
(1)
8. Find the area and perimeter of the following shapes:
a)
3cm
4cm
5cm
Perimeter =
Area =
(4)
6cm
b)
6cm
10cm
Perimeter =
Area =
8cm
(5)
c)
Perimeter =
Area =
5cm
4cm
(4)
9. Find the area and circumference of the circle given below:
20cm
(Take π = 3)
Area:
(3)
Circumference:
(3)
10. Dorothy is painting her shed. 1 litre of paint covers 2m². How much paint does she need?
2m
3m
2m
(4)
11. You are looking at a solid from the side. Draw the front elevation and plan.
FRONT
(3)
Shape C
1. Calculate the areas of the following shapes:
(Take π=3)
a)
2m
(3)
b)
2m
(4)
2. Calculate the volume of the world’s largest Toberlone piece shown below:
50cm
10cm
50cm
(5)
“SUCCESS comes in ‘cans’ not ‘can’ts’”
3.
Calculate the volume of ‘success’ in the can shown.
(Height = 10cm and radius = 3cm - take π=3)
(4)
4. Find the missing sides of the following triangles:
a)
12cm
5cm
x
(3)
b)
x
6cm
10cm
(3)
5. Find the surface area of the solid shown below:
4cm
2cm
3cm
(6)
6. A ship leaves harbour A and sails on a bearing of 050º to harbour B. What is the bearing of harbour A from harbour B?
(2)
7. The Great Western Don’tStandSoCloseToMe (which looks like a cute bunny but isn’t!!!) has a nasty sting which it uses if people get too close to it. The zookeeper is trying to feed him. It is a particularly bad day and The Great Western Don’tStandSoCloseToMe is only happy if:
- the zookeeper doesn’t get any closer than 50cm to him
- the zookeeper stays closer to the North wall than him.
Shade on the diagram below the areas where the zookeeper is ‘safe’.
Use a scale of 1:20 and show all construction lines.
NORTH WALL
(5)
8. Construct a perpendicular bisector through point A. Show all construction lines.
B
A
(3)
9. Bisect the angle below. Show all construction lines.
(3)
Data D
1. The number of silly mistakes a student makes in the first
10 questions of their Maths GCSE are shown in the table below:
Silly Mistakes
Frequency
1
0
2
8
3
2
4
2
5
3
a) Calculate the mean number of silly mistakes.
(4)
b) Calculate the mode for the silly mistakes
(1)
2. The pie chart shows information on how students travel to school.
a) What is the modal form of transport?
(1)
b) If 320 students travel to school, how many use the bus?
(2)
3. Sam was counted the number of sweets in ten ‘Millions’ packets. The number of sweets he counted are as follows:
35, 42, 33, 55, 63, 29, 37, 48, 43, 51
(he was very upset to find that there wasn’t a million sweets even though it did say so on the packet!?!)
Represent this information using a stem and leaf diagram.
(3)
4. a) ‘Only intelligent people think that smoking should be banned in
public places.
Do you think smoking should be banned in public places? Yes No
Is this question appropriate to use in a questionnaire?
Give a reason to support your answer.
(2)
b) Mr Healthy visits a school and asks the first 10 students he can find a question about their lunch. They are all in Year 7 and he is delighted to hear that they all eat healthy sandwiches and no chips. He goes home happy knowing that all students eat healthily.
Is he correct?
(2)
5. The following data was collected - number of hours revision doing past paper questions and the final GCSE %.
Hours
7
6
5
7
9
6
4
8
9
10
GCSE %
58
55
35
65
90
45
35
75
83
95
a) Represent this information using a scatter diagram
GCSE
%
Hours Revision
(2)
b) Draw the line of best fit on your scatter diagram.
(1)
c) Describe the correlation
(1)
6. A bag has 4 colours of sweets. George loves blue sweets. The probability of getting the other colours in the bag are:
Colour
Red
Yellow
Green
Blue
Probability
0∙3
0.25
0.12
?
a) What is the probability of getting a blue sweet
(2)
b) If the bag contains 200 sweets, estimate how many sweets would be red.
(3)
Data C
1. The number of silly mistakes a student makes in the their Maths
GCSE papers are shown in the table below:
Silly Mistakes (m)
Frequency
0m<4
6
4m<8
8
8m<12
4
a) Estimate the mean number of silly mistakes.
(4)
b) In which class interval is the median number of silly mistakes?
(2)
2. Describe the type of correlation in the scatter diagram given below:
(1)
3. Mr Healthy hates fast food. He is interested to find out the eating habits of students at his local school. Design a suitable question for a questionnaire that he could use to collect the data.
(2)
4. Tina rolls a die and records the numbers she gets.
a) Write down the relative frequency of getting a 2.
(2)
b) If Tina rolls the die 450 times, approximately how many times would the number 4 occur?
(3)
5.
What is the probability of getting double six when rolling two dice?
(Hint: draw a sample space)
(3)
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