Download make the grade

MAKE THE
GRADE
NUMBER
1. Estimate the value of:
38 × 197
83
(4)
2. Estimate the answer to:
2·24 × 16·8
(6·8 – 1·9)
(4)
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. A television is bought for £140 and sold for a 30% profit. Calculate the
selling price.
(3)
S A LOMAX 2005
6. 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)
7. 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)
3
of a mile every day. What is the number of miles Bert runs in a
5
week to the nearest mile?
8. Bert runs
(3)
9. Calculate
3 1
−
4 3
(3)
10. Calculate
1 4
+ simplifying your answer.
3 5
(4)
S A LOMAX 2005
11. Which of these fractions is the largest?
4
15
2
9
1
5
(2)
12.
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)
S A LOMAX 2005
Assess your knowledge
Skill
I can estimate answers to calculations
I can multiply and divide by powers of 10
I can increase amounts using percentages
I can express a fraction as a percentage
I can multiply a fraction by an integer
I can add and subtract fractions with different denominators
I can use equivalent fractions
I can use simple proportional reasoning
I can share amounts using ratio
I can calculate speed
Qu
1, 2
3
4, 5, 6
7
8
9, 10
11
12
13
14
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
36 -45
24 – 35
0 – 23
- Well done. You are definitely working at grade D with your
number skills. Bring on the C !!!
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that C !!!
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2005
☺ MAKE THE
GRADE
NUMBER
2. Estimate the value of:
4·24 × 714·8
11·8 + 7·88
(4)
2. Estimate the answer to:
813 × 5·12
0·197
(4)
3.
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)
S A LOMAX 2005
4. If x = 5, write down the value of 2x²
(2)
5. Write down the reciprocal of
a) 6
(1)
b) 0·25
(1)
6. Divide £440 in the ratio 5 : 3
(3)
7. Divide 63kg in the ratio 1 : 4: 2
(3)
S A LOMAX 2005
1
2
turn followed by a 1 turn. He is now
4
3
very dizzy! What is the total ‘turn’ Sam has made?
8. Sam the Skateboarder tries a 2
(4)
9. Work out 4
1
3
-1
3
4
(4)
10. 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)
11. Calculate the % increase from 45cm² to 54cm².
(3)
12. A car decreases in price by 60% each year. If the starting price is £6500 ,
calculate the price of the car at the end of the first year.
(3)
S A LOMAX 2005
13. Calculate the compound interest on £2500 for 3 years at 5% p.a.
(4)
14. A coach carries 54 passengers. How many coaches are needed to
transport 528 supporters to the Man United match?
(3)
15. Steph spends an average of £4·57 a week on fast food. How much does
she spend on average each year?
(4)
S A LOMAX 2005
Assess your knowledge
Skill
I can estimate answers to calculations involving numbers
between 0 and 1
I can write numbers as a product of prime factors
I can find HCF and LCM of two numbers
I can evaluate expressions involving squares
I can find the reciprocal of numbers
I can share amounts using ratio
I can add and subtract fractions involving mixed numbers
I can find upper and lower bounds
I can calculate % increases
I can calculate increases/decreases involving %
I can calculate compound interest
I can divide 3 digit number by a 2 digit number and solve a
problem using my answer
I can multiply a 3 digit number by a 2 digit number and solve a
problem using my answer
Qu
1, 2
3a, b
3c, d
4
5
6, 7
8, 9
10
11
12
13
14
15
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
44 -55
25 – 43
0 – 24
- Well done. You are definitely working at grade C with your
number skills. Bring on the B !!!
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that C !!!
- Serious revision and help is needed if you are going to get
that C. Sort it out now. Don’t wait any longer
S A LOMAX 2005
☺ MAKE THE
GRADE
ALGEBRA
1. Write down the first three terms of the sequence described by the nth
term n² - 3.
(3)
2. A function machine inputs a number, n, multiplies it by 3 and then
subtracts 6. What is the output for n=2?
(1)
3. P = F(B -1) . Calculate the value of P when B = -5 and F = 20.
12
(2)
4. 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)
5.
Sam buys t spiderman toys at 60p and 3 at £1.20. The total cost is £6.
S A LOMAX 2005
a) Construct an equation.
(3)
b) Solve the equation to find the value of t.
