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Math Quiz Essentials: Laws, Transformations, Bearings, and Quadratics

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Math Quiz Essentials: Laws, Transformations, Bearings, and Quadratics

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Core concepts quiz

Created by

Princess Panaligan
Princess Panaligan
Philippines

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Math Quiz Essentials: Laws, Transformations, Bearings, and Quadratics
 

Math Quiz Essentials: Laws, Transformations, Bearings, and QuadraticsOnline version

Core concepts quiz

by Princess Panaligan
1

A point (3,−2) is reflected over the x-axis. What are its new coordinates?

2

A triangle is rotated 90∘ counterclockwise about the origin. What is the image of point (4,−1)?

3

A translation moves point (2,5) by four units to the right and 3 units downwards. The image is now found at:

4

If a=4, b=5, c=7, which angle is largest?

5

A bearing of 045° means

6

The bearing of due west is

7

The roots of x2−7x+10=0 are

8

If a point (x,y) is translated by vector (h,k), what is the new coordinate?

9

90° clockwise around origin maps (x,y) to what?

10

Reflecting a point (x,y) across the x-axis yields which point?

11

Reflection across the y-axis yields which point?

12

What is the bearing from A to B if B is due east of A?

13

A vessel from north goes 45° East of North. Bearing?

14

If a line has bearing 210°, which direction is it pointing?

15

Solve: x2−9>0

16

Bearings: If a ship B is at bearing 030° from A, what is the angle from the north to AB?

17

Solve x^2 - 5x + 6 < 0. Which interval is solution?

18

Solve x^2 - 4x -5 ≥ 0. Which interval?

19

If f(x)=ax^2+bx+c with a>0, f(x)≥0 outside roots. True or false?

20

Solve x^2 + 2x - 3 ≤ 0. Interval?

21

A hiker walks 8 km due north, then 6 km due east. Approximately how far is the hiker from the starting point?

22

Solve (x-4)(x+2) > 0. Which intervals satisfy?

23

Solve x^2 - 6x + 5 ≥ 0. Interval?

Feedback

Largest side c=7 corresponds to largest angle C opposite it.

Addition of the translation vector to coordinates gives new position.

90° clockwise rotation sends (x,y) → (y, -x).

Reflection over x-axis negates the y-coordinate.

Reflection over y-axis negates the x-coordinate.

East corresponds to 90°, but bearings start from north.

Bearing is measured clockwise from north; 45° east of north is 045°.

210° is in the third quadrant, southwest.

Bearing 120° corresponds to 30° below the negative x-axis; standard angle is 300°.

Bearing 030° means 30° east of north.

Factor: (x-2)(x-3) < 0, true between the roots.

Roots are -1 and 5; parabola opens up, so outside the roots.

For a>0, f(x)≥0 outside the real roots of f(x)=0.

Roots are -3 and 1; ≤0 is between roots.

No real roots and parabola above x-axis yields f(x)>0 for all x.

Product positive when x is less than -2 or greater than 4.

Roots 1 and 5; outside the interval between roots satisfies ≥0.

 
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