Year 10 Autumn Term Curriculum List
Equations
Solving Linear Equations
Solving Quadratic Equations
- Factorising
Simultaneous Equations
- Linear
Solving Linear Inequalities
Graphs
Plotting linear graphs
Plotting Quadratic Graphs
Equation of a straight line
Kinematic Graphs
Proportion
Writing proportion as a fraction or percentage
Simplify ratio
Dividing amounts in a given ratio
Calculating with percentage change
Probability
Calculating theoretical probability
Calculating experimental probability
Combinations
Mutually exclusive events
Set theory of Venn Diagrams
Probability from Venn Diagrams
Frequency tree diagrams
Probability tree diagrams
Equations
Solving Linear Equations
- Solve
Q2.
ABC is a triangle.
Angle ABC = angle BCA.
The length of side AB is (3x − 5) cm.
The length of side AC is (19 − x) cm.
The length of side BC is 2x cm.
Work out the perimeter of the triangle.
Give your answer as a number of centimetres.
Solving Quadratic Equations
Q7.
Solve x2 + 3x – 4=0
......
(Total for question is 3 marks)
Simultaneous Equations
Q1.
Solve the simultaneous equations
4x + y = 25
x − 3y = 16
x =......
y =......
(Total for Question is 3 marks)
Solving Linear Inequalities
Q10.
(a) n is an integer.
–1 ≤ n < 4
List the possible values of n.
......
(2)
(b)
Write down the inequality shown in the diagram.
......
(2)
(c) Solve 3y – 2 > 5
......
(2)
(Total for Question is 6 marks)
Graphs
Plotting linear graphs and Coordinates
Q1.
(a) Write down the coordinates of the point S.
(...... , ...... )
(1)
The coordinates of the point T are (−3, 2).
(b) On the grid, mark this point with a cross (×).
Label the point T.
(1)
(c) Write down an equation of the line L.
......
(1)
(Total for Question is 3 marks)
Q3.
(a) Complete the table of values for y = 2x + 5
x / –2 / –1 / 0 / 1 / 2y / 1 / 5
(2)
(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = –2 to x = 2
(2)
(Total for Question is 4 marks)
Plotting Quadratic Graphs
Q5.
(a) Complete the table of values for y = x2 − 5x + 3
(2)
(b) On the grid below, draw the graph of y = x2 − 5x + 3 for values of x from x = −1 to x = 5
(2)
Equation of a straight line
Q6.
Here are the graphs of 6 straight lines.
Match each of the graphs A, B, C, D, E and F to the equations in the table.
Equation / y = ½ x + 2 / y = 2x – 2 / y = – ½ x + 2 / y = – 2x – 2 / y = 2x + 2 / y = – ½ x – 2Graph
(Total for Question is 3 marks)
Kinematic Graphs
8. Usain runs in a race.
The graph shows his speed, in metres per second (m/s), during the first 10 seconds
of the race.
(a)Write down Usain’s speed at 2 seconds.
...... m/s
(1)
(b)Write down Usain’s greatest speed.
...... m/s
(1)
(c)Write down the time at which Usain’s speed was 7 m/s.
...... seconds
(1)
(Total 3 marks)
______
Proportion
Writing proportion as a fraction or percentage
Q5.
Colin, Dave and Emma share some money.
Colin gets 3⁄10 of the money.
Emma and Dave share the rest of the money in the ratio 3 : 2
What is Dave's share of the money?
......
(Total for Question is 4 marks)
Q3.
(a) Write 7⁄10 as a decimal.
......
(1)
(b) Write 0.45 as a percentage.
...... %
(1)
(c) Write 30% as a fraction.
Give your fraction in its simplest form.
......
(2)
Simplify ratio
- Simplify
- 15:10
- 8:24
- 150:90
- 25:10:5
Dividing amounts in a given ratio
Q8.
The cost of 3 calculators is £26.85
(a) Work out the cost of 5 of these calculators.
(2)
The ratio of the number of boys to the number of girls in a class is 3 : 4
(b) What fraction of the class is boys?