(2)
6.
x
x+5
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)
7. Find the value of the largest angle.
S A LOMAX 2005
x
(4)
8. Simplify:
a) 5a + 2b – 3a + b
(2)
b) p² + p² + p²
(2)
9.Expand 3(x – 4)
(2)
10. Factorise completely:
a) 5a – 20
(2)
b) p² - 5p
(2)
11. Solve:
a) 2x – 4 = 14
S A LOMAX 2005
(2)
b)
x
+ 3 = 18
3
(2)
c) 4(3x + 2) = 44
(3)
d) 5x + 3 = 13 + 3x
(3)
12. At the point H, the graph of y = x + 6 crosses y = 4. Find the co-ordinates
of H.
(3)
13.
a) Complete the table of values for y = x² + 3.
S A LOMAX 2005
x
y
-2
7
-1
0
1
4
2
(3)
b) Draw the graph of y = x² + 3
y
x
(2)
14. Draw the graph of y = 2x – 4.
y
x
(2)
12. 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:
S A LOMAX 2005
(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)
Assess your knowledge
S A LOMAX 2005
☺ Yippee!! - I got all the questions correct.
Skill
I can generate terms of a sequence using the nth term
I can substitute values into fomulae
I know the difference between an expression and a formulae
I can construct and solve linear equations
I can collect like terms
I can expand an integer over a bracket
I can factorise expressions
I can solve linear equations with unknowns on one side
I can solve linear equations with unknowns on both sides
I can solve distance/time graphs
I can complete tables of values and plot points
I can draw the graphs of linear equations
I can solve linear graph problems
Qu
1
2,3
4
5,6,7
8
9
10
11a,b,c
11d
12
13
14
15
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
47 - 58
- Well done. You are definitely working at grade D with your
algebra skills. Bring on the C !!!
28 - 46
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that D !!!
0 – 27
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2005
☺ MAKE THE
GRADE
ALGEBRA
6. Write down the nth term for the sequence 4, 10, 16, 22, …
(2)
7. Write down the nth term for the following sequence:
1 × 3, 2 × 4, 3 × 5, 4 × 6, …
(2)
8. Simplify the following:
a) p³ × p²
b) 2t² × 5t4
c) b7
b³
d) 24k6
3k²
e) 5h4 × 4h2
2h3
f) (y3)2
(11)
S A LOMAX 2005
9. Expand y(y³ - 6)
(2)
5.
a) Simplify 3(x + 4) + 2(x +3)
(4)
b) Simplify 5(y + 3) – 4(y – 6)
(4)
6. Make x the subject of the y = 3x -6
(2)
S A LOMAX 2005
7. Solve:
a)
x
- 5 = 30
5
(2)
b)
y +9
=2
4
(2)
c) 5x + 22 = 2( x – 4)
x+5
(3)
8.
Diagram not
drawn to scale
x
x
x-2
The perimeter of the trapezium is 13cm. Calculate the longest side.
(4)
S A LOMAX 2005
9. Find the value of the smallest angle.
x
Diagram not
drawn to scale
x+20º
120º
2x+60º
(3)
10. Solve 4x – 5 ≤ 7.
(2)
Show your answer on the number line below:
(2)
11. n is an integer. Write down the possible values for n if:
-4 ≤ 2n ≤ 5
(4)
S A LOMAX 2005
12.
a) Complete the table of values for y = 2x² + 2x - 3.
x
y
-2
-1
-3
0
1
2
9
(3)
b) Draw the graph of y = 2x² + 2x - 3
y
x
(2)
c) Draw the line y = -1 on the graph.
(1)
d) Hence, or otherwise, solve 2x² + 2x – 3 = -1
(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)
d) What is Hannah’s average speed for the whole journey?
S A LOMAX 2005
Skill
I can find the nth term of a linear sequence
I can spot a pattern and find the nth term of a sequence
I can use the rules of indices
I can expand a term over a bracket
I can expand and simplify an expression involving brackets
I can change the subject of a formulae
I can solve linear equations with unknowns on one side
I can solve linear equations with unknowns on both sides
I can construct and solve linear equations
I can solve linear inequalities
I can complete tables of values and draw graphs of quadratics
I can use graphs to solve equations
I can solve average speed problems
Qu
1
2
3
4
5
6
7a,b
7c
8, 9
10, 11
12a, b
12d
13
(3)
Assess your knowledge
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
50 - 60
- Well done. You are definitely working at grade C with your
algebra skills. Bring on the B !!!
30 - 49
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that C !!!
