SS3 Mathematics Revision Flashcards

Flashcards testing core concepts, formulas, and past exam questions from SS3 Mathematics revision notes.

What equation represents direct variation when $y$ varies directly as $x$?

$$y = kx$$

In direct variation, if distance $d$ varies directly as $t^2$ and $d = 45\,\text{cm}$ when $t = 3\,\text{s}$, what is $d$ when $t = 6\,\text{s}$?

$$180\,\text{cm}$$

In the 2021 variation question where $R$ varies directly as $L$ and inversely as $P$, what is the constant $k$ when $R = 3$, $L = 9$, and $P = 0.8$?

$$k = \frac{4}{15}$$

In the 2022 variation question, if $M$ varies directly as $n^2$ and inversely as $p^2$, with $M = 3$ when $n = 2$ and $p = 1$, what is the formula for $M$?

$$M = \frac{3n^2}{4p^2}$$

In the 2023 joint variation problem where $M = kn^2\sqrt{q}$, if $M = 24$ when $n = 4$ and $q = 2$, what is $M$ when $n = 5$ and $q = 9$?

$$225$$

In the 2025 partial variation problem where $C = a + bn$, if $C = 70$ when $n = 8$ and $C = 90$ when $n = 10$, what is $C$ when $n = 12$?

$$110$$

What is the subject $m$ when rearranged from the formula $k = \sqrt{\frac{m - y}{m + 1}}$?

$$m = \frac{y + k^2}{1 - k^2}$$

Rearranging $x = \frac{2U - 3}{3U + 2}$ to make $U$ the subject gives what expression?

$$U = \frac{2x + 3}{2 - 3x}$$

Making $R$ the subject in the formula $V = \pi l (R^2 - r^2)$ yields what equation?

$$R = \sqrt{\frac{V}{\pi l} + r^2}$$

What is the subject $r$ in terms of $c$, $p$, $t$, and $b$ from the formula \frac{1}{p} = \frac{b}{t} + \frac{c}{r}?

$$r = \frac{cpt}{t - bp}$$

What is the value of $2[x^2 - y^3]$ when $x = 3$ and $y = -1$?

$$20$$

Using the factor theorem, if $x + 2$ is a factor of $x^2 + Px - 10 = 0$, what is the value of $P$?

$$P = -3$$

What are the solution values for $x$ and $y$ in the 2020 simultaneous linear equations $3x - 2y = 10$ and $x + 3y = 7$?

$x = 4$ and $y = 1$

For the 2021 simultaneous equations $4x + 2y = 16$ and $6x - 2y = 4$, what is the value of $y - x$?

$$2$$

In the 2023 simultaneous equations $2x - 3y = -11$ and $3x + 2y = 3$, what is the value of $(y - x)^2$?

$$16$$

What is the expanded result of the algebraic expression $(2x - 3y)(x - 5y)$?

$$2x^2 - 13xy + 15y^2$$

How is the expression $6ax - 12by - 9ay + 8bx$ factorised by grouping?

$$(3a + 4b)(2x - 3y)$$

Factorise the algebraic expression $am + bn - an - bm$.

$$(a - b)(m - n)$$

What is the complete factorisation of $27x^2 - 48y^2$ using the difference of two squares?

$$3(3x - 4y)(3x + 4y)$$

What are the roots of the quadratic equation $8 + 2x - x^2 = 0$?

$x = 4$ or $x = -2$

What are the solutions to the quadratic equation $6x^2 - 5x + 1 = 0$?

$x = \frac{1}{3}$ or $x = \frac{1}{2}$

What quadratic equation is formed by the roots $\frac{2}{3}$ and $-\frac{3}{4}$?

$$12x^2 + x - 6 = 0$$

What quadratic equation is formed by the roots $\frac{2}{3}$ and $-1$?

$$3x^2 + x - 2 = 0$$

At what values of $x$ is an algebraic fraction with denominator $6x(x + 1)$ undefined?

$x = 0$ and $x = -1$

For what values of $y$ is an algebraic fraction with denominator $8y^2 - 10y + 3$ undefined?

$y = \frac{3}{4}$ and $y = \frac{1}{2}$

What is the logical contrapositive of the conditional implication $p \Rightarrow q$?

$$\neg q \Rightarrow \neg p$$

What is the contrapositive of the statement 'If Stephen is intelligent, then Stephen is good at Mathematics'?

If Stephen is not good at Mathematics, then Stephen is not intelligent.

Which logical symbol represents the biconditional statement 'if and only if'?

$$p \Leftrightarrow q$$

What geometric locus is defined as being equidistant from two fixed points?

Perpendicular bisector

What geometric locus is defined as being equidistant from two intersecting lines?

Angle bisectors