GCSE Past Paper Questions & Solutions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 18 th April 2014.

GCSE Past Paper Questions & Solutions

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 18th April 2014

IndexClick to visit section.

Straight Line Equations AlgebraFactorising, Simplifying & Solving

Non-Right Angled Triangles

Congruent Triangle Proofs

Algebraic Proofs & Algebraic Geometry Right-Angled Triangles

NumberIncludes bounds, direct/indirect proportion, standard form, %s

Probability Circle Theorems

Mark Scheme Notes:M1 Method mark. cao Correct Answer Only oe Or equivalentA1 Accuracy mark. C1 ‘Communication Mark’ (used for *-ed questions)B1 ‘Independent mark’. Sort of a ‘miscellaneous’ mark, often used when an explanation is required.

Volumes and Surface Area

Functions and Graph Transformations More Topics >>

IndexClick to visit section.

Loci & Constructions Angles & Bearings

Mark Scheme Notes:M1 Method mark. cao Correct Answer Only oe Or equivalentA1 Accuracy mark. C1 ‘Communication Mark’ (used for *-ed questions)B1 ‘Independent mark’. Sort of a ‘miscellaneous’ mark, often used when an explanation is required.

Vectors

Straight Lines

Gradient = -9/4

2y = -x + 1, so y = -0.5x + 0.5So gradient is -0.5

y = 3x - 4

y = -3x + 16

y = 4x + 3

y = 4x – 5

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Straight Lines

y = 4x - 11

y = (1/3)x + 2

y = -(1/2)x + c (where c can be anything)

y = -(1/5)x – 1

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Straight Lines

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Straight Lines

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Straight Lines

3 , 3.5

-9/5

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Straight Lines

5 1.5?

Reveal

<< Return to Index

Straight Lines

Reveal

<< Return to Index

Straight Lines

2/3

Gradient of 2y = 10 – 3x is -3/22/3 × -3/2 = -1 therefore perpendicular

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Straight Lines

6 1.5 0

-3/2

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Reveal

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Straight Lines

-0.6, 5.5

-1.4, 6.4

x = 0.2, y = -3.8x = 5.8, y = 1.8

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Straight Lines

-1/2

y = -(1/2)x – 1

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Straight Lines[June 2010 NonCalc]

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Algebra

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Algebra

x10

m12

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Algebra

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Algebra

3

-1

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Algebra

12.5

4m2 – 1

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Algebra

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<< Return to Index

Algebra

a9

3

9e5f6

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Algebra

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Algebra

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Algebra

3(2 + 3x)

(y + 4)(y – 4)

(2p – 5)(p + 2)

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Algebra

-3?

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Algebra

45

4 , 5

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Algebra

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Algebra

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Algebra

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Algebra

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Algebra

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<< Return to Index

Algebra

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<< Return to Index

Algebra

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<< Return to Index

Algebra

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<< Return to Index

Algebra

-3 < x ≤ 4

t > 7/2

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Algebra

2x(x – 2y)

(p – 4)(p – 2)

x + 2

6a5b2

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Algebra

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Algebra

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Algebra

x + 42x – 3

7x – 2 (x+2)(x-2)

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Algebra

(x + p)(x + q)

(m + 2)(m – 2)

x + 10(x – 4)(x + 3)

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Algebra

x2 + 3 = 7xx2 – 7x + 3 = 0

x = (7 ±37) / 2?

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Algebra

-2, -1, 0, 1, 2, 3, 4

x > 5/2

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Algebra

16n12?

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Algebra

(2x – 1)(x – 4)

(2x – 1)(x – 4) = (2x – 1)2

x – 4 = 2x – 1x = -3

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Algebra

-160?

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Algebra

4(3n + 1)

3(n + 4)

2n + 1

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Algebra

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Algebra

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Algebra

4x-1 or 4/x?

<< Return to Index

Algebra

8x2 + 6xy – 20y2

x + 10

x – 5x + 2

3 -11

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Algebra

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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<< Return to Index

Non-Right Angled Triangles

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<< Return to Index

Non-Right Angled Triangles

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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Non-Right Angled Triangles

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Congruent Triangles

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Congruent Triangles

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Congruent Triangles

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Congruent Triangles

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Congruent Triangles

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Algebraic Proofs and Geometry << Return to Index

21.

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

5x2?

Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Algebraic Proofs and Geometry << Return to Index

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Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

80.1?

Right Angled Triangles << Return to Index

11.5 47.2? ?

Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

3.52?

Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

33.7 9.44? ?

Right Angled Triangles << Return to Index

13.86 ?

Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

48.2?

Right Angled Triangles << Return to Index

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Right Angled Triangles << Return to Index

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Number << Return to Index

0.00078

9.56 x 107

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Number << Return to Index

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Number << Return to Index

Remember, you choose the greatest degree of accuracy such that the two bounds are the same.