0 – 30
- Serious revision and help is needed if you are going to get
that C. Sort it out now. Don’t wait any longer
S A LOMAX 2005
☺ MAKE THE
GRADE
1. Rotate triangle EFG 90º clockwise about the origin. Label
the new triangle E’F’G’.
y
SHAPE,
SPACE &
MEASURES
E
F
G
x
(3)
2. Reflect triangle PQR in the line y = -1. Label the image P’Q’R’.
y
P
Q
R
x
(3)
3. Describe the transformation of shape A to shape B.
y
B
x
A
(3)
S A LOMAX 2005
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)
S A LOMAX 2005
c)
x=
Reasons:
(2)
d)
s=
Reasons:
(3)
e)
x=
Reasons:
S A LOMAX 2005
(3)
f)
y=
Reasons:
(3)
6. Calculate the interior angle of a regular hexagon
(3)
7. Calculate the exterior angle of a decagon
(2)
8. Draw a plane of symmetry on the solid:
S A LOMAX 2005
(1)
9. Find the area and perimeter of the following shapes:
a)
Perimeter =
3cm
4cm
Area =
5cm
(4)
6cm
b)
6cm
Perimeter =
Area =
10cm
8cm
(5)
c)
Perimeter =
5cm
S A LOMAX 2005
4cm
Area =
(4)
10. Find the area and circumference of the circle given below:
20cm
(Take π = 3)
Area:
(3)
Circumference:
(3)
11. Convert 2·4m² into cm²
S A LOMAX 2005
(2)
12. Dorothy is painting her shed. 1 litre of paint covers 2m². How much paint
does she need?
3m
2m
2m
(4)
13. You are looking at a solid from the side. Draw the front elevation and plan.
S A LOMAX 2005
Skill
FRONT
I can transform using rotations and reflections
I can describe transformations fully
I can transform using enlargements
I can solve angle problems involving triangles and parallel lines
I can solve angles involving polygons
Qu
1, 2
3
4
5a-5e
5f
(3)
Assess your knowledge
S A LOMAX 2005
☺ I can calculate interior and exterior angles of regular polygons
I can draw planes of symmetry
I can solve perimeter and areas of triangles
I can solve perimeter and areas of shapes made of rectangles
and triangles
I can solve perimeter and areas of trapezia
I can find areas and circumferences of circles
I can convert between units of area
I can draw elevations and plans
6,7
8
9a
9b, 12
9c
10
11
13
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
50 – 62
- Well done. You are definitely working at grade D with your
shape and space skills. Bring on the C !!!
31 – 49
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that D !!!
0 – 30
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2005
MAKE THE
GRADE
SHAPE,
SPACE &
MEASURES
1.
a) Describe fully the transformation of P
R.
(2)
b) Describe fully the transformation of Q
S.
(2)
2. Enlarge the trapezium by a factor of
y
S A LOMAX 2005
1
from the origin.
4
x
(3)
3. Calculate the areas of the following shapes:
(Take π=3)
a)
2m
(3)
b)
2m
S A LOMAX 2005
(4)
4. Calculate the perimeter of a semi-circle radius 5cm. (Take π=3)
(3)
5. a) Calculate the volume of the world’s largest Toberlone piece shown
below:
50cm
50cm
S A LOMAX 2005
10cm
(5)
b) How many litres of chocolate are needed to make the piece?
(2)
6.
“SUCCESS comes in
‘cans’ not ‘can’ts’”
Calculate the volume of ‘success’ in the can shown.
(Height = 10cm and radius = 3cm - take π=3)
S A LOMAX 2005
(4)
7. Mike reckons that 2·5m³ is the same as 250cm³. Is he correct?
Explain your answer.
(3)
8. Find the missing sides of the following triangles:
a)
5cm
12cm
x
(3)
b)
x
6cm
S A LOMAX 2005
10cm
(3)
9. Find the surface area of the solid shown below:
4cm
2cm
3cm
S A LOMAX 2005
(6)
10. a) A regular polygon has an exterior angle of 45º. How many sides does it
have?
(3)
b) Does this polygon tessellate with itself?
(1)
11. 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?
S A LOMAX 2005
(2)
12. 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 1:10 and show all construction lines.
NORTH WALL
S A LOMAX 2005
(5)
Skill
I can transform shapes using rotations and reflections
I can transform shapes using enlargements
I know the formula for the area of a circle
I know the formula for the circumference of a circle
I can calculate volumes of prisms
☺ Qu
1
2
3
4
5a,6
13. Construct a perpendicular bisector through point A. Show all construction
lines
B
A
(3)
Assess your knowledge
S A LOMAX 2005
I can convert between units of volume and area
I can use Pythagoras to find missing sides in right angled
triangles
I can calculate the surface area of prisms
I can calculate the exterior angle of a regular polygon
I can solve problems involving bearings
I can solve problems involving loci
I can construct perpendicular bisectors using a pair of
compasses
5b,7
8
9
10
11
12
13
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
46 – 57
- Well done. You are definitely working at grade C with your
shape and space skills. Bring on the B !!!
