Transcript Slide 1

GCSE LINEAR GRADE D STARTER
QUESTIONS
(FOUNDATION)
AUTHOR
www.mistrymaths.co.uk
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1)
2)
3x1–1= 2
3x2–1= 5
3x3–1= 8
3 x 4 – 1 = 11
3 x 5 – 1 = 14
Jack and Thomas find a bag of marbles that they
share between them in the ratio of their ages. Jack is
10 years old and Thomas is 15 years old. What
fraction of the marbles did Jack get?
Jack : Thomas
10 : 15
Total parts = 10 + 15 = 25
3) Distance = ? kilometres 4) Distance = 48 m 5)
Speed = 4 m/s
Speed = 13 km/h
Time = ? seconds
Time = 3 hours
Distance = 13km/h x 3hours
= 39km
Time =
48m
4m/s
= 12seconds
Distance = 60 miles
Speed = ? mph
Time = 30 minutes
Speed =
60miles
0.5hour
= 120mph
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4) Construct triangle EFG where EG=12cm,
1)
EF=8cm and FG=7cm.
F
7cm
8cm
(a) Probability of a left handed female from the class?
E
(b) Probability of a right handed student from the class?
12cm
G
(c) Probability of a right handed male from all the males?
2) A cloth bag contains a mix of black, white and red balls.
Selecting one ball at random, the probability of getting a
black ball is 0.2, while the probability of getting a white ball
is 0.5. What is the probability of getting a red ball?
Probability adds up to one whole
P(Red) = 1 – 0.2 – 0.5 = 0.3
8cm
7cm
3) A paper bag contains 5 red, 7 green and 8 blue sweets.
If a sweet is selected at random from the bag, find the
probability that the sweet is:
(a) Red or blue
(b) Not blue
=
E
12cm
G
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1) Find the bearing of B from A
N
054°
B
MUST BE
WRITTEN
AS 3
FIRGURES
2)
A is due North of B. The bearing of C from A is
115°.The bearing of C from B is 075°.
Mark the position of C on the diagram.
A
C
3) Find the value of 12 – 2p when:
2
p
(a)
= 3
Replace p with 3
= 12 – 2 x 3
2
= 12 – 6 = 6 = 3
2
2
(b) p = 8
Replace p with 8
= 12 – 2 x 8
2
= 12 – 16 = -4
2
2
= -2
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1)
Design a data collection sheet to see
where the class want to go for their
school trip this year.
Place
Tally
2) The headteacher wants to find out many hours his
students spend on homework in a week. Design a
two way table to help him collect results.
Frequency
Alton Towers
Year 7
Lightwater Valley
Year 8
Bradley Woods
Year 9
Xscape
Year 10
3) Translate the red triangle 2 units left and 5 units down
2 left
Year 11
4) A jar of instant coffee contains 200g and cost £2.
There are two special offers.
5 down
2 left
2 left
5 down
Which offer is the best value?
OFFER A
OFFER B
5 down
Click to reveal
200g + 50g
= 200g for £1.50
= 250g for £2
133.3g for £1
125g for £1
Therefore, offer B is better value
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2) There are 7.5million people living in London.
1)
One-eight of these are over 65. Of the over65s, three-fifths are women. How many
women over 65 live in London?
7500000
7.5million
Therefore, no one got
the most. They all had
the same share.
3) Write £5 as a fraction of £20
4) Write 4 days as a fraction of 2 weeks
2 weeks
14 days
=
=
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1) Fill in the table below and draw the graph of y = 2x + 3
2) Solve the following equation:
Write the coordinates of where the graph crosses y = 4
Coordinates
2 x -3
-3 + 3
(-3,-3)
2 x -1
-2 + 3
(-2,-1)
2 x -1
1+3
(-1,1)
2 x 03+ 3
y=4
3(𝑥 + 5) = 42
3𝑥 + 15 = 42
-15
(0.5,4)
3𝑥
= 27
(0,3)
÷3
÷3
2 x 15+ 3
(1,5)
𝑥
= 9
2 x 27+ 3
(2,7)
2 x 39+ 3
(3,9)
3) Write down the inequality represented by the lines below:
(a)
0
- 15
(b)
1
2
3
4
5
(c)
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1) Solve the following equation:
2) Rotate the shape 90º clockwise about the origin:
7𝑥 + 9 = 2𝑥 + 19
- 2𝑥
- 2𝑥
5𝑥 + 9 =
-9
-9
5𝑥
=
÷5
𝑥
19
10
÷5
=
2
3) Reflect the shape in the line y = 3:
4)
y=3
Cuts the
y-axis at 3
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1) Work out the value of angles a, b and c. Give reasons for your answers
120º
a
120º
50º
70º
130ºc
70º
Alternate angles
b
Corresponding angles
2) Work out the values of:
3)
(b)
(d)
(a)
(c)
= 3 x 3 = 8 x 8 = 4 & -4 = 9 & -9
= 64
=9
(a)
2
0
0
1 14
6
4 x
0
0 0
2
8 7
8
ANSWER = 1.68
Work out the values of:
(b)
(c)
=2x2x2 =5x5x5 =3
= 125
=8
(d)
=5
5) The line graph shows temperature over a week :
4) Multiply:
(a) 2.4 x 0.7
Interior angles
(b) 8.2 x 3.9
8
3 12 4
1 72
9
2 x
0
6 3
1
8 9
8
ANSWER = 31.98
What was difference between the highest and
lowest temperatures? 38 - 30 = 8ºC
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1) Interpret the scatter graph below:
2) Increase £60 by 30% 3) Decrease £80 by 40%
x3
10% = £6
30% = £18
x3
x4
£60 + £18 = £78
10% = £8
40% = £32
x4
£80 - £32 = £48
4) Increase £40 by 35% 5)Decrease £120 by 17.5%
10% = £4
30% = £12
5% = £2
35% = £14
£40 + £14 = £54
x3
As height increases, handspan increases
(ignoring anomalies). Positive correlation.
