Copy of P2F Key skills.docx

GCSE Exam Questions Compilation

Top 10 Topics for Paper 2

Complete the questions first, and then use the video to mark/uplevel your work in red pen. Video link: https://youtu.be/32xPzcdPX_0

Suitable for Foundation Tier Students

Factors and Multiples
Perimeter
Frequency Trees
Algebraic Expressions
Pythagoras’ Theorem
Angles
Linear Graphs
Quadratic Graphs
Trigonometry
Quadratic Expressions and Equations
Tree Diagrams

Thank you to Dawn Crighton @Spencer Academies Trust for compiling this worksheet

Factors and Multiples

Q1. Write down all the factors of 12

_______________________________________________________________________

Answer ______________________________

(Total 2 marks)

Q2. (a) Write down all the factors of 18

Answer _________________________________________(2)

(b) Work out the lowest common multiple (LCM) of 12 and 15

___________________________________________________________________

Answer _________________________________________(2)

(Total 4 marks)

Q3. Work out the highest common factor (HCF) of 12 and 18

_______________________________________________________________________

Answer _________________________

(Total 2 marks)

Q4. (a) Work out the highest common factor (HCF) of 12 and 20

___________________________________________________________________

Answer _________________________________________

(2)

(b) Work out the lowest common multiple (LCM) of 6 and 8

___________________________________________________________________

Answer _________________________________________(2)

(Total 4 marks)

Q5. Complete the boxes using

a factor of 12

and

a factor of 40

(Total 2 marks)

Q6. Write 300 as a product of its prime factors.

Answer ______________________________

(Total 2 marks)

Q7. Write 140 as a product of prime numbers in index form.

_______________________________________________________________________

Answer _________________________________________

(Total 3 marks)

Perimeter

Q8. In this isosceles triangle,

AB = AC

Not drawn
accurately

The perimeter of the triangle is 22 cm

Work out the length of AB.

_______________________________________________________________________

Answer ____________________ cm

(Total 3 marks)

Q10. Lines AB and BC are shown on the centimetre grid.

(a) Write down the coordinates of point A.

Answer ( _____ , _____ )

(1)

(b) A, B and C are three corners of a rectangle ABCD.

Complete the rectangle on the grid.

(1)

___________________________________________________________________

Answer __________________________ cm

(2)

(Total 4 marks)

Q9. On this centimetre grid, draw one rectangle with

Perimeter = 20 cm and Area = 24 cm2

(Total 2 marks)

Q11. This shape is made by cutting out an equilateral triangle from a square.

Work out the perimeter of the shape.

_______________________________________________________________________

Answer ______________________________________ cm

(Total 2 marks)

Q12. A triangle has perimeter 32 cm

A square has perimeter 40 cm

Two sides of the shapes are put together to make a pentagon.

Work out the perimeter of the pentagon.

_______________________________________________________________________

Answer _________________________________________ cm

(Total 4 marks)

Frequency Trees

Q13. 60 people took a test. Before the test, they predicted whether they would pass or fail.

40 people predicted they would pass.

32 of the people who predicted they would pass did pass.

51 people passed altogether.

Complete the frequency tree.

(Total 2 marks)

Q14. 480 people are asked if they eat sushi.

20% say Yes.

of the people who say Yes eat sushi at least once a month.

Complete the frequency tree.

(Total 4 marks)

Q15. 50 people took a test. Before the test, they predicted whether they would pass or fail.

30 people predicted they would pass.

36 people did pass.

Of these 36 people, three times as many predicted pass as predicted fail.

Complete the frequency tree.

(Total 3 marks)

Q16. Some students were asked about their daily exercise.

(a) 12 more students answered Yes than answered No. Complete the frequency tree.

(3)

(b) One of the 35 students who answered Yes is chosen at random.

What is the probability that they exercise for at least 1 hour?

Answer _________________________(1)

(Total 4 marks)

Algebraic Expressions

Q17. Simplify fully 3a + 5c – a + 6c

_______________________________________________________________________

Answer ____________________

(Total 2 marks)

Q18. Simplify 7c + 5d − 4c + 3d

_______________________________________________________________________

Answer ______________________________

(Total 2 marks)

Q19. Simplify 12x2 − 8x2 − 5x + 2x

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q20. (a) Simplify y × y

Answer _________________________________________(1)

(b) Simplify 5a + 2 − a + 9

___________________________________________________________________

Answer _________________________________________(2)

(Total 3 marks)

Q21. Simplify fully 8a + 5b + 6a – 2b

_______________________________________________________________________

Answer _________________________

(Total 2 marks)

Q22. Simplify fully

_______________________________________________________________________

Answer _________________________________________

(Total 3 marks)

Q23. Simplify fully d × d

Answer ______________________________

(Total 1 mark)

Q24. Simplify fully p2 × p

_______________________________________________________________________

Answer ____________________

(Total 1 mark)

Q25. Match each expression on the left with one on the right.

