| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find coordinates of turning points |
| Difficulty | Moderate -0.3 This is a straightforward C2 trigonometry question testing standard transformations of sine graphs. Part (a) requires sketching y=sin(x) with amplitude 5 and period compression, part (b) is direct reading from the sketch, and part (c) involves solving 5sin(3x)=2.5 which simplifies to sin(3x)=0.5, a routine inverse trig problem. All parts are textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
Total
Question 7:
7
Total
PhysicsAndMathsTutor.com
1. A circle C has equation
x2 + y2 – 10x + 6y – 15 = 0.
(a) Find the coordinates of the centre of C. (2 marks)
(b) Find the radius of C. (2 marks)
y+3 y+1
2. Express − as a single fraction in its simplest form.
(y+1)(y+2) (y+2)(y+3)
(5 marks)
3. Given that 2 sin 2θ = cos 2θ ,
(a) show that tan 2θ = 0.5. (1 marks)
(b) Hence find the values of θ , to one decimal place, in the interval 0 ≤ θ < 360 for which
2 sin 2θ ° = cos 2θ °. (5 marks)
4. f(x) = x3 – x2 – 7x + c, where c is a constant.
Given that f(4) = 0,
(a) find the value of c, (2 marks)
(b) factorise f(x) as the product of a linear factor and a quadratic factor. (3 marks)
(c Hence show that, apart from x = 4, there are no real values of x for which f(x) = 0.
(2 marks)
PhysicsAndMathsTutor.com
5. Figure 1
R
A B
r r
O
Figure 1 shows the sector OAB of a circle of radius r cm. The area of the sector is 15 cm2
and ∠AOB = 1.5 radians.
(a) Prove that r = 2√5. (3 marks)
(b) Find, in cm, the perimeter of the sector OAB. (2 marks)
The segment R, shaded in Fig 1, is enclosed by the arc AB and the straight line AB.
(c) Calculate, to 3 decimal places, the area of R. (3 marks)
6. The third and fourth terms of a geometric series are 6.4 and 5.12 respectively.
Find
(a) the common ratio of the series, (2 marks)
(b) the first term of the series, (2 marks)
(c) the sum to infinity of the series. (2 marks)
(d) Calculate the difference between the sum to infinity of the series and the sum of the first 25
terms of the series. (4 marks)
3 Turn over
PhysicsAndMathsTutor.com
7. f(x) = 5sin3x°, 0 ≤ x ≤ 180.
(a) Sketch the graph of f(x), indicating the value of x at each point where the graph intersects
the x-axis (3 marks)
(b) Write down the coordinates of all the maximum and minimum points of f(x). (3 marks)
(c) Calculate the values of x for which f(x) = 2.5 (4 marks)
8. (i) Solve, for 0° < x < 180°, the equation
sin (2x + 50°) = 0.6,
giving your answers to 1 decimal place. (7 marks)
(ii) In the triangle ABC, AC = 18 cm, ∠ABC = 60° and sin A = 1.
3
(a Use the sine rule to show that BC = 4√3. (4 marks)
(b) Find the exact value of cos A. (2 marks)
4 Turn over
PhysicsAndMathsTutor.com
9. Figure 2
y
A
R
B
O x
Figure 2 shows the line with equation y = 9 – x and the curve with equation
y = x2 – 2x + 3. The line and the curve intersect at the points A and B, and O is the origin.
(a) Calculate the coordinates of A and the coordinates of B. (5 marks)
The shaded region R is bounded by the line and the curve.
(b) Calculate the area of R. (7 marks)
END
5 Turn over$$f(x) = 5\sin 3x°, \quad 0 \leq x \leq 180.$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $f(x)$, indicating the value of $x$ at each point where the graph intersects the $x$-axis [3]
\item Write down the coordinates of all the maximum and minimum points of $f(x)$. [3]
\item Calculate the values of $x$ for which $f(x) = 2.5$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [10]}}