6)
7)
8)
Find the area of the triangle.
Find
10% = £12
5% = £6
2.5% = £3
17.5% = £21
£120 - £21 = £99
x3
Find the area of the
1
Area of a triangle =
x base x vertical height
parallelogram.
2
Area of a parallelogram = base x vertical height
1
Area of triangle =
x 10 x 6
the modal class from the table.
2
Area of parallelogram = 9 x 4
2
One with highest frequency
Area of triangle = 30cm
2
4<P≤5
Area of parallelogram = 36cm
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7cm
1)
A
B
4x4
7x2
2)
1m
2cm
6m
4cm
A
7m
B
4cm
Find the area of the compound shape.
10m
TOTAL AREA =
Find the area of the compound shape.
B = 10 x 6
3)
4cm
TOTAL AREA =
3cm
5cm
10cm
Work out the area shaded black.
4) Expand the following:
(a) 3(m - 5)
(b) 4t(t + 2)
= 3m - 15
= 4t2 + 8t
Area of large rectangle = 10 x 5
Area of small rectangle = 4 x 3
AREA SHADED =
(c) y(y 2 – 4x)
= y3 - 4xy
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1) Factorise the following:
(b) 6my + 4py
(a) 6t + 9m
= 3( 2t + 3m )
2) Divide £15 in the ratio 3:2
÷
4)
Enlarge triangle T by scale
factor 2, with (0,0) as the
centre of enlargement.
2
of £15 = £6
5
3
of £15 = £9
5
= 2y( 3m+ 2p )
3)
x
x
÷
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1)
2)
Draw the plan, side elevation and front
elevation for the object shown.
Draw the plan, side elevation and front
elevation for the object shown.
3) Label the expression, equation, formula
and identity below:
Equation
Identity
P = 2l + 2w
Formula
Expression
4)
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1)1.
a)
Complete this table of values for y= x²
2)2.
a)
Complete this table of values for y= 2x²
x
-3
-2
-1
-0.5
0
0.5
1
2
3
x
-3
-2
-1
-0.5
0
0.5
1
2
3
y
9
4
1
0.25
0
0.25
1
4
9
y
18
8
2
0.5
0
0.5
2
8
18
b)
Plot these points and draw a smooth curve through
these points
y
X
b)
Plot these points and draw a smooth curve through
these points
20
X
9
y
X
8
X
7
15
6
5
X
X
4
10
X
X
3
2
X
X
-3
-2
-1
X
1
X
5
X
x
1
2
X
X
3
X
-3
c)
Use your graph to solve the equation x² = 3
-1.8 and _______
1.8
x = ______
d)
Give the coordinates of the minimum point (
-2
-1
X
X
x
1
2
3
c) Use your graph to solve the equation 2x² = 10
-2.3 and _______
2.3
x = ______
y
0
,
0
)
d) Give the coordinates of the minimum point (
y
0
,
0
)
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1) This is from a questionnaire on healthy
2)
eating.
Fast food is bad for you. Don’t you agree?
□ Strongly agree □ Agree □ Don’t know
Give two criticisms of the question.
1) It is a leading question.
2) No response section for disagree boxes.
3)
A
Describe fully the transformation that maps
triangle A onto triangle B
A reflection in the line x = -1
B
4) Change the following decimals to
fractions:
(a) 0.6
(b) 0.42
Describe fully the transformation that maps
flag A onto flag B
Rotation of 90° anticlockwise from
centre (0,0)
0
6
=
0
4
=
(c)
2
0
0.004
0
0
=
4
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1) Change the following fractions to
decimals:
(a)
(b)
2)
(d)
(c)
0 0 9
0 3
0 4
0 0 5
= 0.09
= 0.3
= 0.4
= 0.05
3x + 10 + 2x – 4 + x + 8 + 28 = 360
6x + 42 = 360
3) Draw an ordered stem and leaf
diagram for the following data:
21, 47, 35, 32, 11, 19, 28, 22,
25, 39, 38, 41, 42, 33, 17, 35
Smallest = 11
1 17 9
2 12 5 8
3 235 5 8 9
4 12 7
Biggest = 47
KEY:
3 2 means 32
4)
Shape A
5cm
4cm
6x
= 318
x
= 53º
Shape B
8cm
10cm
How many times bigger is the area of
shape B in comparison to shape A
Area of parallelogram = base x vertical height
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1) Draw a histogram with equal class
2)
intervals for the data in the table:
Write down the
properties of a rectangle.
No. of students
A histogram to show
the test scores
- Two pairs of equal sides
- Four right angles
- Opposite sides are parallel
- Two lines of symmetry
- Rotational symmetry of order 2
- Diagonals bisect each other
Test Scores
3) Calculate the mean from the table:
4)
20mins
fx
x
x
x
x
x
x
40
5
8
27
32
40
36
148
(a) How long was the stop? 20mins
(b) Average speed from E to F?
= 50km/h
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1) Find the area of the circle:
4cm
2) Find the area of the circle:
14m
diameter
Area of circle = 3.14 x 4 x 4
Area of circle = 50.2cm 2 (1d.p.)
3) Find the circumference of the circle:
8cm
Area of circle = 3.14 x 7 x 7
Area of circle = 153.9 m2 (1d.p.)
4) Find the circumference of the circle:
11m
radius
Circumference of a circle = 3.14 x 8
Circumference of a circle = 25.1cm (1d.p.)
Circumference of a circle = 3.14 x 22
Circumference of a circle = 69.1m(1d.p.)