Revision (Grade 12 NSC Matric Mathematics): Quizzes

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What is the formula for distance between points A(x1;y1)A(x_1; y_1) and B(x2;y2)B(x_2; y_2)?

AB=(x2−x1)2+(y2−y1)2AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

What does the gradient represent?

How steep a line is and rate of change

The midpoint of points (2;6)(2; 6) and (8;4)(8; 4) is:

(5;5)(5; 5)

Which form is used when you know the gradient and one point on the line?

Gradient-point form: y−y1=m(x−x1)y - y_1 = m(x - x_1)

What is the equation of a horizontal line?

y=ky = k (where k is a constant)

What is the gradient of a vertical line?

Undefined

What is the relationship between gradient mm and angle of inclination θ\theta?

m=tan⁡θm = \tan \theta for 0°≤θ<180°0° \leq \theta < 180°

When a line has a negative gradient, what type of angle is the inclination?

Obtuse angle (90° < θ\theta < 180°)

What is the condition for two lines to be parallel?

m1=m2m_1 = m_2 (identical gradients)

What is the condition for two lines to be perpendicular?

m1×m2=−1m_1 \times m_2 = -1

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