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Number << Return to Index

820 000

3.76 x 10-4

0.5 x 109

= 5 x 108

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

Non

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Number << Return to Index

Non

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

643 000

16 x 10-5

= 1.6 x 10-4

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

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Number << Return to Index

1

0.000067

2.7 x 1014

2.4 x 1016

6.4 x 108

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Number << Return to Index

109.8847047?

Number << Return to Index

8.25 x 107

1.456 x 10-15

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Number << Return to Index

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Probability << Return to Index

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Probability << Return to Index

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Probability << Return to Index

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Probability << Return to Index

242

1642

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Probability << Return to Index

222380

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Probability << Return to Index

64110

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Probability << Return to Index

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Probability << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

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Circle Theorems << Return to Index

Circle Theorems

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Circle Theorems << Return to Index

Angle DAB = 180 – 103 = 77 (opposite angles of cyclic quadrilateral)Angle DBA = 39 (Alternate Segment Theorem)Angle ADB = 180 – 77 – 39 = 64

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Circle Theorems << Return to Index

116

Angle OCB = (180 – 116)/2 = 32Angle OCA = 74 – 32 = 42

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Circle Theorems << Return to Index

Angle BOA = 152Angle APB = 360 – 152 – 90 – 90 = 28

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

236

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

3 2 41? ? ?

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Volumes and Surface Area << Return to Index

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Volumes and Surface Area << Return to Index

Yes Yes?

8 x 1003 = 8 000 000?

Functions and Graph Transformations << Return to Index

General Tips:

1. When asked to sketch a transformed graph, e.g. f(x + 3), pick key points on the original graph to transform first (e.g. ones that go exactly through grid points, or y-intercepts, etc.) then join up with a line. This will ensure you draw it accurately.

2. Remember that changes inside the function brackets affect the x-axis and do the opposite of what you expect.

3. Learn the shape of y = sin(x), y = cos(x) and y = tan(x). In particular, learn that coordinates for which the graphs cross the x-axis, and the maximum/minimum points.

On to questions >>>

Functions and Graph Transformations << Return to Index

Reveal

To get the curve perfectly mirrored, mirror points that go through squares first, i.e. (-4, 4), (-3, 1), (-1, 1), (0.4), then join up with a line.

Functions and Graph Transformations << Return to Index

y = f(x – 6)?

Functions and Graph Transformations << Return to Index

90 0?

Reveal

Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

EBFCD

A

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Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

Reveal

Functions and Graph Transformations << Return to Index

-15 -7 -6 1

Reveal

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Functions and Graph Transformations << Return to Index

Reveal

x = -1.6, y = 2.6x = 2.6, -1.6 ?

Functions and Graph Transformations << Return to Index

f(x – 5)

4 3

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3 -3 -1? ? ?

Reveal

Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Vectors << Return to Index

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Loci & Constructions << Return to Index

#1: Use compass the get some fixed distance across the lines AC and AB.

#2: Find perpendicular bisector of these two points.

Reveal

Loci & Constructions << Return to Index

Reveal

Loci & Constructions << Return to Index

#1: Use two arcs with radius the width of the line to form an equilateral triangle (only one side needed).This gives you an angle of 60.

#2: Find the angle bisector of these two lines in the usual way, in order to find the angle half of 60.

Reveal Step #1

Reveal Step #2

Loci & Constructions << Return to Index

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Loci & Constructions << Return to Index

5cm

3cm

Angle bisector of angle DAB

Reveal

Angles & Bearings << Return to Index

40

Angle PQT = 70 (angles on straight line). Angle PTQ = 70 (isosceles triangle)

Angle TPQ = 40 (angles in triangle add to 180)

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Angles & Bearings << Return to Index

360 ÷ 5 = 72?

Angles & Bearings << Return to Index

112

Angle LNB = 68 (corresponding angles) so y = 112 (angles on straight line add to 180)

OR Angle ANM = 68 (alternate angles) so y = ...

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Angles & Bearings << Return to Index

55

Corresponding angles.

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Angles & Bearings << Return to Index

360 ÷ 30 = 12?

Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

360 – 90 – 120 = 150?

Angles & Bearings << Return to Index

42?

Angles & Bearings << Return to Index

Angle PBA = 180 – (x + 50) – (2x – 10) = 140 – 3xy = 180 – (140 – 3x) = 3x + 40

3x + 40 = 145x = 35

35 + 50 = 85

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Angles & Bearings << Return to Index

3x – 15 = 2x + 24x = 39 ?

Angles & Bearings << Return to Index

Interior angle of hexagon = 180 – (360 / 6) = 120Interior angle of octagon = 180 – (360 / 8) = 135x = 360 – 120 – 135 = 105

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

150?

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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Angles & Bearings << Return to Index

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