Free VCE Foundation Mathematics Flashcard Review

The agreed sequence for evaluating an expression: Brackets, then Indices (powers and roots), then Division and Multiplication working left to right, then Addition and Subtraction working left to right. Multiplication is NOT automatically done before division, and addition is NOT automatically done before subtraction — equal-ranking operations are worked left to right.

60. The index is evaluated first (4^2 = 16), then the multiplication (3 x 16 = 48), then the addition (12 + 48 = 60). A common error is 15 x 16 = 240, caused by adding before multiplying.

9. Brackets first: 8 + 4 = 12. Index next: 2^2 = 4. Then division and multiplication left to right: 12 / 4 = 3, then 3 x 3 = 9. Doing 4 x 3 = 12 first (dividing by 12) gives 1 and is wrong.

Everything above the bar and everything below the bar is grouped and must be evaluated completely before the division is carried out. On a scientific calculator this means typing brackets around both the numerator and the denominator: (15 + 9) / (2 x 3) must be entered as (15+9)/(2x3), not 15+9/2x3.

'Is approximately equal to'. Use it when a value has been rounded or estimated, for example π ≈ 3.14 or cost ≈ $2400. Use = only when the two sides are exactly equal, so writing an unrounded exact line with = and a rounded final line with ≈ shows the assessor you know the difference.

< is 'less than' and > is 'greater than' (the endpoint is excluded); ≤ is 'less than or equal to' and ≥ is 'greater than or equal to' (the endpoint is included). A load limit written as m ≤ 750 kg means exactly 750 kg is allowed; m < 750 kg means it is not.

36 000 = 3.6 x 10^4 and 0.0025 = 2.5 x 10^-3. Scientific notation is a number between 1 and 10 multiplied by a power of 10; a positive index means the decimal point moves right, a negative index means it moves left.

-6 - (-4) = -6 + 4 = -2. Subtracting a negative is the same as adding a positive. On a scientific calculator use the (-) sign-change key for the negative value, not the subtraction key, and wrap negatives in brackets when they follow an operation.

Sum = the result of adding; difference = the result of subtracting (usually larger minus smaller); product = the result of multiplying; quotient = the result of dividing. Exam stems such as 'find the product of the length and the width' are telling you which operation to use.

Any number that can be written as a fraction a/b where a and b are integers and b is not zero. This includes whole numbers, negatives, terminating decimals such as 0.375 = 3/8, and recurring decimals such as 0.333... = 1/3. Every measurement you read off a ruler or a digital scale is rational.

A number that cannot be written as a fraction of two integers; its decimal expansion never terminates and never recurs. Examples in Foundation contexts are π and surds such as √2 and √3, which appear when a circle's circumference or a diagonal is calculated.

22/7 is rational because it is a ratio of two integers. It is only an approximation to π (22/7 = 3.142857..., π = 3.141592...), so using 22/7 introduces a small error. In an exam use the calculator's π key unless told otherwise.

Because the contexts are physical (water in a tank, paint on a cylinder) and the question specifies a rounding instruction such as 'to the nearest litre' or 'correct to two decimal places'. Keep the full π value in the calculator through every step and round only in the final line.

√16 = 4 exactly, so it is rational. √20 = 4.4721... never terminates or recurs, so it is irrational. A square root is only irrational when the number under the root is not a perfect square.

4√2 = 5.6568... m is irrational and is the exact value; 5.66 m is a rational decimal approximation forced by the measuring instrument. Every real measurement is a rational approximation of an exact quantity, which is why measurement error and rounding always exist.

A comparison of two or more quantities of the same kind, measured in the same unit, written with colons such as 3 : 5. Ratios have no units, are simplified by dividing every part by the highest common factor, and must be expressed in whole numbers unless the question says otherwise.

5 : 8. Divide both parts by the highest common factor 50. Both quantities must be in the same unit before simplifying — if one were given in kilograms you would convert first.

$120 and $200. There are 3 + 5 = 8 parts, so one part = 320 / 8 = $40; then 3 x 40 = $120 and 5 x 40 = $200. Always check the two amounts add back to the original total.

A statement that two ratios are equal, such as 3/4 = 15/20. Practical problems are solved by setting up the proportion with matching quantities in matching positions and then cross-multiplying, or by finding the scale multiplier between the two situations.

1500 g (1.5 kg). The multiplier is 10 / 4 = 2.5, so 600 x 2.5 = 1500 g. Alternatively find the unit amount 600 / 4 = 150 g per person and multiply by 10.