1.
Find the gradient of the line through (1, 2) and (5, 14). [2]
JD SCIENCE
Pure — coordinate geometry and trigonometry
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Find the equation of the line perpendicular to y = 3x − 1 that passes through (3, 4). [3]
3.
Find the distance between (2, −1) and (6, 2). [2]
4.
Find the midpoint of (2, −1) and (6, 2). [1]
5.
A circle has equation (x − 3)² + (y + 1)² = 25. State the centre and radius. [2]
6.
Find the equation of the circle with centre (1, 2) passing through (4, 6). [3]
7.
Show that the line y = 2x + 1 intersects the circle x² + y² = 5 and find the points. [4]
8.
State the condition for a line to be a tangent to a circle in terms of the discriminant. [2]
9.
Convert 30° to radians and 2π/3 to degrees. [2]
10.
Find the exact value of sin 150° and cos 210°. [2]
11.
Solve sin θ = 0.5 for 0 ≤ θ ≤ 360°. [3]
12.
Solve 2 cos θ = −1 for 0 ≤ θ ≤ 2π. [3]
13.
Prove sin²θ + cos²θ = 1 using a right triangle or the unit circle. [3]
14.
Express 2 sin θ cos θ as a single sine. [1]
15.
Use cos 2θ = 2cos²θ − 1 to find the exact value of cos 15° if needed, or find cos 2θ when cos θ = 0.6. [3]
16.
Find the area of a triangle with sides 7 cm and 10 cm and included angle 30°. [3]
17.
Use the cosine rule to find the third side when a = 5, b = 8, C = 60°. [3]
18.
Use the sine rule: a/sin A = b/sin B. A = 40°, a = 10, B = 60°. Find b. [3]
19.
Sketch y = 2 sin(x − 30°) for 0 ≤ x ≤ 360°, stating amplitude, period and shift. [4]
20.
Find the period of y = 3 cos(2x). [2]
21.
The line l1: x = 1 + 2t, y = −1 + t. Find a Cartesian equation. [3]
22.
Find the angle between the lines y = x and y = 2x. [3]
23.
State the small-angle approximations for sin θ, cos θ and tan θ when θ is in radians. [3]
24.
A sector of radius 6 cm has angle 0.5 rad. Find the arc length and sector area. [3]
25.
Find the equation of the tangent to the circle x² + y² = 25 at (3, 4). [3]
26.
Solve tan 2θ = 1 for 0 ≤ θ ≤ 180°. [3]
27.
Write the identities for sin(A+B) and cos(A−B). [3]
28.
Find R and α such that 3 sin θ + 4 cos θ = R sin(θ + α). [4]
29.
The points A(0,1), B(4,3), C(2,7) form a triangle. Find the area using the determinant / shoelace method. [3]
30.
On AQA papers, a 5-mark trig equation needs all solutions in the interval. Write a checklist. [3]
31.
Find the centre and radius of x² + y² − 6x + 4y − 12 = 0. [3]
32.
A triangle has sides 6, 7, 8. Find the largest angle using the cosine rule. [3]