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Trigonometric & exp. Graphs

Free Printable Trigonometric & exp. Graphs PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 7)

Download free trigonometric & exp. graphs worksheets (PDF), GCSE maths past paper questions and worked solutions for Trigonometric & exp. Graphs (7G). This is a Grade 7 algebra topic from the GCSE questions by topic collection for Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, 1st Class Maths, Maths DIY, Dr Austin, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our trigonometric & exp. graphs revision notes and worked examples with diagrams, try real GCSE past paper trigonometric & exp. graphs questions with step-by-step solutions, or download a PDF of all trigonometric & exp. graphs worksheet links.

Free Trigonometric & exp. Graphs PDF Worksheets & Answers

Grade 7 • Topic 7G
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
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Practice Questions & answers
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Textbook Exercise & answers
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MME worksheet & model answers
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Edexcel exam questions & solutions
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AQA exam questions & solutions
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Exam-style booklet & solutions
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Practice questions & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Self-marking online worksheet
 Page
Grade 7 topics
7A - Surds7B - Bounds
7C - Proportion (harder)7D - Algebraic fractions
7E - The quadratic formula7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs7H - Rearranging (harder)
7J - Functions (harder)7K - Iteration
7L - Area of any triangle7M - The sine rule
7N - The cosine rule7P - Congruent triangles
7Q - 3D pythagoras / trig.7R - Histograms
7S - Conditional probability7T - Exact trig. values (harder)
7U - Area of a segment
GCSE Maths Grade 7 Revision Notes & Method

Guide to Trigonometric & exp. Graphs: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Both y = sin x and y = cos x oscillate between −1 and 1 with a period of 360°: sin x starts at (0°, 0), peaks at (90°, 1), crosses at (180°, 0), reaches (270°, −1), and returns to (360°, 0); cos x starts at (0°, 1) and is symmetrical about x = 180°. y = tan x has period 180° with vertical asymptotes at 90° and 270°.

Exponential graphs y = abx (b > 0) always pass through (0, a) because b0 = 1, and have the x-axis (y = 0) as a horizontal asymptote. When b > 1 the graph shows exponential growth; when 0 < b < 1 it shows exponential decay.

Example 1: Solve sin x = −0.5 for 0° ≤ x ≤ 360°.

1 −0.5 −1 90° 180° 270° 360° 210° 330°

Solution:

Base acute angle: sin−1(0.5) = 30°
sin x is negative in 180° < x < 360° (by wave symmetry):
x = 180° + 30° = 210° and x = 360° − 30° = 330°
Answer: x = 210° and x = 330°

Example 2: The curve y = abx passes through (0, 5) and (3, 40). Find a and b.

(0, 5) (3, 40) y = abx 3 40

Solution:

Substitute (0, 5): 5 = a × b0 ⇒ a = 5
Substitute (3, 40) into y = 5bx: 40 = 5b3
b3 = 405 = 8 ⇒ b = ∛8 = 2
Answer: a = 5, b = 2
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Trigonometric & exp. Graphs Questions & Answers

Past Paper Example 1 GCSE Jun 2025 2H Q17 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is a sketch of part of the graph of y = kx where k is a positive constant.
The graph passes through the point with coordinates (-1, 1.5)
xyO(–1, 1.5)
Find the value of k.
Worked Solution & Mark Scheme (2 marks)
Substitute (–1, 1.5): 1.5 = k⁻¹ M1
⇒ 1/k = 3/2
⇒ k = 2/3. A1
Answer: k = 23
Past Paper Example 2 AQA Jun 2025 1H Q14 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Complete table of values for y = 2x. [2 marks]
14 (b) Draw the graph of y = 2x for x from –1 to 3. [2 marks]
(a) Complete the table of values for y = 2x
@@TABULAR0@@ [2 marks]
(b) Draw the graph of y = 2x for values of x from -1 to 3 [2 marks]
–1123–2–112345678910Oxy
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
2⁻¹ = 1/2 = 0.5 M1
2¹ = 2
2³ = 8 A1
Answer (a): x = –1: 0.5 (or 1/2); x = 1: 2; x = 3: 8
Part (b) Solution:
Plot all points and connect with a smooth increasing curve M1 A1
–1123–2–112345678910Oxy
Answer (b): Smooth curve drawn through (–1, 0.5), (0, 1), (1, 2), (2, 4), (3, 8)
Past Paper Example 3 GCSE Jun 2024 1H Q22 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Sketch the graph of y = sin x° for 0 ≤ x ≤ 360. (2) (b) Solve 2 sin x° = –1 for 0 ≤ x ≤ 360. (2)
(a) Sketch the graph of y = \sin x° for 0 ≤ x ≤ 360 [2 marks]
xyO90180270360
(b) Solve the equation 2\sin x° = -1 for 0 ≤ x ≤ 360 [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Sine wave from (0,0) to peak (90,1), through (180,0), trough (270,–1), to (360,0) with 1 and –1 labelled on y-axis M1 A1
xyO901802703601–1
Answer (a): Sine wave from (0,0) to peak (90,1), through (180,0), trough (270,–1), to (360,0) with 1 and –1 labelled on y-axis
Part (b) Solution:
sin x° = –1/2. Since sin 30° = 1/2, in 3rd and 4th quadrants x = 180 + 30 = 210 and x = 360 – 30 = 330 M1 A1
Answer (b): 210, 330

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