One has been done for you.

(Total 3 marks)

Q26. Expand w(w + 6)

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q27. Expand and simplify fully 5(3x + 4) – 2(x – 1)

_______________________________________________________________________

Answer _________________________

(Total 2 marks)

Q28. Expand and simplify fully 4(2c + 3) – (5c – 1)

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q29. (a) Multiply out 3(2x – 7)

___________________________________________________________________

Answer _________________________________________(1)

(b) Factorise x2 + 8x

___________________________________________________________________

Answer _________________________________________(1)

(Total 2 marks)

Q30. (a) Multiply out 3(2x + 5)

___________________________________________________________________

Answer _________________________(2)

(b) Factorise 8x – 4

___________________________________________________________________

Answer _________________________(1)

(Total 3 marks)

Q31. Factorise 21x + 28

_______________________________________________________________________

Answer _________________________

(Total 1 mark)

Q32. Factorise 15x + 5y

_______________________________________________________________________

Answer ______________________________

(Total 1 mark)

Q33. Factorise 12a + 15b

_______________________________________________________________________

Answer ____________________

(Total 1 mark)

Q34. Factorise 15x + 35y − 40z

_______________________________________________________________________

Answer _________________________________________

(Total 1 mark)

Q35. Factorise fully 2x2 + 6x

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Pythagoras’ Theorem

Q36. Use Pythagoras’ theorem to work out the value of x. Not drawn accurately

_______________________________________________________________________

Answer _________________________ cm

(Total 3 marks)

Q37. Here is a triangle.

Not drawn
accurately

Use Pythagoras’ theorem to work out the value of y.

Give your answer as a decimal.

_______________________________________________________________________

y = _________________________ cm

(Total 3 marks)

Q38.

Not drawn accurately

Work out the length x.

Give your answer to 1 decimal place.

_______________________________________________________________________

Answer ______________________________________ cm

(Total 4 marks)

Q39.

Work out the value of x as a decimal.

_______________________________________________________________________

Answer _________________________________________

(Total 3 marks)

Q40. A shape is made by joining a right-angled triangle to a rectangle.

Not drawn
accurately

Work out the area of the shape.

_______________________________________________________________________

Answer _______________________ cm2

(Total 5 marks)

Angles

Q41. Here are two different straight lines.

Not drawn
accurately

Work out the size of angle x.

_______________________________________________________________________

x = ___________________________ degrees

(Total 1 mark)

Q42. In a triangle, two of the angles are 51° and 74°.

Work out the size of the third angle.

_______________________________________________________________________

Answer ____________________ degrees

(Total 1 mark)

Q43. The diagram shows a triangle ACD and an equilateral triangle BCD

Work out the size of angle x Not drawn accurately

_______________________________________________________________________

Answer ___________________________ °

(Total 3 marks)

Q44. ABDE is a parallelogram.

AB = AC

Not drawn accurately

Show that x = 38°

_______________________________________________________________________

(Total 3 marks)

Q45. ABC and DEFG are parallel lines.

BEH is a straight line.

(a) Work out the size of angle x.

___________________________________________________________________

x = ___________________________________°

(1)

(b) Work out the size of angle y.

___________________________________________________________________

y = ___________________________________°

(2)

(Total 3 marks)

Q46. (a) Part of a regular polygon is shown.

Not drawn
accurately

Assume that the polygon is an octagon.

Work out the size of angle x.

___________________________________________________________________

Answer ____________________ °

(2)

(b) In fact, the polygon has more sides than an octagon.

What does this mean about the size of angle x ?

Tick one box.

	It is more than the answer to part (a)
	It is the same as the answer to part (a)
	It is less than the answer to part (a)
	It could be any of the above

(1)

(Total 3 marks)

Q47. Part of a regular polygon with 15 sides is shown.

Not drawn accurately

Work out the size of an interior angle.

_______________________________________________________________________

Answer _________________________ degrees

(Total 2 marks)

Q48.

A regular polygon has an exterior angle of 20°

Work out the number of sides of the polygon.

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Linear Graphs

Q49. (a) Complete the table of values for y = 2x + 1

x	–1	1	3
y	–1	3

(1)

(b) On the grid draw the graph of y = 2x + 1 for values of x from −1 to 3.

(2)

(1)

(Total 4 marks)

Q50. (a) Complete the table of values for y = 8 – 2x

x	0	1	2	3	4	5
y	8		4		0

(2)

(b) On the grid below draw the graph of y = 8 − 2x for values of x between 0 and 5.

(2)

(Total 4 marks)

Q51. Draw the graph of y = 3x – 1 for values of x from –1 to 3

(Total 3 marks)

Q52. A line has the equation y = 3x − 5

(a) Write down the gradient of the line.

Answer ______________________________(1)

(b) Write down the y-intercept of the line.

