Free Ontario MPT Exam Flashcards

Evaluate expressions in this order: Brackets, Exponents, Division and Multiplication (left to right), then Addition and Subtraction (left to right). Working strictly left to right instead is a common source of errors on the no-calculator questions.

The GCF is the largest number that divides two values evenly and is used to reduce fractions to lowest terms. The LCM is the smallest number both values divide into evenly and is used to find a common denominator.

A negative exponent means "take the reciprocal," not "make the number negative": a^-n equals 1 divided by a^n. For example, 2^-3 equals 1/8, not -8.

When the bases are the same, multiply powers by adding the exponents and divide powers by subtracting them: a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n). For example, 2^4 x 2^3 = 2^7 = 128. The rules do not apply when the bases differ.

Writing a number as the sum of each digit times its place value, such as 4,306.5 = 4 x 1000 + 3 x 100 + 0 x 10 + 6 x 1 + 5 x 0.1. A zero digit holds the place so the other digits keep their value.

Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 divided by 2/5 equals 3/4 x 5/2 = 15/8. Only the divisor (the second fraction) is flipped, never the first.

Two integers with the same sign give a positive product or quotient; two integers with different signs give a negative one. For example, (-6) x (-4) = 24, while (-6) x 4 = -24.

The square root of n is the non-negative number whose square is n, so the square root of 144 is 12. Nearby perfect squares let you estimate other roots: the square root of 50 lies between 7 and 8 because 49 < 50 < 64.

Round each number to its leading (highest place-value) digit before adding, subtracting, or multiplying to get a quick, reasonable estimate. Use it to check whether a calculated answer is in the right range on no-calculator questions.

Gross income is total earnings before any deductions. Net income is what remains after taxes and other deductions such as CPP and EI are subtracted, and it is what actually reaches a person's bank account.

The total extra amount paid beyond the principal on a loan, mainly interest and fees: total repaid minus amount borrowed. Comparing the cost of borrowing, not just the size of the monthly payment, shows the true price of different loan or credit options.

A ratio compares two quantities measured in the same units (e.g., 3 boys : 4 girls). A rate compares two quantities in different units (e.g., km per hour), so it always needs a unit label to make sense.

A rate simplified so the second quantity is 1, such as price per single item or distance per hour. Unit rates make it easy to compare deals or convert between quantities using multiplication.

A proportion states that two ratios are equal, a/b = c/d, so the cross products are equal: a x d = b x c. For example, 5/8 = x/40 gives 8x = 200, so x = 25. Keep matching quantities in matching positions in both ratios.

Divide the numerator by the denominator to get the decimal, then multiply by 100 to get the percent: 7/20 = 0.35 = 35%. Rewriting values in one common form is the reliable way to compare or order them.

Percent change equals the amount of change divided by the original value, multiplied by 100. Always divide by the original (starting) value, not the new value, or the result will be wrong.

Ontario's Harmonized Sales Tax is 13%, made up of the 5% federal GST portion and an 8% provincial portion. It applies to most goods and services purchased in Ontario.

Multiply the original price by (1 minus the discount rate) to find the sale price in one step. For example, a 20% discount means the buyer pays 80% of the original price.

Simple interest equals Principal multiplied by the annual rate multiplied by time in years (I = Prt). Because interest is always calculated on the original principal, it grows by the same dollar amount every year.

Compound interest is calculated on the principal plus all previously earned interest, so it grows faster over time. Simple interest is always calculated only on the original principal.

Allocating income across categories such as housing, food, and savings by percentage of the total, rather than by fixed dollar amounts. This lets each category's dollar amount scale automatically if total income changes.

Slope equals rise over run: the change in y divided by the change in x between two points on a line. It describes how steeply a linear relation increases or decreases for every one-unit increase in x.

In this form, m is the slope of the line and b is the y-intercept, the value of y when x equals 0. Reading a table or graph into this form lets you write the equation of a linear relation directly.

A linear relation has a constant rate of change: equal steps in x give equal first differences in y, and the graph is a straight line. If the first differences change, as in y = x^2, the relation is non-linear and its graph is a curve.

Add or subtract the same variable term from both sides of the equation until the variable appears on only one side, then isolate it the same way you would with a one-step equation. The order in which you move terms does not change the final solution.

a(b + c) equals ab + ac: multiply the term outside the brackets by every term inside before combining like terms. Forgetting to distribute to every term inside the brackets is a frequent algebra error.

