🌧️ • Module 7 : Measurement, Trigonometry and Graphing Flashcards
Learn key concepts including unit conversions, trigonometric ratios solving linear equations and inequalities, scale drawings, and interpreting more graphs.
How do you convert between metric units?
Multiply or divide by powers of 10 (ex. 1km =1000m, and 1cm =10mm.
How do you solve simultaneous equations graphically?
Plot both equations on a graph and identify the point where the lines intersect—this is the solution for (x, y).
How do you solve simultaneous equations using the elimination method?
1 — Make the coefficients of one variable the same.
2 — Add or subtract the equations to eliminate that variable.
3 — Solve for the remaining variable.
4 — Substitute back to find the other variable.
What are upper and lower bounds, and how do you find them for a given measurement?
Upper and lower bounds are the range a rounded value could belong to.
If a number is rounded to the nearest 10, the bounds are ±5 from that value.
Example : 250 (rounded to the nearest 10) has bounds 245 ≤ x < 255.
How do you represent an inequality on a number line?
Use a solid dot (●) for ≤ or ≥.
Use an open dot (○) for < or >.
Shade the direction that satisfies the inequality.
Example:
x > 3 → Open dot on 3, arrow pointing right.
How do you find the region that satisfies two inequalities on a graph?
Graph both inequalities and shade the correct regions.
The overlapping shaded area is the solution.
What is a scale drawing, and how do you use a given scale to find real measurements?
A scale drawing is a proportional representation of an object.
If the scale is 1:50, every 1cm on the drawing represents 50cm in real life. Multiply or divide accordingly.
How do you calculate a three-figure bearing?
Measure the angle clockwise from North (0°) to the direction of travel, always writing it as three digits (ex. 045°, 230°).
What is the tangent ratio, and how do you use it to find a missing side in a right-angled triangle?
tan(θ)=opposite/adjacent.
To find a missing side, rearrange;
— Opposite = adjacent x tan(θ)
— Adjacent = opposite ÷ tan(θ)
What is the sine ratio, and how do you use it to find a missing side?
sin(θ)=opposite/hypotenuse
To find a missing side, rearrange;
— Opposite = hypotenuse x sin(θ)
— Hypotenuse = Opposite ÷ sin(θ)
What is the cosine ratio, and how do you use it to find a missing side?
cos(θ)=adjacent/hypotenuse
To find a missing side, rearrange;
— Adjacent = hypotenuse x cos(θ)
— Hypotenuse = adjacent ÷ cos(θ)
How do you find a missing angle in a right-angled triangle using trigonometry?
Use inverse trigonometry functions:
θ = sin⁻¹(opposite / hypotenuse)
θ = cos⁻¹(adjacent / hypotenuse)
θ = tan⁻¹(opposite / adjacent)
What are exact trigonometric ratios, and why are they important?
They are exact values for special angles (30°, 45°, 60°), useful in non-calculator exams:
sin 30° = 1/2,
cos 30° = √3/2,
tan 30° = √3/3
sin 45° = √2/2,
cos 45° = √2/2,
tan 45° = 1
sin 60° = √3/2,
cos 60° = 1/2,
tan 60° = √3
How do you calculate an estimated value using a line of best fit?
1 — Find the x-value on the graph.
2 — Move vertically to the line of best fit.
3 — Move horizontally to read the estimated y-value.
What is an error interval, and how do you write it for a given rounded value?
It shows the range of possible values before rounding.
Example : 5.4 rounded to 1dp → 5.35 ≤ x < 5.45
How do you draw a line of best fit, and what does it do?
A line of best fit is a straight line that best represents the trend in scatter graph data, used to make predictions.
It should pass through as many points as possible while balancing the spread.
How can you estimate a value using the line of best fit?
Use the equation of the line (y=mx+c) or extend the line to find missing values for interpolation (within range) or extrapolation (beyond range).
Solve the simultaneous equations using the elimination method :
4𝑥 + 3y = 18
2𝑥 - 3y = 6
1 — Add both equations to eliminate y:
(4𝑥 +3y)+(2𝑥-3y)=18+6
6𝑥 = 24
2 — Solve for x:
𝑥 = 24/6=4
3 — Substitute 𝑥=4 into one of the original equations:
4(4)+3y=18
16+3y=18
3y=2
Y=2/3
Solution, when 𝑥=4, y=2/3.
How do you solve a linear inequality step by step?
1 — Isolate the variable by adding, subtracting, multiplying or dividing.
2 — If multiplying or dividing by a negative number, FLIP the inequality sign!
3 — Represent the solution on a number line.
Example : Solve 3x - 5 > 10
1 — Add 5 to both sides :
3x > 15
2 — Divide by 3 :
x > 5
3 — On a number line → open circle at 5, arrow going right.
How do you interpret correlation from a scatter graph?
Positive correlation = As one variable increases, the other increases. (Ex. Height vs shoe size)
Negative correlation = As one variable increases, the other decreases. (Ex. Speed vs travel time)
No correlation = No clear relationship between variables. (Ex. Hair color vs IQ)
How do you use map scales in real-life problems?
A map has a scale of 1:50,000. The distance between two cities is 8cm on the map. What is the real distance?
1cm on the map represents 50,000cm (or 0.5km) in real life.
8cm x 0.5km/cm =4km
The actual distance between the cities is 4km.
