Year 10 Crit A (Tech FREE) Revision Flashcards

Comprehensive revision flashcards covering Surds, Algebra, Linear Relationships, and Index Laws for a Year 10 Tech-Free assessment.

When determining the exact perimeter and area of a right-angled triangle with a side of $2\text{\,}\\sqrt{5}\,\text{cm}$ and a hypotenuse of $10\,\text{cm}$, what theorem should be used first?

Pythagoras' theorem ($a^2 + b^2 = c^2$) to find the length of the unknown side.

What is the distributive law used for in algebraic expressions?

To expand expressions by multiplying the term outside the parentheses by every term inside the parentheses, such as in $a(b + c) = ab + ac$.

How do you check the solution to an algebraic equation?

By using substitution: replace the variable in the original equation with your calculated value to see if the left side equals the right side.

What is the formula for the gradient $m$ of a line passing through the points $(x_1, y_1)$ and $(x_2, y_2)$?

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

What is the gradient of the line joining the points $(6, 3)$ and $(9, 8)$?

$$m = \frac{8 - 3}{9 - 6} = \frac{5}{3}$$

What is the gradient of the line joining the points $(-1, 5)$ and $(2, -7)$?

$$m = \frac{-7 - 5}{2 - (-1)} = \frac{-12}{3} = -4$$

What is the distance formula used to find the exact distance between points $(x_1, y_1)$ and $(x_2, y_2)$?

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

What are the coordinates of the midpoint of the line segment joining $(3, 2)$ and $(1, -5)$?

$$(\frac{3+1}{2}, \frac{2+(-5)}{2}) = (2, -1.5)$$

What relationship exists between the gradients of two parallel lines?

The gradients are equal ($m_1 = m_2$).

What is the relationship between the gradients of two perpendicular lines?

Their product is $-1$, or $m_1 \times m_2 = -1$.

According to the siblings problem, if the sum of ages for Frank and Beth is $23$ and the difference is $7$ ($f > b$), what is the pair of equations?

$f + b = 23$ and $f - b = 7$

Based on the shopping problem with Jason and Eddy, what equations represent the costs of highlighters ($h$) and pens ($p$)?

$2h + 5p = 16$ and $4h + 3p = 18$

In indices, what is the value of any base raised to the zero power ($a^0$)?

$$1$$

How should highlighters and pens costs be calculated with simultaneous equations?

By using the method of substitution or the elimination method to isolate and solve for variables $h$ and $p$.

How do you express the index form $100^{\frac{1}{5}}$ in surd form?

$$\sqrt[5]{100}$$

What is the evaluation of $1000^{\frac{2}{3}}$?

$100$ (because $(\sqrt[3]{1000})^2 = 10^2$).

What is the evaluation of $16^{\frac{3}{4}}$?

$8$ (because $(\sqrt[4]{16})^3 = 2^3$).