Year 10 Crit A (Tech FREE) Revision Booklet Flashcards

Comprehensive practice flashcards based on the Year 10 Tech Free Revision Booklet covering Surds, Algebra, Linear Relationships, and Indices.

The process of removing a radical from the divisor of a fraction is called __________ the denominator.

rationalising

To determine the exact perimeter and area of a right-angled triangle with side $\sqrt{50}\,\text{cm}$ and hypotenuse $10\,\text{cm}$, you must first use the __________ theorem to find the missing side.

Pythagoras'

In algebra, expressions like $3x + 5y - x$ are simplified by __________ like terms.

collecting

The method of expanding brackets using the formula $a(b + c) = ab + ac$ is known as the __________ law.

distributive

Algebraic fractions can be simplified by __________ common factors from the numerator and denominator.

cancelling

After solving an equation, you should check your solution by __________ the value back into the original equation.

substitution

To determine if a point like $(-1, 4)$ is on a specific line, you must substitute the coordinates into the line's __________.

equation

The gradient $m$ of a line joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the formula __________.

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

The equation of a straight line is expressed in the form __________ where $m$ is the gradient and $c$ is the y-intercept.

$$y = mx + c$$

If two lines are __________, their gradients are the same ($m_1 = m_2$).

parallel

If two lines are __________, the product of their gradients is $-1$ ($m_1 \times m_2 = -1$).

perpendicular

The __________ of the line segment joining points $(3, 2)$ and $(1, -5)$ is the average of their $x$ and $y$ coordinates.

midpoint

The two primary algebraic methods for solving simultaneous equations are the elimination method and the __________ method.

substitution

According to the index laws, any base raised to the zero power, such as $a^0$, is equal to __________.

1

An expression with a negative index like $x^{-n}$ can be written using a positive index as __________.

$$\frac{1}{x^n}$$

The index form of the surd $\sqrt[n]{x^m}$ is __________.

$$x^{\frac{m}{n}}$$

The expression $13^{\frac{3}{4}}$ can be expressed in surd form as __________.

$$\sqrt[4]{13^3}$$

Evaluating the fractional index expression $1000^{\frac{2}{3}}$ results in the value __________.

100

Evaluating the expression $16^{\frac{3}{4}}$ requires finding the fourth root of 16 and then raising it to the power of __________.

3

In the word problem regarding sibling ages, the sum of their ages is 23 and the older brother is named __________.

Frank

In the consumer arithmetic simultaneous equations problem, Jason and Eddy buy highlighters and __________.

pens