SK SSA Math 5 cheat sheet

Place value: each position to the left is 10 times the value of the position to its right, so 4,703 = 4×1000 + 7×100 + 0×10 + 3×1.

Order of operations: evaluate parentheses/brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Rounding rule: locate the target place, look at the single digit to its right; 5 or more rounds up, 4 or less keeps the digit unchanged and the rest become zeros.

Multiplying by powers of 10 shifts digits left (×10, ×100, ×1000); dividing shifts digits right, so 3.6 ÷ 100 = 0.036.

A fraction a/b equals a ÷ b; to compare fractions with unlike denominators, rewrite them with a common denominator or compare to a benchmark such as 1/2.

To add or subtract fractions, use a common denominator and combine numerators only; to multiply, multiply numerators and multiply denominators.

Dividing by a fraction is multiplying by its reciprocal: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

Decimal place values to the right of the point are tenths, hundredths, thousandths; 0.7 = 0.70, but 0.07 is ten times smaller.

A percent is a ratio out of 100: 35% = 35/100 = 0.35; to find 35% of 80, compute 0.35 × 80 = 28.

A variable is a letter standing for an unknown or changing number; an expression has no equals sign, while an equation states two expressions are equal.

Evaluate an expression by substituting the given value for the variable and following order of operations, e.g. 3n + 5 for n = 4 gives 17.

Solve one-step equations by applying the inverse operation to both sides: x + 9 = 14 gives x = 5; 4x = 28 gives x = 7.

Distributive property: a(b + c) = ab + ac; combine like terms (same variable and exponent) before solving.

Arithmetic sequences change by a constant difference d; the nth term is a + (n − 1)d, where a is the first term.

Geometric sequences change by a constant multiplier r; each term is r times the previous term, e.g. 2, 6, 18, 54 has r = 3.

To find a rule from a table, test whether the output changes by a constant amount (linear) or by a constant factor (multiplicative).

An inequality uses <, >, ≤, ≥; the solution is a range of values, and multiplying or dividing by a negative number reverses the inequality sign.

Coordinate pairs (x, y): x is horizontal distance from the origin, y is vertical; a point on the x-axis has y = 0.

Perimeter is the distance around a figure; area is the number of square units covering it, so area is reported in square units and perimeter in linear units.

Rectangle area = length × width; triangle area = ½ × base × height, where height is perpendicular to the chosen base.

Parallelogram area = base × height; trapezoid area = ½ × (base₁ + base₂) × height.

Circle: circumference = 2πr or πd; area = πr²; the diameter is twice the radius.

Volume of a rectangular prism = length × width × height; volume is measured in cubic units.

A right angle measures 90°; a straight angle measures 180°; angles in a triangle sum to 180° and in a quadrilateral to 360°.

Complementary angles sum to 90°; supplementary angles sum to 180°; vertical (opposite) angles are equal.

Unit conversions: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL, 1 hour = 60 minutes.

To convert between units, multiply when moving to a smaller unit and divide when moving to a larger unit, e.g. 2.5 m = 250 cm.

Mean = sum of values ÷ number of values; median is the middle value of an ordered list (average the two middle values if the count is even).

Mode is the most frequent value; range is maximum minus minimum; an outlier can pull the mean far from the median.

A bar graph compares categories, a line graph shows change over time, and a circle graph shows parts of a whole as percentages totaling 100%.

Probability of an event = number of favorable outcomes ÷ total equally likely outcomes, so it always lies between 0 and 1.

The complement rule: P(not A) = 1 − P(A); if P(rain) = 0.3, then P(no rain) = 0.7.

For two independent events, multiply probabilities: P(A and B) = P(A) × P(B).

With replacement, probabilities stay the same for each draw; without replacement, the total and the favorable count both decrease.

Theoretical probability comes from counting outcomes; experimental probability comes from observed results and approaches the theoretical value with more trials.

Four-step approach: read and restate the question, identify the given information, choose an operation or strategy, then check whether the answer is reasonable.

Key operation cues: 'total' and 'in all' suggest addition; 'difference' and 'how many more' suggest subtraction; 'each' and 'per' often suggest multiplication or division.

Estimate first by rounding to compatible numbers; use the estimate to judge whether the exact answer is plausible.

Work backward from the answer by reversing operations, useful when the result of a sequence of steps is given.

Unit rate reasoning: find the value of one unit, then multiply by the number of units needed (if 3 items cost $12, one costs $4).

Check by substitution: put the solution back into the original equation or word problem to confirm both sides match.

A ratio compares two quantities; a proportion states two ratios are equal and can be solved by cross-multiplying.

Multi-step problems: identify the hidden sub-question first, solve it, then use that result in the final step.

Reject impossible answers: a length cannot be negative, a probability cannot exceed 1, and a part cannot be larger than the whole unless stated.

Four-step approach: read and restate the question, list the given information, choose a strategy, then check whether the answer is reasonable.

Operation cues: 'in all' and 'total' suggest addition; 'how many more' suggests subtraction; 'each' and 'per' often suggest multiplication or division.

Estimate first by rounding to compatible numbers, then use the estimate to judge whether the exact answer is plausible.

Work backward by reversing operations when the final result of a sequence of steps is given.

Unit-rate reasoning: find the value of one unit, then multiply by the number of units needed; if 3 items cost $12, one costs $4.

Check by substitution: place the solution back into the original equation or word problem to confirm both sides match.

A proportion states two ratios are equal and is solved by cross-multiplying; a ratio simply compares two quantities.

Multi-step problems: identify and solve the hidden sub-question first, then use that result in the final step.

Reject impossible answers: lengths cannot be negative, probabilities cannot exceed 1, and a part cannot exceed the whole unless stated.

Four-step approach: restate the question, list the given information, choose a strategy, then verify the answer is reasonable.

Operation cues: 'in all' and 'total' suggest addition; 'how many more' suggests subtraction; 'each' and 'per' often suggest multiplication or division.

Estimate first by rounding to compatible numbers, then use the estimate to judge whether the exact answer is plausible.

Work backward by reversing operations when the final result of a sequence of steps is given.

Unit-rate reasoning: find the value of one unit, then multiply by the number of units needed; if 3 items cost $12, one costs $4.

Check by substitution: place the solution back into the original equation or word problem to confirm both sides match.

A proportion states two ratios are equal and is solved by cross-multiplying; a ratio simply compares two quantities.

Multi-step problems: identify and solve the hidden sub-question first, then use that result in the final step.

Reject impossible answers: lengths cannot be negative, probabilities cannot exceed 1, and a part cannot exceed the whole unless stated.