Math exam 2026

when simplifying or evaluating an expression

show all of the intermediate steps in your solution, do one operation in each line of your solution until you are comfortable doing several at a time (always obeying order of operations!), line up the equal signs along the left-hand side of the page, 'edit' the expression as you work through it.

what do parentheses do

separate number signs from operators, show multiplication, indicate groupings, indicate substituted values in algebraic values

equivalent fractions

different fractions that name the same number.

Rational numbers

can be expressed as the quotient of two integers where the denominator isn't zero

reciprocal

a number and a fraction whose product is 1

base (of a power)

it is the number that is (repeatedly) multiplied

Square number

any whole number that can be represented as the area of a square with a whole number side length.

sign of a negative base raised to an even exponent

When the base is negative and the exponent is even, the number in standard form is positive.

sign of a negative base raised to an odd exponent

When the base is negative and the exponent is odd, the number in standard form is negative.

negative exponent

Reciprocal of the base raised to positive exponent.

multiplying or dividing powers with the same base

add or subtract the exponents

set of integers symbol

Z

rational numbers symbol

Q

Real numbers symbol

R

Natural numbers symbol

N

radical sign

a symbol to indicate the square root

index (on the radical sign)

the small number written just above and to the left of the radical sign that determines the degree of the root being taken

degree of a monomial

the sum of the exponents of the variables

estimating square roots

- Find two numbers either side of the two numbers farthest from the decimal sign in the root

- Make a sensible estimate depending on which one it is closer to

- add a 0 for every pair of numbers closer to the decimal point

Term

a constant, variable, or product of the two

polynomial

an expression winth more than one monomial

leading coefficient

The coefficient of the term with the highest degree in a polynomial

acsending order (polynomials)

ordering terms from lowest degree to highest

linear equation

A linear equation in one variable is true for only one value of the variable. This single value is the solution to the equation.

linear inequality

A linear inequality in one variable is true for many values of the variable. This range of values is the solution to the inequality.

multiplying/dividing by a positive number on both sides of an inequality

When each side of an inequality is multiplied or divided by the same positive number, the resulting inequality is still true.

multiplying/dividing by a negative number on both sides of an inequality

When each side of an inequality is multiplied or divided by the same negative number, the inequality sign must be reversed for the inequality to remain true.

Cartesian Coordinate plane

a plane divided into four quadrants by the intersection of the x-axis and the y-axis at the origin

four quadrants of the coordinate plane

I (+,+)

II (-,+)

III (-,-)

IV (+,-)

linear relation (coordinate plane)

A set of ordered pairs that, when graphed, form a straight line.

the one magical proof of is it a linear equation

Constant change in x results in constant change in y

when should discrete points be used instead of a continuous line

a continuous line should only be used when any real number along that line fufills the criteria. if it is only integers, or it skips any values, seperate points should be used.

horizontal slope

0

slope-intercept form

y = mx + b

standard form (do not need to know)

Ax+By=C

interpolation

estimating a value within the range of measured data

extrapolation

Estimating a value outside the range of measured data.

integer

any positive and negative natural numbers including zero

prime number

A whole number that has exactly two factors, 1 and itself.

communative property

a•b = b•a

associative property

(a•b)•c = a•(b•c)

identity property of multiplication

a•1 = a

Zero Property of Multiplication

a•0 = 0

order of operations

PEMDAS (parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)

expression

a mathematical phrase made up of numbers and variables connected by operators

For any multiplication statement, there are 2 related division statements. Ex. (+3)x(+5) =+15

15÷3=5 and 15÷5 = 3

if the signs of the dividend and the divisor are the same, then the quotient is...

positive

if the signs of the dividend and the divisor are different, then the quotient is...

negative

GCF

Greatest Common Factor

LCM

Least Common Multiple

Rule for multiplying fractions into simplest form

First simplify numerator/denominator, then multiply across the top and bottom.

Divide a number by a fraction

To divide a number by a fraction, multiply the dividend by the reciprocal of the divisor. Reduce, if possible.

Powers

Express repeated multiplication more concisely, 2^4 = 2 × 2 × 2 × 2 = 16

Exponent (of a power)

is the number of factors of the base in the repeated multiplication statement

zero exponent

The number always will equal one

raising a power to a power

multiply the exponents

Whole numbers symbol

W

Prime factorisation

Expressing a positive integer as a product of its prime factors.

radicand

The number or expression inside a radical symbol

right triangle

A triangle that has a 90 degree angle.

hypotenuse

the side of a right triangle opposite the right angle

Pythagorean Theorem

a²+b²=c²

coefficient

number multiplying a variable

variable

an unknown

equation

A mathematical sentence that contains an equals sign.

inverse operations

operations that undo one another

inequality

A statement that compares two quantities using <, >, ≤,≥, or ≠

strict inequalities

> or < (NOT ≤ or ≥)

adding and subtracting from both sides of an inequality

When the same number is added to or subtracted from each side of an inequality, the resulting inequality is still true.

slope (of a line)

Rise over run

vertical slope

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left-side, right-side check

A left side right side check verifies a mathematical solution by substituting the found value into both sides of an equation independently

Still learning (37)

You've started learning these terms. Keep it up!

unit conversion

example: km/h to m/s - 5km/1h x 1h/60min x 1min/60s - cancel out all the units - 13.9m/1s is the process of converting a measurement from one unit to another, ensuring that the value is adjusted according to the conversion factors.