Graph both lines on the same axes; the point where they intersect is the one (x, y) pair that satisfies both equations. Parallel lines never intersect, so a system with equal slopes and different y-intercepts has no solution.

The mean is the sum of the values divided by how many there are, the median is the middle value once the data is ordered, and the mode is the value that occurs most often. An extreme outlier pulls the mean much more than the median or the mode.

Theoretical probability is calculated from possible outcomes (favourable outcomes divided by total equally likely outcomes). Experimental probability is calculated from the results of actual trials, and it tends to move closer to the theoretical value as the number of trials increases.

For two independent events, multiply their individual probabilities: P(A and B) equals P(A) times P(B). "Independent" means the outcome of one event does not change the probability of the other.

In a right triangle, a squared plus b squared equals c squared, where c is the hypotenuse (the side opposite the right angle). It only applies to triangles that contain a 90-degree angle.

Area equals (a + b) multiplied by h, divided by 2, where a and b are the lengths of the two parallel sides and h is the perpendicular height between them. The slanted side lengths are used for perimeter, never for area.

Both shapes follow the same idea: volume equals the area of the base multiplied by the height. A rectangular prism's base area is length times width; a cylinder's base area is pi times the radius squared.

Add the two circular bases to the lateral surface: 2 x pi x r^2 + 2 x pi x r x h. The lateral surface unrolls into a rectangle whose length is the circumference of the base and whose width is the height of the cylinder.

Lengths change by powers of 10 (1 m = 100 cm), but the factor is squared for area and cubed for volume: 1 m^2 = 10,000 cm^2 and 1 m^3 = 1,000,000 cm^3. Multiply when converting to a smaller unit and divide when converting to a larger one.

In assessment for learning, the teacher gathers evidence during instruction to see where students are and plan next steps. In assessment as learning, students monitor their own progress through self- and peer-assessment. Growing Success treats both as improving learning, not as evidence for a grade.

Summative assessment at or near the end of a period of learning that judges how well a student achieved the curriculum expectations and assigns a value to it. This is the evidence that determines the grade reported to students and parents.

A learning goal states what students are learning, framed from a curriculum expectation. Success criteria describe how students and teachers will recognize that the goal was achieved, and are usually co-constructed with students.

Specific, actionable comments about a student's work tied directly to the success criteria, given while learning is still happening rather than only at the end. It gives students a chance to improve before a summative assessment.

Growing Success organizes every subject's achievement chart into four categories of knowledge and skills: Knowledge and Understanding, Thinking, Communication, and Application. Teachers are expected to assess and evaluate student work in a balanced way across all four.

An accommodation changes how a student accesses or demonstrates learning, such as extra time or assistive technology, without changing the curriculum expectation being assessed. A modification changes what is being assessed by altering the grade-level expectation itself.

Adjusting the content, process, product, or learning environment of a lesson to suit students' readiness, interests, and learning preferences, while the curriculum expectation stays the target for every student. Learning for All treats it as a response to individual learners, not a separate program.

Planning from the outset for the full range of learners in the class, with multiple means of representation, of action and expression, and of engagement. Learning for All sums it up as support that is "necessary for some, and good for all," which reduces the need for individual retrofits later.

A framework that moves from universal, whole-class supports (Tier 1), to targeted small-group supports (Tier 2), to individualized, intensive supports (Tier 3), based on how a student responds to instruction.

A class profile is a snapshot of the strengths, needs, interests, and readiness of every student in the class, used to plan whole-class assessment and instruction. An individual student profile gathers more detailed information about one student who needs more precise, personalized support.

The zone of proximal development is the gap between what a student can do alone and what the student can do with help. Scaffolding is temporary support given at that point of readiness and then withdrawn as the student becomes independent.

Social-Emotional Learning Skills, Number, Algebra, Data, Spatial Sense, and Financial Literacy. Financial Literacy and explicit Social-Emotional Learning Skills expectations were both new additions when the curriculum was revised in 2020.

Problem solving, reasoning and proving, reflecting, selecting tools and strategies, connecting, representing, and communicating. Ontario's curriculum expects students to use these processes across every strand, not just in a dedicated unit.

Research-based practices named in the 2020 Ontario mathematics curriculum context, including learning goals with success criteria and descriptive feedback, direct instruction, problem-solving tasks, tools and representations, math conversations, small-group instruction, deliberate practice, and flexible groupings. Teachers choose the practice that fits the learning goal rather than relying on one.

Starting with the 2021 curriculum, Ontario replaced separate academic and applied Grade 9 math courses with a single de-streamed course, intended to give all students equal access to senior math pathways.