Final Exam-Math Practice

1 foot equals how many inches?

12 inches

Feet to inches: what do you do?

Multiply feet by 12.

Inches to feet: what do you do?

Divide inches by 12; the remainder is inches.

6'-8" in total inches

80 inches

92 inches in feet and inches

7'-8"

4'-7" in total inches

55 inches

137 inches in feet and inches

11'-5"

12'-6" in total inches

150 inches

15'-6" in total inches

186 inches

2.5 metres in centimetres

250 cm

350 cm in metres

3.5 m

Right angle

90°

Acute angle

An angle less than 90°.

Obtuse angle

An angle greater than 90° and less than 180°.

Straight angle

180°

Reflex angle

An angle greater than 180° and less than 360°.

Complementary angles

Two angles whose sum is 90°.

Supplementary angles

Two angles whose sum is 180°.

Vertex

The point where the arms/sides of an angle meet.

Interior angles of a triangle

180° total.

Isosceles triangle

A triangle with two equal sides/angles.

Equilateral triangle

A triangle with three equal sides.

Scalene triangle

A triangle with three unequal sides.

Right triangle

A triangle with one 90° angle.

Obtuse triangle

A triangle with one angle greater than 90°.

Acute triangle

A triangle with all angles less than 90°.

Pythagorean theorem

a² + b² = c²

When do you use the Pythagorean theorem?

For a right triangle when finding a missing side.

3-4-5 rule

A 3-4-5 proportion creates/checks a 90° right angle.

6-8-10 triangle

A scaled 3-4-5 right triangle.

9-12-15 triangle

A scaled 3-4-5 right triangle.

Right triangle: legs 3 and 4. Hypotenuse?

5

Right triangle: legs 6 and 8. Hypotenuse?

10

Right triangle: legs 9 and 12. Hypotenuse?

15

Right triangle: hypotenuse 13 and leg 5. Other leg?

12

Right triangle: hypotenuse 15 and leg 9. Other leg?

12

Quadrilateral

A four-sided figure.

Square

Four equal sides and four right angles.

Rectangle

Opposite sides equal and four right angles.

Rhombus

Four equal sides; right angles are not required.

Parallelogram

Opposite sides are parallel.

Trapezoid

A quadrilateral with one pair of parallel sides, per the study material.

Rectangle area formula

Length × width.

Rectangle perimeter formula

2L + 2W, or add all four sides.

Triangle area formula

½ × base × height. Verify this is required by the course.

12' × 8' rectangle area

96 square feet.

12' × 8' rectangle perimeter

40 linear feet.

14' × 18' room area

252 square feet.

20' × 9' wall area

180 square feet.

10' × 12' room perimeter

44 linear feet.

12' × 16' rectangle diagonal

20 feet.

How do you check if a rectangular layout is square?

Compare the diagonals; equal diagonals indicate a square/true rectangular layout.

Why measure diagonals during layout?

To check that the layout is square/true.

Room 12' × 15': area

180 square feet.

4' × 8' sheet area

32 square feet.

240 square feet covered with 4' × 8' sheets: area-only estimate

7.5 sheets, so approximately 8 sheets before waste.

Why add material beyond an area-only estimate?

Cuts, waste, and job conditions can require additional material.

Estimate vs. exact calculation

An estimate is an approximate quantity; an exact calculation gives a precise result.

What should you ask before choosing a math formula?

What am I being asked to find?

12' × 16' room: diagonal calculation

12² + 16² = 20², so the diagonal is 20'.

12' × 16' room: perimeter

2(12) + 2(16) = 56'.

12' × 16' room: area

12 × 16 = 192 square feet.

12' × 16' room: what should both diagonals be?

20' each if the rectangular layout is square/true.

9' × 12' right triangle: hypotenuse

15'.

5' × 12' right triangle: hypotenuse

13'.

A triangle has 35° and 65°. Third angle?

80°.

A straight line has an angle of 115°. Other angle?

65°.

Complementary angle to 37°

53°.

Supplementary angle to 68°

112°.

42° is what type of angle?

Acute.

125° is what type of angle?

Obtuse.

What is a benchmark?

A point of reference for elevations.

What two reference marks are needed for ceiling layout?

Benchmark and building control lines.

What is AFF?

Above finish floor.

What is equal-border layout?

Count full tiles, divide the leftover by two, and use that result as the border at each side.

Diagonal ceiling layout: what should dimensions be converted to?

Convert all dimensions to inches.

Roof slope

The steepness of a roof; rise for a given run.

Roof layout needs what basic dimensions?

Building span/total run and pitch/slope.

12' run and 9' rise: rafter/hypotenuse

15'.

Dead load

The weight of the roof/materials themselves.

Live load example in roof framing

Snow load.

Why are rafter ties/ceiling joists used?

They help keep the roof from spreading the walls.

What is a cantilever?

A floor/deck extension beyond a load-bearing framing member.

Why are holes in steel framing webs a concern?

They can substantially reduce structural capacity.

Steel stud gauge: 25 gauge

18 mil; no colour shown on the study chart.

Steel stud gauge: 20 gauge

33 mil; white.

Steel stud gauge: 18 gauge

43 mil; yellow.

Steel stud gauge: 16 gauge

54 mil; green.

Steel stud gauge: 14 gauge

68 mil; orange.

Steel stud gauge: 12 gauge

97 mil; red.

Steel stud gauge: 10 gauge

118 mil; blue.

1 mil

0.001 inch.

Thickest to thinnest in the steel gauge chart

10, 12, 14, 16, 18, 20, 25 gauge.

Steel gauge: which is thicker, 10 or 25?

10 gauge.

Steel gauge: which has greater mil thickness, 12 or 18?

12 gauge.

Steel stud code: S

Stud or joist with flange stiffeners.

Steel stud code: T

Track section.

Steel stud code: U

Cold-formed channel.

Steel stud code: F

Framing channel.

Steel stud code: 350

3-1/2-inch web depth.