Answer ______________________________(1)

(Total 2 marks)

Q53. Work out the gradient of the straight line through (–2, 3) and (1, 9)

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q54. A straight line

has gradient 6 and

passes through the point (3, 19)

Work out the equation of the line.

Give your answer in the form y = mx + c

_______________________________________________________________________

Answer ______________________________

(Total 3 marks)

Q55. A straight line

has gradient 4 and

passes through the point (5, 23)

Work out the equation of the line.

Give your answer in the form y = mx + c

_______________________________________________________________________

Answer _________________________________________

(Total 3 marks)

Quadratic Graphs

Q56.

(a) Complete the table of values for y = x2 – 5 for values of x from –3 to 3

x	–3	–2	–1	0	1	2	3
y	4		–4			–1	4

(2)

(b) Draw the graph of y = x2 – 5 for values of x from –3 to 3

(2)

Answer _________________ and _________________

(1)

(Total 5 marks)

Q57. (a) Complete the table of values for y = x2 + 2x

x	–3	–2	–1	0	1
y	3		–1	0

(2)

(b) Draw the graph of y = x2 + 2x for values of x from –3 to 1

(2)

(Total 4 marks)

Q58. Here is the graph of y = x2 – 7x + 10 for values of x from 0 to 7

(a) Write down the roots of x2 – 7x + 10 = 0

Answer _________________________________________ (2)

(b) Write down the x-coordinate of the turning point of the curve.

___________________________________________________________________

Answer _________________________________________ (1)

(Total 3 marks)

Q59. Here is a sketch of the curve

y = x2 – 4x – 5

(a) Write down the two roots of x2 – 4x – 5 = 0

Answer _______________ and _______________(1)

(b) Work out the coordinates of T, the turning point of the curve.

___________________________________________________________________

Answer ( _______ , _______ ) (2)

(Total 3 marks)

Trigonometry

Q60. Use trigonometry to work out the value of x.

Not drawn
accurately

_______________________________________________________________________

x = ______________________________ cm

(Total 3 marks)

Q61. Use trigonometry to work out the length x.

_______________________________________________________________________

Answer _________________________________________ cm

(Total 2 marks)

Q62. Use trigonometry to work out the size of angle x.

Not drawn
accurately

_______________________________________________________________________

x = ______________________ °

(Total 3 marks)

Q63. Here is a right-angled triangle.

Not drawn accurately

Use trigonometry to work out the size of angle x.

_______________________________________________________________________

Answer _________________________________________ degrees

(Total 2 marks)

Quadratic Expressions and Equations

Q64. Solve x2 = 30.25

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q65. When x² = 16 the only value that x can be is 4

Is this true or false?

Tick a box.

True

False

Reason ________________________________________________________________

_______________________________________________________________________

(Total 1 mark)

Q66. Multiply out and simplify (x − 8)2

_______________________________________________________________________

Answer _________________________________________

(Total 2 marks)

Q67. Expand and simplify (y + 8)(y − 3)

_______________________________________________________________________

Answer ______________________________

(Total 2 marks)

Q68. (a) Expand and simplify (x + 6)(x – 3)

___________________________________________________________________

Answer _________________________

(2)

(b) Solve (x – 9)(x + 4) = 0

___________________________________________________________________

x = _______________ or _______________

(1)

(Total 3 marks)

Q69. (a) Expand and simplify (x + 5)(x − 4)

___________________________________________________________________

Answer _________________________________________

(2)

(b) Solve (x − 8)(x + 7) = 0

___________________________________________________________________

Answer _________________________________________

(1)

(Total 3 marks)

Q70. (a) Factorise x2 − 9x + 20

___________________________________________________________________

Answer _________________________________________

(2)

(b) Solve x2 − 9x + 20 = 0

___________________________________________________________________

Answer _________________________________________

(1)

(Total 3 marks)

Q71.

Factorise x2 – 100

_______________________________________________________________________

Answer __________________________________________

(Total 1 mark)

Tree Diagrams

Q72.

An ordinary fair dice is rolled.

(a) Complete the tree diagram for the dice landing on 4

First spin Second spin

(1)

(b) Work out the probability of the dice landing on 4 both times.

___________________________________________________________________

Answer _________________________________________

(2)

(Total 3 marks)

Q73. Two ordinary fair dice are rolled.

(a) Complete the tree diagram.

(1)

(b) Work out the probability that both dice land on a number less than 3

___________________________________________________________________

Answer _________________________________________

(1)

(Total 2 marks)

Q74. Jose and Maria each take a test.

The probability that Jose passes is 0.8

The probability that Maria passes is 0.4

(a) Complete the tree diagram.

(2)

(b) Work out the probability that they both pass.

___________________________________________________________________

Answer _________________________

(1)

(Total 3 marks)

Mr Tompkins Edtech Top 10 Topics for Paper 2 (Foundation)