Ordering Positive and Negative Integers,
Decimals and Fractions
Place in ascending order of size.
1. 0.5, 0.12, 0.1, 0.45, 0.3
2. 1, 2, 5, 1, 7
3 5 9 4 11
3. -2, 0.55, -2.5, 1, -0.3
4. 0.2, 3, 0.15, 1, 5%
5
2
5. 0.55, 1, 0.35, 3, 0.5%
9
4
Select the smallest value from each answer and place them in ascending
order.
Recognise and Use Relationships between
Operations (BIDMAS)
Calculate the answers.
1. 2 + 7 × 4
2. 5 × 32 – 4 ÷ 2
3. (5 + 2) × 6 – 2
4. 4 × 23 + 8 ÷ 2
5. 2 × 33 – 52 + 150 + 32
Place the answers in ascending order.
Positive Integer Powers and Associated
Real Roots
Evaluate the following.
1. 32 + 23
144 – 120
2.
105
3.
104
4.
5.
3
15 625 – 22
16
4
+ 33
Place the answers in descending order.
Calculate with and Interpret
Standard Form
Write as ordinary numbers.
1. 4 × 105
2. 3.1 × 104
3. 27 × 104
4. 5.1 × 105 – 2.1 × 103
5. 6 × 10-2 + 3 × 104
Place the answers in descending order.
Terminating Decimals and Corresponding
Fractions
Place the correct sign >, < or = between the fractions and decimals.
1. 0.4
1
4
2. 0.3
3
10
3.
1
8
0.13
4.
3
8
0.375
5. 0.25
2
5
Place the fractions from each question in ascending order.
Units of Mass, Length and Time
Place the correct sign >, < or = between the units.
1. 10cm
1m
2. 5.5kg
5050g
3. 7200 seconds
4. 6250ml
6.025l
5. 6550m
7km
2 hours
Calculations Using Approximation and
Estimation
Estimate answers by rounding the numbers in the questions to one
significant figure.
1. 3.27 × 3.562
2. 485 ÷ 24.71
3. 5.5 + 11.99
0.54
4.
2.1 × 3.7
1.2 + 2.56
5. 9.6 – 3.05 × 1.8
Place the answers in descending order.
Round Numbers and Measures to an Appropriate
Degree of Accuracy
Round the numbers to the given degree of accuracy.
1. 5.76 (1d.p.)
2. 5.76 (1s.f.)
3. 4.997 (2d.p.)
4. 5.65 (2s.f.)
5. 0.004567 (3s.f.)
Place the answers in ascending order.
Substitute Numerical Values into Formulae
and Expressions
Substitute Numerical Values into Formulae and Expressions.
1. x + 6
where x = 2
2. 5(x + 2) where x = 1
3. (x – 2)
where x = 8
4. x2 + y
where x = 2 and y = -3
5. x(x – y)
where x = 5 and y = -2
2
Place the answers in descending order.
Simplify and Manipulate Algebraic
Expressions
Fully simplify the expressions, expanding where necessary.
1. x + 5x
2. 3x + 2y + 4x – 5y
3. 2(x + 3)
4. (x + 3)(x + 2)
5. (2x + 5)(x – 1)
From each answer, select the co-efficient of x (not x2) and list them in
descending order.
Coordinates in All Four Quadrants
Identify the co-ordinate pairs.
4
1.
2
-4
-2
0
2
4.
-2
2
4
2
5.
2
0
-4
2
4
-4
4
-2
2
-2
-2
2.
0
4
6
-2
-2
0
2
-2
-4
4
3.
2
-4
-2
0
2
4
-2
Find the sum of each co-ordinate pair and place them in ascending order.
Identify and Interpret Gradients
Identify the gradient (m) from the linear equations represented graphically.
4
1.
6
4.
4
2
-4
-2
0
2
2
4
-2
-4
-2
-4
-2
0
2
4
-2
-4
-2
0
-2
-2
-4
-4
2
-4
0
2
4
2
4
3.
4
4
5.
2
-4
2
-2
4
2.
0
2
4
-2
-4
Place the answers in descending order.
Solve Linear Algebraic Equations with
One Unknown
Calculate the value of x.
1. x + 3 = 7
2. 2x – 1 = 9
3. 3x + 4 = -5
4. 2x – 1 = x + 2
5. 5x – 4 = x + 4
Place the answers in ascending order.
Solve Quadratic Equations by Factorising
Solve the quadratic equations by factorisation.
1. x2 + 5x + 6 = 0
4. x2 – 2x – 3 = 0
2. x2 + 9x + 17 = -3
5. x2 + 2x – 21 = 3
3. x2 – 3x + 2 = 0
Select the greater value of x from each solution and place the answers
in descending order.
Solve Linear Simultaneous Equations
Solve the pairs of simultaneous equations.
1. x + y = 7
x–y=3
4. 2x – y = -5
4x + 2y = 2
2. 2x + 3y = 11
5. 2x + y = 1.5
5x + 3y = 14
x + 13 = 2y
3. x + 2y = 8
2x + 3y = 14
Calculate the sum of x and y in each question and place the answers in
ascending order.
