Skip to content

Course home

1.5 Coordinate Geometry

1.5 Coordinate Geometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117
Question 103

The cross-section of a curved acoustic reflector is modelled by the curve C C\,C with parametric equations

x=−4cos⁡2θ,h=5cos⁡θ,0≤θ≤π2 x = -4 \cos 2\theta, \quad h = 5 \cos \theta, \quad 0 \le \theta \le \frac{\pi}{2} x=−4cos2θ,h=5cosθ,0≤θ≤2π​

where x x\,x is the horizontal displacement in metres from a central axis and h h\,h is the height in metres. The region R R\,R is bounded by the curve CCC, the xxx-axis, and the hhh-axis for the portion of the curve where x≥0x \ge 0x≥0.

a.

(i) Show, making your working clear, that the area of R=∫π/4π/280cos⁡2θsin⁡θ dθR = \int_{\pi/4}^{\pi/2} 80 \cos^2 \theta \sin \theta \, d\thetaR=∫π/4π/2​80cos2θsinθdθ.

[3]
b.

(ii) Hence find, by algebraic integration, the exact value of the area of RRR.

[3]
c.

Show that all points on C C\,C satisfy h=ax+bh = \sqrt{ax+b}h=ax+b​, where a a\,a and b b\,b are constants to be found.

[3]
d.

State the range of the function f(x)=ax+bf(x) = \sqrt{ax+b}f(x)=ax+b​ for the domain −4≤x≤4-4 \le x \le 4−4≤x≤4.

[1]
Markscheme

1.5 Coordinate Geometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Coordinate Geometry

178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank