Find the distance between the points A(1, 2) and B(4, 6).
Coordinate Geometry
Question · Easy
Factor it
Short
The midpoint of the line segment joining A(−2, 5) and B(6, −1) is
The gradient of the line through (0, 3) and (4, −1) is
The equation of the straight line that passes through (3, 1) with gradient 2 is
Question · Medium
A line perpendicular to 4x + 2y − 1 = 0 has gradient
The area of the triangle with vertices (1, 1), (5, 1) and (3, 6) is
The line through (2, 0) that is parallel to x − 2y + 3 = 0 has equation
The equation of the perpendicular bisector of A(0, 2) and B(4, 6) is
Question · Hard
Solve 3x − 7 = 8.
Equations And Functions
The solutions of x² − 9 = 0 are
If f(x) = x² − 3x, then f(5) is
The domain of the real-valued function f(x) = √(x − 4) is
The discriminant of x² − 6x + 5 = 0 is
x² − 4x + 1 written in completed-square form is
The roots of 3x² − 5x − 2 = 0 are
If f(x) = 4x + 1, then f⁻¹(x) is
If f(x) = 2x and g(x) = x − 3, then (f ∘ g)(5) is
The solutions of |3x − 6| = 9 are
The minimum value of y = x² − 6x + 10 is
If f(x) = (2x − 1)/(x + 3) for x ≠ −3, then f⁻¹(x) is
The solutions of the simultaneous equations y = 2x − 1 and x² + y = 7 are
The values of x, y and z that satisfy x + y = 5, y + z = 7 and x + z = 6 are
π/6 radians is equal to
Circular Measure
90° in radians is
A circular arc has radius 8 cm and subtends 1.5 radians at the centre. The arc length is
A sector of a circle of radius 6 cm has angle π/3 radians. Its area is
A sector of radius 8 cm has area 16π cm². The angle at the centre, in radians, is
sin 90° is equal to
Trigonometry
cos 0° is equal to
tan 60° is equal to
sin 180° is equal to
The exact value of cos 135° is
The exact value of tan 210° is
Which identity is true for all θ where the functions are defined?
If sin θ = 5/13 and θ is acute, then cos θ is
The solutions of sin θ = √3 / 2 for 0° ≤ θ ≤ 360° are
If cos θ = 3/5 and θ is acute, then sin 2θ is
The exact value of cos 15° is
The solutions of 2 sin² θ − sin θ − 1 = 0 for 0° ≤ θ ≤ 360° are
6! is equal to
Permutations And Combinations
The value of ⁶P₂ is
The value of ¹⁰C₂ is
The number of distinct linear arrangements of 5 different letters is
A committee of 2 boys and 2 girls is chosen from 5 boys and 4 girls. The number of possible committees is
In the expansion of (1 + x)⁴, the coefficient of x² is
Binomial Theorem
The coefficient of x³ in the expansion of (1 + x)⁷ is
The third term in the expansion of (3 + x)⁵, written in ascending powers of x, is
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