Solve Linear Inequalities with One
Variable
Solve the inequalities.
1. 2x > 10
2. 5x < 20
3. 3x + 1 ≥ 7
4. 7x – 4 ≤ 3
5. -2x + 1 ≥ 0
Place the answers in descending order.
Generate Terms of a Sequence
Calculate the first five terms in the following sequences.
1. Start at 2 and count up in steps of 5.
2. Start at 3 and count down in steps of 2.
3. nth term = 4n
4. nth term = 3n + 2
5. nth term = 7 – 2n
Select the 5th term from each sequence and place in ascending order.
nth Term of Linear Sequences
Find the nth term of the following sequences.
1. 2, 4, 6, 8, 10
2. 4, 7, 10, 13, 16
3. 4, 3, 2, 1, 0
4. 2, 6, 10, 14, 18
5. -3, -9, -15, -21, -27
Select the co-efficient of n from each sequence and place in descending
order.
Change between Related Standard Units
and Compound Units
Convert to the unit given in brackets.
1. 350cm (m)
2. 3.6kg (g)
3. 5.6 hours (minutes)
4. 10 miles (km), rounding your answer to the nearest km.
5. 5km/h (m/s)
Place the numerical values of your answers in descending order.
Scale Factors, Scale Diagrams and Maps
A map has a scale of 5cm : 100 000cm.
1. How many km are represented by 5cm?
2. How many km are represented by 12.5cm?
3. How many km are represented by 1cm?
4. The distance between two towns is 10cm on the map.
Calculate the real life distance, giving your answer in km.
5. Carleigh’s home is 1.5km in a straight line from her school. How
many cm apart should they be shown on the map?
Place the numerical values of your answers in descending order.
Express One Quantity as a Fraction of Another
Express as a fraction, simplifying your answer where possible.
1. Ten minutes as a fraction of one hour.
2. Three hours as a fraction of two days.
3. 50 seconds as a fraction of one hour.
4. 50cm as a fraction of five metres.
5. 800g as a fraction of 1.6kg.
Place the numerical values of the denominators from your answers in
ascending order.
Apply Ratio to Real Contexts and Problems
Solve the ratio problems.
1. Find the smallest share when
7kg is shared in the ratio
7:3:4.
2. Mel is making a pastry top
for her apple pie. The ratio
of flour to fat is 2:1. She has
0.2kg of fat. Calculate the
quantity in kg of flour she
will need to make her pastry
top.
3. If three builders take four
days to build a wall, how
many days would it take four
builders to build the same
wall?
4. Janice and Sandra share
some soup in the ratio 2:3.
Sandra has 210ml of soup.
How manly litres of soup do
they share?
5. 250g of fruit are needed for
a fruit punch that serves five
people. How many kilograms
of fruit would be needed if
the same punch was made
to serve six people?
Place the numerical values of your answers in descending order.
Solve Problems Involving Percentages
Solve the percentage problems.
1. 35% of 90
2. Decrease £50 by 55%
3. Janni has £1000 in her bank account. The bank pays her 3.5%
simple interest. How much interest is she paid?
4. Bethany scored 25 marks out of 60 in her science exam. What
percentage, rounded to one decimal place, did Bethany achieve?
5. A museum raises the price of its entry ticket by 11%. The original
cost of the ticket was £15. How much will it cost to buy two
tickets?
Place the numerical values of your answers in descending order.
Solve Problems Involving Direct and Inverse Proportion
Solve the problems.
1. y ∝ x
y = 16 when x = 8.
Calculate the value of y when x = 40.
2. y ∝ x2
y = 125 when x = 5.
Calculate the value of y when x = 3.
3. y ∝
x
y = 90 when x = 81.
Calculate the value of y when x = 36.
Place the values of y in ascending order.
4. y ∝
x
y = 90 when x = 81.
Calculate the value of x when y = 110.
5. y ∝
1
x
y = 12 when x = 4.
Calculate the value of y when x = 2.
Compound Units
Solve the problems.
1. A car travels at a constant speed of 60mph for 2 hours. Calculate
the distance travelled.
2. The density of aluminium is 2.6g/cm3. Work out the mass of
50cm3 of aluminium.
3. Jim cycles a distance of 42 miles in 2 hours and 30 minutes. What
was his average speed in miles per hour?
4. Kate’s car has a brake pedal with a surface area of 8cm2. To
perform an emergency stop, she needs to apply a force of 320N
to the pedal. Calculate the pressure this puts on the brake pedal.
5. The density of gold is 19.32g/cm3. Find the mass of a cube of gold
with an edge measuring 2cm in length.
Place the numerical values of your answers in ascending order.
Lengths, Areas and Volumes
The shapes or objects in each question are similar.
1. Calculate the value of x.
4. Suzy draws a picture on a rectangular
piece of paper 10cm wide and 12cm long.
She scans her picture into a computer and
prints an enlarged copy that is 7.5cm wide
and xcm long. Calculate the value of x.