(1)
Shane and Gemma share 35 sweets in the ratio 1 : 4
Gemma eats 10 of her sweets and then gives Shane of the sweets she has left.
(c) How many sweets does Shane have now?
(3)
(Total for question = 6 marks)
Calculating with percentage
Q9.
Work out 65% of 300
......
(Total for question = 2 marks)
Q11.
Greg sells car insurance and home insurance.
The table shows the cost of these insurances.
Insurance / car insurance / home insuranceCost / £200 / £350
Each month Greg earns
£530 basic pay
5% of the cost of all the car insurance he sells
and 10% of the cost of all the home insurance he sells
In May Greg sold
6 car insurances
and 4 home insurances
Work out the total amount of money Greg earned in May.
......
(Total for Question is 5 marks)
Probability
Probability
Q1.
Here is a fair 6-sided spinner.
Jack will spin the spinner once.
The spinner will land on one of the colours.
Draw a circle around the word to best describe the probability of the following events.
(a) The spinner will land on White.
(1)
impossible / unlikely / even / likely / certain(b) The spinner will land on Red.
(1)
impossible / unlikely / even / likely / certain(c) The spinner will land on Pink.
(1)
impossible / unlikely / even / likely / certainHere is a different fair 6-sided spinner.
Jack will spin this spinner once.
The spinner is more likely to land on Blue than to land on Red.
(d) Write the missing colours on the spinner.
(1)
(Total for Question is 4 marks)
Calculating theoretical probability
Q2.
Here is a fair 4-sided spinner.
The spinner can land on blue or on red or on green.
Lance spins the spinner once.
(a) On the probability scale, mark with a cross (×) the probability that the spinner will land on red.
(1)
(b) On the probability scale, mark with a cross (×) the probability that the spinner will land on yellow.
(1)
(c) On the probability scale, mark with a cross (×) the probability that the spinner will not land on green.
(1)
(Total for Question is 3 marks)
Q7.
There are 72 guests staying in a hotel.
They are French or German or Spanish.
The two-way table shows some information about the guests.
(a) Complete the two-way table.
(2)
One of these guests is picked at random.
(b) Write down the probability that the guest is female.
......
(1)
One of the male guests is picked at random.
(c) Write down the probability that this male guest is German.
......
(1)
(Total for Question is 4 marks)
Calculating experimental probability
Q8.
There are only blue counters, green counters, red counters and yellow counters in a bag.
George is going to take at random a counter from the bag.
The table shows each of the probabilities that George will take a blue counter or a green
counter or a yellow counter.
(a)Work out the probability that George will take a red counter.
......
(1)
There are 120 counters in the bag.
(b)Work out the number of green counters in the bag.
......
(2)
(Total for question = 3 marks)
Combinations
Q4.
Jessica goes to an activity centre.
She can choose to do one of the three morning activities and one of the three afternoon activities.
Cookery (C) Painting (P) Football (F) / Hockey (H) Acting (A) Swimming (S)
List all the possible combinations of activities she can choose to do.
The first combination has been done for you.
......
......
(Total for Question is 2 marks)
Mutually exclusive events
Q3.
There are some boys and girls in a classroom.
The probability of picking at random a boy is
What is the probability of picking a girl?
......
(Total for question = 1 mark)
Probability from Venn Diagrams
Q14.
Here is a Venn diagram.
(a)Write down the numbers that are in set
(i)A∪B
......
(ii)A ∩ B
......
(2)
One of the numbers in the diagram is chosen at random.
(b)Find the probability that the number is in set A'
......
(2)
(Total for question = 4 marks)
Probability tree diagrams
Q12.
Wendy goes to a fun fair.
She has one go at Hoopla.
She has one go on the Coconut shy.
The probability that she wins at Hoopla is 0.4
The probability that she wins on the Coconut shy is 0.3
(a) Complete the probability tree diagram.
(2)
(b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy.
......
(2)
(Total for Question is 4 marks)