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Grade 12 Quiz: Geometry — Easy Version 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Transformations of Graphs: P(-1, -5) is on the graph of y = f(x). Which point must be on the graph of y = f(x + 1)?
Answer: (-2, -5)
✓ Correct!
Not quite. The answer is
💡 How to solve: Double-Angle Formulas
sin 2θ = 2 sin θ cos θ, cos 2θ = cos2 θ - sin2 θ = 1 - 2sin2 θ = 2cos2 θ - 1, and tan 2θ = 2tan θ / (1 - tan2 θ). First find the missing sin or cos with a right triangle (watch the quadrant signs), then substitute.
Try a similar one
cos θ = 45 and θ is acute. Find the exact value of cos 2θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(1, -4) is on the graph of y = f(x). Which point must be on the graph of y = f(x) - 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Double-Angle Formulas
sin 2θ = 2 sin θ cos θ, cos 2θ = cos2 θ - sin2 θ = 1 - 2sin2 θ = 2cos2 θ - 1, and tan 2θ = 2tan θ / (1 - tan2 θ). First find the missing sin or cos with a right triangle (watch the quadrant signs), then substitute.
Try a similar one
sin θ = 2425 and θ is acute. Find the exact value of sin 2θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(3, 1) is on the graph of y = f(x). Which point must be on the graph of y = f(x) + 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Double-Angle Formulas
sin 2θ = 2 sin θ cos θ, cos 2θ = cos2 θ - sin2 θ = 1 - 2sin2 θ = 2cos2 θ - 1, and tan 2θ = 2tan θ / (1 - tan2 θ). First find the missing sin or cos with a right triangle (watch the quadrant signs), then substitute.
Try a similar one
cos θ = 45 and θ is acute. Find the exact value of cos 2θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(3, -5) is on the graph of y = f(x). Which point must be on the graph of y = f(x + 5)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Double-Angle Formulas
sin 2θ = 2 sin θ cos θ, cos 2θ = cos2 θ - sin2 θ = 1 - 2sin2 θ = 2cos2 θ - 1, and tan 2θ = 2tan θ / (1 - tan2 θ). First find the missing sin or cos with a right triangle (watch the quadrant signs), then substitute.
Try a similar one
sin θ = 1517 and θ is acute. Find the exact value of cos 2θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-3, -1) is on the graph of y = f(x). Which point must be on the graph of y = f(x) + 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Double-Angle Formulas
sin 2θ = 2 sin θ cos θ, cos 2θ = cos2 θ - sin2 θ = 1 - 2sin2 θ = 2cos2 θ - 1, and tan 2θ = 2tan θ / (1 - tan2 θ). First find the missing sin or cos with a right triangle (watch the quadrant signs), then substitute.
Try a similar one
cos θ = 817 and θ is acute. Find the exact value of sin 2θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-4, -3) is on the graph of y = f(x). Which point must be on the graph of y = f(x) - 3?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 12 Quiz: Geometry — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.