29 – 45
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that C !!!
0 – 28
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2005
MAKE THE
GRADE
HANDLING
DATA
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
1
2
3
4
5
Frequency
0
8
2
2
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)
S A LOMAX 2005
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
Is this question appropriate to use in a questionnaire?
Give a reason to support your answer.
No
(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)
S A LOMAX 2005
5. The following data was collected - number of hours revision doing past
paper questions and the final GCSE %.
Hours
GCSE %
7
58
6
55
5
35
7
65
9
90
6
45
4
35
8
75
9
83
10
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) If a student hopes to get at least 50% on his Intermediate GCSE paper to
try and get a C. Use your line of best fit to estimate the minimum number
of hours revision using the past papers the student must do.
(2)
S A LOMAX 2005
6. A bag has 4 colours of sweets. George loves blue sweets. The probability
of getting the other colours in the bag are:
Colour
Probability
Red
0·3
Yellow
0.25
Green
0.12
Blue
?
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)
S A LOMAX 2005
Assess your knowledge
Skill
I can find the mean from a frequency table
I can find the mode from a frequency table
I can find the modal class from a diagram
I can analyse pie charts
I can draw stem and leaf diagrams using a key
I can identify why questions are sometimes inappropriate
I can spot problems with samples
I can plot points on a scatterdiagram
I can draw a line of best fit
I can use the line of best fit to estimate results
I can complete probability tables
I can use probabilities to predict results
Qu
1a
1b
2a
2b
3
4a
4b
5a
5b
5c
6a
6b
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
20 -25
- Well done. You are definitely working at grade D with your
handling data skills. Bring on the C !!!
13 – 19
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that D !!!
0 – 12
- Serious revision and help is needed. Sort it out now.
Don’t wait any longer
S A LOMAX 2005
☺ MAKE THE
GRADE
HANDLING
DATA
1. The number of silly mistakes a student makes in the their Maths
GCSE papers are shown in the table below:
Silly Mistakes
(m)
0 ≤ m<4
4 ≤ m<8
8 ≤ m<12
Frequency
6
8
4
a) Estimate the mean number of silly mistakes.
(4)
b) In which class interval is the median number of silly mistakes?
(2)
2.
a) Describe the type of correlation in the scatter diagram given below:
(1)
b) Suggest two variables that A and B could represent.
(1)
S A LOMAX 2005
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. Mr Healthy collects information about the number of portions of chips
students eat each week.
Minimum
Maximum
Median
Upper quartile
Inter-quartile range
2
10
6
9
5
Draw a box and whisker plot to represent the information
0
(4)
S A LOMAX 2005
5. The Box and Whisker plots show the results of the survey to find the
average amount of water drunk by each student in Classes A and B.
.
Comment on the diagrams.
(2)
6. Mr. PinchanInch is trying to lose weight. He loses different amounts each
month.
Month
Weight loss
Jan
3
Feb
1
Mar
2
Apr
0
May
4
Calculate 3 point moving averages to help him analyse the trend.
(4)
S A LOMAX 2005
7. 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)
8.
What is the probability of getting double six when rolling two dice?
(3)
S A LOMAX 2005
Assess your knowledge
Skill
I can estimate the mean from grouped data
I can work out the class interval which contains the median
I can describe the type of correlation in a scatter diagram
I can design suitable questions for questionnaires
I can draw box and whisker plots
I can use box and whisker plots to compare distributions
I can calculate moving averages
I can calculate relative frequencies
I can use relative frequencies to estimate results
I can calculate probabilities involving two events
Qu
1a
1b
2
3
4
5
6
7a
7b
8
☺ Yippee!! - I got all the questions correct.
I made mistakes and need to practise this topic more.
Top 3 topics I need to revise are
☺
☺
☺
If your score is:
22 -28
- Well done. You are definitely working at grade C with your
handling data skills. Bring on the B !!!
13 – 21
- Promising work – make sure you ask for help and revise the
topics that you had difficulty with. You can still get that C !!!
0 – 12
- Serious revision and help is needed if you are going to get
that C. Sort it out now. Don’t wait any longer
S A LOMAX 2005
☺