4cm
2cm
x
3cm
2. Calculate the value of x.
15cm
x
5. The volume of the smaller cube is 8cm3.
The larger cube is an enlargement of the
smaller one by a linear scale factor of 2.5.
Calculate the value of x.
12cm
15cm
xcm
3. Rectangle A has an area of 11.25cm2.
Rectangle B is an enlargement of rectangle
A by a linear scale factor of 3.5. Calculate
the value of x.
2.5cm
A
B
xcm
Place the values of x in ascending order.
Growth and Decay Problems
Solve the following interest problems. All interest rates are compound
interest.
1. £1000 is invested at an interest rate of 2% per annum. Find the
value after 3 years.
2. £5200 is invested at an interest rate of 3.5% per annum. Find the
value after 5 years.
3. The value of a mobile home depreciates by 5% per annum. If the
mobile home was purchased for £50 000, what is its value after 10
years?
4. A house was purchased for £250 000 seven years ago. Its value
increased by 8% in the first year then by 11.5% for the next six
years. By how much has it increased in value?
5. A car was purchased for £24 000 three years ago. Its value
depreciated by 20% in the first year then by 10% for the next two
years. What is its current value?
Place the answers in descending order.
Basic Angle Rules
Calculate the value of the missing angle, x.
1.
4.
x
75°
50°
x
45°
5.
2.
x
80°
100°
3.
40°
x
x
Place the answers in ascending order.
115°
Properties of Quadrilaterals
Name the quadrilaterals.
1. My diagonals are equal in length and so are all my sides.
2. I have no pairs of parallel sides. I have one pair of equal opposite
angles.
3. My sides are not all equal in length but all my angles are equal.
4. I have one pair of parallel sides.
5. All my sides are equal in length but not all my angles are equal.
My diagonals bisect at 90°.
Place the answers in alphabetical order.
Further Angle Rules
Calculate the value of the missing angle, x.
1.
x
4.
x
125°
5. A and B are similar triangles.
2.
85°
5cm
x
10cm
A
40°
6cm
3.
x
40°
Place the values of x in ascending order.
x
B
12cm
Faces, Edges and Vertices
Answer the following:
1. The number of edges on a cuboid.
2. The number of faces on a tetrahedron.
3. The number of faces on a hexagonal prism.
4. The number of vertices on a square-based pyramid.
5. The number of equal faces on a cube.
Place the answers in descending order.
Pythagoras’ Theorem and Trigonometry
Calculate the value of x, rounding your answers to the nearest whole
number, where appropriate.
1.
4.
x
4cm
11cm
x
50°
3cm
2.
7cm
x
3.
5.
4cm
x
9cm
5cm
7cm
x
10cm
Place the values of x in ascending order.
Two-Way Tables and Frequency Trees
Complete the diagrams to answer the questions.
1. How many students are in class 9b?
4. How many year 9 students are there?
Year 7 Year 8 Year 9
y
tor
61
ss
Cla
Cla
ss
9A
31
His
Geo
grap
hy 10
tory 14
His
9B
Ge
ogr
aph
y
2. How many students studied
geography and are in 9b?
ory
t
A
s9
61
s
Cla
Cla
ss
31
His
Geo
grap
hy 10
tory 14
His
9B
Ge
ogr
aph
y
Football
25
Netball
40
30
Basketball
40
Total
90
85
20
55
95
280
5. How many students choose netball?
Year 7 Year 8 Year 9
Football
25
Netball
40
30
Basketball
40
Total
90
20
55
95
y
tor
s
las
61
C
Cla
ss
9A
9B
31
Geo
grap
hy 10
tory 14
His
Ge
ogr
aph
y
Total
85
3. How many students studied history?
His
Total
Place the answers in descending order.
280
Averages and the Range
Answer the following:
1. Calculate the median of this data set: 25, 37, 41, 22, 33, 20
2. Calculate the mode of this data set: 25, 27, 21, 27, 25, 29, 27
3. Calculate the range of this data set: 77, 79, 55, 51, 65, 68
4. Ms Brown recorded her year 11 students’ percentage achievement in a recent maths
exam. State the modal class and calculate its midpoint.
Percentage in exam, x
Frequency
0 ≤ x < 25
1
25 ≤ x < 50
9
50 ≤ x < 75
15
75 ≤ x ≤ 100
5
5. Ms Brown recorded her year 11 students’ percentage achievement in a recent maths
exam. Estimate the mean percentage achieved by her class.
Percentage in exam, x
Frequency (f)
0 ≤ x < 25
1
25 ≤ x < 50
9
50 ≤ x < 75
15
75 ≤ x ≤ 100
5
Place the answers in ascending order.
Mid-point
(fx)
Relative and Theoretical Probability
All questions are based on this spinner.
3
2
1
2
2
3
1. Calculate the probability of the spinner landing on a 3.
2. Calculate the probability of landing on a 1 or a 2.
3. The spinner is spun 50 times. Calculate how many times it is likely
to land on a 2.
4. Calculate the probability of not landing on a 2 or a 3.
5. The spinner is spun twice. Calculate the probability of landing on
a 1, then a 3.
Place the answers in ascending order.