Practice Flashcards: National 5 Mathematics: relationships | Zestly

Question 1

Gradient formula

Accepted Answer

The gradient $m$ between $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Example: for $(1, 2)$ and $(3, 6)$, $m = \frac{6 - 2}{3 - 1} = 2$.

Question 2

Equation of a line

Accepted Answer

The equation is $y - b = m(x - a)$ for a line with gradient $m$ through $(a, b)$. Example: $m=2$ through $(1, 3)$ is $y - 3 = 2(x - 1) \implies y = 2x + 1$.

Question 3

Discriminant formula

Accepted Answer

The discriminant is $D = b^2 - 4ac$. If $D > 0$ two real roots, $D = 0$ one repeated root, $D < 0$ no real roots. Example: $x^2 - 4x + 4 = 0$ has $D = (-4)^2 - 4(1)(4) = 0$.

Question 4

Vertex form of a quadratic

Question 5

Solving inequalities

Question 6

Roots of a quadratic

Question 7

Slope-intercept form

Question 8

Functional notation

Question 9

Simultaneous equations

Question 10

Expanding brackets

Question 11

Quadratic factorisation

Question 12

Turning point type