ADF JOA Numerical flashcards
ADF JOA Numerical · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Arithmetic sequence rule
- A sequence with a constant first difference d, where the nth term equals the first term plus (n-1) times d.
- Geometric sequence rule
- A sequence with a constant ratio r between consecutive terms; the nth term equals the first term multiplied by r to the power n-1.
- Second differences test
- If first differences are not constant but their differences are, the sequence follows a quadratic rule of the form an squared plus bn plus c.
- Interleaved series
- A series that hides two separate patterns in alternating positions; examine odd-positioned and even-positioned terms independently to reveal each rule.
- Fibonacci-type rule
- A pattern in which each term equals the sum of the two preceding terms, sometimes with a constant added or subtracted each step.
- Difference of squares
- The identity a squared minus b squared equals (a minus b)(a plus b), which turns products such as 63 times 57 into 60 squared minus 3 squared.
- Order of operations
- Evaluate brackets first, then indices, then multiplication and division left to right, and finally addition and subtraction left to right.
- Divisibility by 3 and 9
- A number is divisible by 3 or by 9 when the sum of its digits is divisible by 3 or by 9 respectively.
- Divisibility by 4 and 8
- A number is divisible by 4 when its last two digits form a multiple of 4, and by 8 when its last three digits do.
- Squaring numbers ending in five
- The square ends in 25, and the leading digits equal n times (n plus 1), where n is the number formed by the remaining digits.
- Percent change formula
- Percent change equals the new value minus the old value, divided by the old value, then multiplied by 100; a negative result is a decrease.
- Successive percentage changes
- Consecutive percentage changes multiply rather than add; two 10 percent increases give a multiplier of 1.21, a total rise of 21 percent.
- Percentage points versus percent
- A move from 20 percent to 25 percent is a 5 percentage-point rise but a 25 percent relative increase, so the two measures must not be confused.
- Dividing a quantity by ratio
- For a ratio a to b, the total is split into a plus b equal parts; each part equals the total divided by a plus b.
- Inverse proportion
- Two quantities are inversely proportional when their product stays constant, so doubling one halves the other.
- Reversing a percentage change
- To recover an original value after a percentage change, divide by the multiplier (1 plus or minus the rate), never subtract the stated percent.
- Pie chart sector value
- Each sector represents its stated percentage of the whole total; all sectors together must sum to 100 percent and to 360 degrees.
- Axis scale check
- Confirm the units and the step size of each axis before reading values, because scales that jump by 5, 20 or 100 cause misreads.
- Category average
- When averaging across categories, divide the total by the number of categories rather than by the number of individual data points.
- Trend versus magnitude
- Line graphs best show rates of change over time, while bar charts best compare sizes across categories at one point.
- Combined work rate
- For two workers completing a job in a and b hours alone, the time together equals a times b divided by a plus b.
- Average speed, equal distances
- When equal distances are covered at speeds x and y, average speed equals 2xy divided by (x plus y), not the mean of x and y.
- Mixture conservation rule
- The amount of pure substance stays constant, so concentration times volume before mixing equals concentration times volume after mixing.
- Word-to-equation translation
- In word problems, 'is' signals equals, 'of' signals multiply, 'per' signals divide, and 'more than' signals addition.
- Metric length ladder
- Each metric length step moves by a factor of ten: kilometres to metres is 1000, metres to centimetres is 100, centimetres to millimetres is 10.
- Litre and cubic units
- One litre equals 1000 millilitres and 1000 cubic centimetres, and one cubic metre equals 1000 litres.
- Circle formulas
- Circumference equals 2 times pi times the radius, and area equals pi times the radius squared, using pi approximately 3.14.
- Unit cancellation method
- Multiply by a conversion fraction equal to one, such as 1000 metres over 1 kilometre, so unwanted units cancel and the desired unit remains.
- Estimation cross-check
- Round each quantity to one significant figure, compute roughly, then confirm the exact answer falls within about ten percent of the estimate.
- Benchmark fraction equivalents
- Useful conversions include one eighth as 12.5 percent, one sixth as about 16.7 percent, one third as 33.3 percent and three eighths as 37.5 percent.
- Elimination by last digit
- When answer choices differ in their final digit, compute only the units column of the operation to discard wrong options quickly.
- Question-first reading
- Read the question stem before the table or graph so you locate only the figures needed, saving time on data interpretation items.